SPL_uw|SPL_w|TB.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/neelabhro/Deep-Learning-based-Wireless-Communications/blob/main/SPL_uw%7CSPL_w%7CTB.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YIoYASfEf7go"
      },
      "source": [
        "#### Import libraries"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kKl9e4A0H1lk",
        "outputId": "121c6301-b172-4f6b-90c1-3dbc9947d2a0"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Using tensorflow version: 2.9.2\n"
          ]
        }
      ],
      "source": [
        "# magic command to use TF 1.X in colaboraty when importing tensorflow\n",
        "#%tensorflow_version 1.x \n",
        "import tensorflow as tf                       # imports the tensorflow library to the python kernel\n",
        "#tf.logging.set_verbosity(tf.logging.ERROR)    # sets the amount of debug information from TF (INFO, WARNING, ERROR)\n",
        "import time\n",
        "import random\n",
        "print(\"Using tensorflow version:\", tf.__version__)\n",
        "#print(\"Num GPUs Available: \", len(tf.config.list_physical_devices('GPU')))\n",
        "\n",
        "import tensorflow.compat.v1 as tf\n",
        "\n",
        "tf.disable_v2_behavior() "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "id": "QiCDuiGqf7gr"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.cm as cm\n",
        "from scipy import signal\n",
        "import math\n",
        "pi = tf.constant(math.pi)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mrLsO1Nxf7g3"
      },
      "source": [
        "#### System parameters"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "spN0MeqFD7x-",
        "outputId": "4a380100-c06c-4143-d811-8002dfd17db1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[166. 162. 228. ...  70. 130. 170.]\n",
            "[166. 162. 228. ...  70. 130. 170.]\n",
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6341, 6515, 6801, 7136, 7198, 7439, 7795, 8201, 8266, 8680, 8759, 9355, 9420, 9699, 9842, 9930], 238: [10, 332, 358, 408, 553, 591, 804, 943, 2014, 2043, 2166, 2422, 2462, 2508, 2616, 2668, 2861, 2954, 3518, 3758, 4120, 4734, 4838, 5065, 5213, 5981, 6025, 6121, 6508, 6618, 6701, 6812, 6829, 6834, 7008, 7269, 7488, 7523, 7708, 7842, 7857, 7916, 8037, 8536, 8617, 9238, 9285, 9434, 9657, 9712, 9992], 239: [219, 324, 396, 621, 754, 1145, 1158, 1243, 1729, 2024, 2131, 2177, 2347, 2434, 2461, 2708, 2829, 3048, 3094, 3748, 3834, 4210, 4955, 5458, 5911, 5916, 6001, 6690, 6913, 7032, 7040, 7769, 7911, 8114, 8307, 8360, 8382, 8706, 9098, 9187, 9250, 9466], 240: [574, 773, 946, 1203, 1261, 1419, 2157, 2870, 3147, 3217, 3359, 3567, 4147, 4395, 4434, 4594, 4667, 5088, 5539, 6455, 6562, 6671, 6813, 6836, 6844, 6867, 7372, 7597, 7780, 8487, 8527, 8555, 8645, 8707, 9294, 9482, 9524, 9669], 241: [218, 760, 1250, 1286, 1504, 1547, 1565, 1704, 1870, 1996, 2028, 2492, 2619, 2674, 3050, 3411, 3667, 3826, 4229, 4281, 5174, 5193, 5322, 5323, 5840, 5851, 6087, 6210, 6259, 6276, 6947, 7028, 7091, 7195, 7596, 7875, 8086, 8095, 8151, 8255, 8483, 8563, 8916, 9349, 9439, 9484, 9661, 9685, 9741], 242: [80, 90, 135, 571, 1041, 1523, 1650, 1816, 1927, 2103, 2141, 2212, 2218, 2741, 2796, 2895, 2922, 2970, 3436, 3602, 4376, 4664, 4854, 5336, 5864, 6960, 7254, 7542, 7636, 7639, 7677, 8367, 8559, 9387, 9481, 9599, 9773, 9796, 9895], 243: [97, 254, 343, 803, 815, 902, 1095, 2163, 2264, 2489, 2496, 2709, 2814, 2937, 3377, 3732, 4274, 4289, 4555, 4846, 4847, 5349, 5360, 5620, 5990, 6354, 6872, 7497, 7681, 7815, 7859, 7879, 7889, 8112, 8199, 8320, 8376, 9036, 9618, 9803, 9880, 9940, 9979], 244: [266, 368, 1182, 1219, 1272, 1559, 1634, 1955, 2127, 2147, 2577, 2816, 3703, 3737, 3790, 3830, 3918, 3956, 4207, 5437, 5658, 5681, 5724, 6091, 6230, 6380, 6446, 6545, 6691, 6733, 6788, 6985, 7177, 7894, 7997, 8415, 8752, 9026, 9209, 9279, 9438], 245: [89, 96, 713, 783, 882, 1085, 1099, 1252, 1520, 1674, 1793, 1907, 2221, 2656, 2896, 4037, 4123, 4228, 4243, 4464, 4779, 4925, 5500, 5505, 5515, 6330, 6445, 6645, 6720, 6857, 7006, 7332, 7403, 7939, 8765, 8980, 9065, 9073, 9164, 9207, 9506, 9640, 9673, 9812], 246: [209, 390, 398, 576, 584, 1756, 1812, 2017, 2080, 2819, 3722, 3745, 3762, 3796, 3810, 4533, 4608, 4890, 5281, 5439, 5786, 5876, 5929, 6085, 6201, 6415, 6439, 6535, 6703, 6866, 6892, 7414, 7487, 7517, 7957, 7964, 8154, 8186, 8477, 8753, 8794, 8961, 8987, 8989, 9144, 9325, 9736, 9946], 247: [81, 428, 663, 1485, 1550, 2334, 2769, 2975, 3982, 4064, 4086, 4118, 5046, 5084, 5460, 5829, 6082, 6086, 6714, 6793, 7304, 8060, 8162, 8260, 8937, 9656, 9908], 248: [29, 42, 508, 1009, 1116, 1325, 1838, 1880, 2013, 2215, 2380, 2627, 2872, 2877, 2966, 3018, 3192, 3318, 3573, 3859, 4159, 4326, 4378, 4804, 4819, 5029, 5287, 5514, 5789, 5867, 6258, 6656, 6978, 7086, 7354, 7818, 8057, 8787, 8827, 8934, 9198, 9578, 9620], 249: [1118, 1122, 1924, 2061, 2253, 2938, 2978, 3402, 3440, 3453, 3498, 3504, 3591, 3875, 4264, 4448, 4773, 4797, 5155, 5679, 5700, 5861, 6003, 6005, 6371, 6524, 6648, 6694, 6780, 7017, 7064, 7077, 7368, 7666, 8069, 8161, 8522, 8562, 8677, 8730, 8785, 9188, 9203, 9331, 9850], 250: [23, 288, 450, 471, 817, 1383, 1953, 2110, 2557, 2575, 2827, 3096, 3162, 3241, 3327, 3952, 3990, 4261, 4625, 4783, 5130, 5297, 5309, 5756, 6179, 6198, 6302, 6383, 6740, 6831, 6888, 7281, 7302, 7999, 8054, 8101, 8649, 8940, 9254, 9446, 9709], 251: [653, 944, 945, 965, 1110, 1513, 1611, 1719, 1852, 2331, 2522, 2729, 3406, 3538, 3555, 3831, 4276, 4607, 5041, 5417, 5431, 5884, 6022, 6630, 6832, 6870, 7027, 8159, 8349, 8492, 8540, 8586, 9338, 9562, 9755, 9760, 9768, 9922], 252: [282, 1134, 1184, 1405, 1587, 1677, 1947, 2361, 2580, 2781, 3360, 3419, 3515, 4329, 4449, 4655, 5091, 5221, 5267, 5470, 5486, 5510, 5628, 5657, 6077, 6133, 6226, 6247, 6479, 6635, 7241, 7508, 7558, 7779, 7812, 8088, 8455, 8475, 8869, 9053, 9151, 9323, 9359, 9472, 9535, 9885, 9926], 253: [183, 287, 339, 397, 518, 970, 1163, 2091, 2124, 2481, 2604, 2615, 2775, 2787, 3449, 4404, 4574, 4764, 4932, 5204, 5363, 5849, 6697, 6828, 6860, 7159, 7233, 7300, 7435, 7718, 8434, 8526, 8777, 8812, 8855, 8902, 9423, 9480, 9928], 254: [41, 328, 432, 547, 856, 1146, 1160, 1425, 1571, 1600, 1669, 1707, 1841, 2006, 2044, 2062, 2184, 2287, 2338, 2602, 3183, 3263, 3979, 4008, 4166, 4224, 4624, 4648, 4680, 4702, 4740, 5000, 5156, 5184, 5194, 5295, 5306, 6894, 6959, 7106, 7296, 7866, 7959, 8284, 8580, 9320, 9459, 9504, 9689], 255: [234, 516, 588, 868, 934, 1537, 1972, 2416, 2624, 3324, 3394, 3657, 4032, 4109, 4456, 5176, 5331, 5547, 5568, 6600, 6877, 7146, 7337, 7604, 8001, 8111, 8144, 8153, 8252, 8596, 9061, 9868]}\n"
          ]
        }
      ],
      "source": [
        "batch_size = 10000\n",
        "########## BIT FLIPPING OFF\n",
        "#print(tr)\n",
        "#plt.plot(t, tr)\n",
        "T1 = random.randint(1, 10)\n",
        "T2 = random.randint(1, 10)\n",
        "M = 256\n",
        "t = np.linspace(0, 1, batch_size)\n",
        "triangle1 = signal.sawtooth(T1 * np.pi * 5 * t, 0.5)\n",
        "triangle1 = M/2*(triangle1)\n",
        "triangle1 = triangle1.clip(min=0)\n",
        "\n",
        "triangle2 = signal.sawtooth(T2 * np.pi * 5 * t, 0.5)\n",
        "triangle2 = M/2*(triangle2)\n",
        "triangle2 = triangle2.clip(min=0)\n",
        "\n",
        "triangle3 = triangle1 + triangle2\n",
        "#triangle3 = triangle3/15*(7)\n",
        "tr = triangle3\n",
        "bins = np.arange(M-1)\n",
        "tr = np.digitize(triangle3, bins, right=True)\n",
        "#plt.plot(t, triangle3)\n",
        "\n",
        "#tr = np.flip(tr)\n",
        "#print(tr)\n",
        "tr = np.floor(np.random.uniform(1,M, batch_size))\n",
        "print(tr)\n",
        "#replacements = {0:7, 1:6, 2:5, 3:4, 4:3, 5:2, 6:1, 7:0}\n",
        "#replacements = {0:15, 1:14, 2:13, 3:12, 4:11, 5:10, 6:9, 7:8, 8:7, 9:6, 10:5, 11:4, 12:3, 13:2, 14:1, 15:0}\n",
        "rp1 = np.arange(1,M)\n",
        "rp2 = np.flip(np.arange(1,M))\n",
        "replacements = dict(zip(rp1,rp2))\n",
        "#print(rp2)\n",
        "replacer = replacements.get\n",
        "#tr = ([replacer(n, n) for n in tr])\n",
        "\n",
        "print(tr)\n",
        "\n",
        "s_ind = {}\n",
        "for j in range(1,M):\n",
        "  s_ind[j] = [i for i, x in enumerate(tr) if x == j]\n",
        "print(s_ind)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "id": "4eRvwZ5Nf7g6"
      },
      "outputs": [],
      "source": [
        "k = 8       # Number of information bits per message, i.e., M=2**k\n",
        "n = 4       # Number of real channel uses per message\n",
        "seed = 2    # Seed RNG reproduce identical results"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "28KCbvYif7hD"
      },
      "source": [
        "#### The Autoencoder Class\n",
        "In order to quickly experiment with different architecture and parameter choices, it is useful to create a Python class that has functions for training and inference. Each autoencoder instance has its own Tensorflow session and graph. Thus, you can have multiple instances running at the same time without interference between them."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "U0hIseee8ira",
        "outputId": "6800acce-1016-4e29-92e0-01d61432b0a5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(10000,)\n",
            "(10000, 2, 2)\n"
          ]
        }
      ],
      "source": [
        "f = 5.9*10**9;#in Hz corresponding to IEEE 802.11p\n",
        "lamda = 0.05;  #in metres\n",
        "Pt = 1; #BS transmitted power in watts\n",
        "\n",
        "BW = 10*10**6; #in Hz\n",
        "PLE = 2.8; #Path Loss exponent\n",
        "Beta = {}\n",
        "Pr = {}\n",
        "SNR_var = {}\n",
        "ad_noise_SNR = []  #The values of the dictionary, finally providing an array of stdevs\n",
        "NoW = 0.02\n",
        "\n",
        "Transmitted_Power = 23.010299957 #in dBm\n",
        "Noise_Figure = 95 #in -dBm\n",
        "\n",
        "noise_factor = Transmitted_Power + Noise_Figure\n",
        "#|β| =λ/(4πD)2.31 \n",
        "\n",
        "\n",
        "s = np.floor(np.random.uniform(1,M, batch_size))\n",
        "s = s.astype('int64')\n",
        "#s = ([replacer(n, n) for n in s])  \n",
        "std_shadow = 3          \n",
        "rand1 = np.random.normal(0,std_shadow,batch_size)\n",
        "for i in range(batch_size):\n",
        "  Beta[i] = 10*(np.log10(lamda/((4*np.pi*s[i])**PLE)))\n",
        "  SNR_var[i] = Beta[i] + noise_factor + rand1[i]\n",
        "#SNR_var = SNR_var + np.random.normal(0, 3, batch_size) \n",
        "  #SNR_var[i] = 10*(np.log10(np.divide((Pt*[(Beta[i])**2]),NoW)))\n",
        "  #SNR_var[i] = ((M)/((s[i]+1)*4))*25   #For M=8\n",
        "  #SNR_var[i] = ((M)/((s[i]+1)*4))      #For M=256\n",
        "\n",
        "for i in SNR_var.values():\n",
        "  ad_noise_SNR.append(i)\n",
        "print(np.shape(ad_noise_SNR))\n",
        "ad_noise_SNR = np.transpose(np.tile(ad_noise_SNR, (2,2,1)))\n",
        "print(np.shape(ad_noise_SNR))\n",
        "\n",
        "#print(np.shape(np.tile(ad_noise_SNR[7], (1000, 1, 1))))\n",
        "#print(np.shape(tr[7]*np.ones(batch_size)))\n",
        "rand2 = np.random.normal(0,std_shadow,batch_size)\n",
        "\n",
        "for j in range(1,M):\n",
        "\n",
        "\n",
        "  #SNR_var[j] = ((M)/((j+1)*4))*25\n",
        "  #SNR_var[j] = ((M)/((j+1)*4))\n",
        "  Beta[j] = 10*(np.log10(lamda/((4*np.pi*j)**2.8)))\n",
        "  SNR_var[j] = Beta[j] + noise_factor + rand2[j]\n",
        "\n",
        "const_noise_SNR = []  #The values of the dictionary, finally providing an array of stdevs\n",
        "for j in SNR_var.values():\n",
        "  const_noise_SNR.append(j)  \n",
        "const_noise_SNR = np.transpose(np.tile(const_noise_SNR, (2,2,1)))\n",
        "#print(const_noise_std)\n",
        "\n",
        "seven_noise_SNR = np.add(np.ones(batch_size)*15, np.random.normal(0,3,batch_size))\n",
        "\n",
        "seven_noise_SNR = np.transpose(np.tile(seven_noise_SNR, (2,2,1)))\n",
        "#print(np.random.normal(0,std_shadow,batch_size))\n",
        "\n",
        "tr_noise_SNR = []\n",
        "rand3 = np.random.normal(0,std_shadow,batch_size)\n",
        "\n",
        "for i in range(batch_size):\n",
        "\n",
        "  #SNR_var[i] = ((M)/((tr[i]+1)*4))*25\n",
        "  #SNR_var[i] = ((M)/((tr[i]+1)*4))\n",
        "\n",
        "  Beta[i] = 10*(np.log10(lamda/((4*np.pi*tr[i])**2.8)))\n",
        "  SNR_var[i] = Beta[i] + noise_factor + rand3[i]\n",
        "for i in SNR_var.values():\n",
        "  tr_noise_SNR.append(i)\n",
        "\n",
        "tr_noise_SNR = np.transpose(np.tile(tr_noise_SNR, (2,2,1)))\n",
        "#print(s)\n",
        "\n",
        "#print(ad_noise_SNR[7])\n",
        "#print(np.tile(ad_noise_SNR[7], (1000, 1, 1)))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "hs9Rtd01f7hG"
      },
      "outputs": [],
      "source": [
        "\n",
        "class AE(object):\n",
        "    def __init__(self, k, n, seed=None, filename=None):\n",
        "        assert (n%2 == 0), \"Channel only allows complex symbols -> n must be a multiple of 2\"\n",
        "        self.k = k \n",
        "        self.n = n\n",
        "        self.n_complex = int(self.n/2)\n",
        "        self.bits_per_symbol = self.k/self.n_complex\n",
        "        self.M = 2**self.k\n",
        "        self.seed = seed if (seed is not None) else int(time.time())           \n",
        "        self.graph = None\n",
        "        self.sess = None   \n",
        "        self.vars = None\n",
        "        self.saver = None   \n",
        "        self.constellations = None\n",
        "        self.blers = None\n",
        "        self.create_graph()\n",
        "        self.create_session()\n",
        "        if filename is not None:    \n",
        "            self.load(filename)       \n",
        "        return\n",
        "    \n",
        "    \n",
        "    def create_graph(self):\n",
        "        '''This function creates the computation graph of the autoencoder'''\n",
        "        self.graph = tf.Graph()        \n",
        "        with self.graph.as_default():    \n",
        "            tf.set_random_seed(self.seed)\n",
        "            batch_size = tf.placeholder(tf.int32, shape=())\n",
        "            \n",
        "            # Transmitter\n",
        "            s = (tf.random_uniform(shape=[batch_size], minval=0, maxval=self.M, dtype=tf.int64))\n",
        "\n",
        "            ad_noise_std = tf.random_uniform(shape=[batch_size], minval=0, maxval=M, dtype=tf.int64)\n",
        "            ones = tf.ones([2,2,1],dtype=tf.int64)\n",
        "            ad_noise_std = tf.transpose(ad_noise_std*ones)\n",
        "            #ad_noise_std = tf.transpose(tf.tile(ad_noise_std, [2,2,1]))           \n",
        "            x = self.encoder(s)                         \n",
        "            \n",
        "            # Channel\n",
        "            #noise_std = tf.placeholder(tf.float32, shape=())\n",
        "            noise_std = tf.placeholder(tf.float32, shape=[10000,2,2])\n",
        "            noise = tf.random_normal(tf.shape(x), mean=0.0, stddev=noise_std) \n",
        "\n",
        "            fade = tf.random.normal(shape=tf.shape(x))\n",
        "            sparr1,sparr2 = tf.split(fade,num_or_size_splits=2, axis=2)\n",
        "            complex_fade = tf.complex(sparr1, sparr2)\n",
        "            fade = tf.abs(complex_fade)\n",
        "            #fade = tf.math.sqrt(1/2)*fade\n",
        "\n",
        "            fade = 1\n",
        "            y = tf.multiply(x,fade) + noise\n",
        "            #y = x + noise\n",
        "            #fade = 1            \n",
        "           \n",
        "            # Receiver\n",
        "            s_hat = self.decoder(y)\n",
        "            correct_s_hat = tf.argmax(tf.nn.softmax(s_hat), axis=1)\n",
        "\n",
        "            \n",
        "            # Loss function\n",
        "            #cross_entropy = tf.losses.sparse_softmax_cross_entropy(labels=s, logits=s_hat)\n",
        "            cross_entropy = tf.losses.sparse_softmax_cross_entropy(labels=s, logits=s_hat)\n",
        "            #cross_entropy_0 = tf.losses.sparse_softmax_cross_entropy(labels=s, logits=s_hat)\n",
        "            #cross_entropy = tf.losses.sparse_softmax_cross_entropy(labels=s, logits=s_hat, weights= (s+1)**(4))\n",
        "      \n",
        "           # Performance metrics\n",
        "            #correct_predictions_0 = tf.equal(tf.argmax(tf.nn.softmax([s_hat[x] for x in s_ind_0]), axis=1), [s[x] for x in s_ind_0])\n",
        "\n",
        "            correct_predictions = tf.equal(tf.argmax(tf.nn.softmax(s_hat), axis=1), s)\n",
        "            accuracy = tf.reduce_mean(tf.cast(correct_predictions, tf.float32))\n",
        "            bler = 1-accuracy\n",
        "\n",
        "            lr = tf.placeholder(tf.float32, shape=()) # We can feed in any desired learning rate for each step     \n",
        "            train_op = tf.train.AdamOptimizer(lr).minimize(cross_entropy)\n",
        "            #train_op_0 = tf.train.AdamOptimizer(lr).minimize(cross_entropy_0)\n",
        "            #lr = tf.train.exponential_decay(1e-10, global_step=cross_entropy, decay_steps=100, decay_rate=1.30)\n",
        "\n",
        "            # References to graph variables we need to access later \n",
        "            self.vars = {\n",
        "                'accuracy': accuracy,\n",
        "                'batch_size': batch_size,\n",
        "                'bler': bler,\n",
        "                'cross_entropy': cross_entropy,\n",
        "                'init': tf.global_variables_initializer(),\n",
        "                'lr': lr,\n",
        "                'noise_std': noise_std,\n",
        "                'train_op': train_op,\n",
        "                #'s': (np.floor(np.random.uniform(0,256, 1000))).astype('int64'),\n",
        "                's': s,\n",
        "                's_hat': s_hat,\n",
        "                'correct_s_hat': correct_s_hat,\n",
        "                'x': x,\n",
        "            }            \n",
        "            self.saver = tf.train.Saver()\n",
        "        return\n",
        "    \n",
        "    def create_session(self):\n",
        "        '''Create a session for the autoencoder instance with the compuational graph'''\n",
        "        self.sess = tf.Session(graph=self.graph)        \n",
        "        self.sess.run(self.vars['init'])\n",
        "        return\n",
        "    \n",
        "    def encoder(self, input):\n",
        "        '''The transmitter'''\n",
        "        self.weight_var_rec = self.weight_variable((self.M,self.M)) # shape = (8,8)\n",
        "        self.embedding_lookup_rec = tf.nn.embedding_lookup(self.weight_var_rec, input)\n",
        "        print(self.embedding_lookup_rec)\n",
        "        x = tf.nn.elu(self.embedding_lookup_rec)\n",
        "        #x = tf.layers.dense(self.embedding_lookup_rec, self.M, activation=tf.nn.relu)\n",
        "        x = tf.layers.dense(x, self.M, activation=None)\n",
        "        x = tf.layers.dense(x, self.n, activation=None)\n",
        "        #x = tf.layers.dense(x, self.n, activation=None)\n",
        "        #x = tf.layers.dense(x, self.n, activation=None)\n",
        "        #x = tf.layers.dense(x, self.n, activation=None)\n",
        "        #x = tf.layers.dense(x, self.n, activation=None)\n",
        "        x = tf.reshape(x, shape=[-1,self.n_complex,2])\n",
        "        print(x);\n",
        "        #Average power normalization\n",
        "        x = x/tf.sqrt(2*tf.reduce_mean(tf.square(x))) \n",
        "        return x\n",
        "    \n",
        "    def decoder(self, input):\n",
        "        '''The Receiver'''\n",
        "        #input = self.flip_decoder(input)\n",
        "        y = tf.reshape(input, shape=[-1,self.n])\n",
        "        y = tf.layers.dense(y, self.M, activation=None)\n",
        "        y = tf.layers.dense(y, self.M, activation=None)\n",
        "        y = tf.layers.dense(y, self.M, activation=None)\n",
        "        #y = tf.layers.dense(y, self.M, activation=None)\n",
        "        #y = tf.layers.dense(y, self.M, activation=None)\n",
        "        #y = tf.layers.dense(y, self.M, activation=None)\n",
        "        #y = tf.layers.dense(y, self.M, activation=None)\n",
        "        #y = tf.layers.dense(y, self.M, activation=None)\n",
        "        print(y);\n",
        "        return y\n",
        "    \n",
        "    def EbNo2Sigma(self, ebnodb):\n",
        "        '''Convert Eb/No in dB to noise standard deviation'''\n",
        "        ebno = 10**(ebnodb/10)\n",
        "        return 1/np.sqrt(2*self.bits_per_symbol*ebno)\n",
        "    \n",
        "    def gen_feed_dict(self, batch_size, ebnodb, lr):\n",
        "        '''Generate a feed dictionary for training and validation'''        \n",
        "        return {\n",
        "            self.vars['batch_size']: batch_size,\n",
        "            self.vars['noise_std']: self.EbNo2Sigma(ebnodb),\n",
        "            self.vars['lr']: lr,\n",
        "        }\n",
        "\n",
        "    def gen_e2e_feed_dict(self, batch_size, ebnodb, s_input, lr):\n",
        "        '''Generate a feed dictionary for training and validation'''        \n",
        "        return {\n",
        "            self.vars['batch_size']: batch_size,\n",
        "            self.vars['noise_std']: self.EbNo2Sigma(ebnodb),\n",
        "            self.vars['s']: s_input,\n",
        "            self.vars['lr']: lr,\n",
        "        }    \n",
        "    \n",
        "    def load(self, filename):\n",
        "        '''Load an pre_trained model'''\n",
        "        return self.saver.restore(self.sess, filename)\n",
        "        \n",
        "    def plot_constellation(self, noise_std, maxrange=None):\n",
        "        '''Generate a plot of the current constellation'''\n",
        "        x = self.transmit(range(self.M), noise_std)\n",
        "        if (maxrange is None):\n",
        "            maxrange = np.max(np.abs(x))\n",
        "        for k in range(self.n_complex):\n",
        "            image = plt.figure(figsize=(6,6))\n",
        "            plt.grid(True)\n",
        "            plt.xlim(-maxrange,maxrange)\n",
        "            plt.ylim(-maxrange,maxrange)\n",
        "            for i in range(self.M):       \n",
        "              #if (i <=150):\n",
        "                #plt.scatter(x[i,k,0],x[i,k,1],c=\"black\")\n",
        "                plt.scatter(x[i,k,0],x[i,k,1],color=cm.Spectral(i/255.0))\n",
        "                #plt.annotate(i, (x[i,k,0],x[i,k,1]))  \n",
        "              #if (i > 150):\n",
        "                #plt.scatter(x[i,k,0],x[i,k,1],c=\"red\")\n",
        "                #plt.annotate(i, (x[i,k,0],x[i,k,1]))      \n",
        "                #plt.scatter(x[i,k,0],x[i,k,1],c=\"black\",marker='x')  \n",
        "            image.axes[0].set_xticks(np.array([-2,-1,0,1,2]))\n",
        "            image.axes[0].set_yticks(np.array([-2,-1,0,1,2]))\n",
        "            image.suptitle('%d. complex symbol' % (k+1))\n",
        "            plt.xlabel('Re')\n",
        "            plt.ylabel('Im')\n",
        "        return x, image\n",
        "    \n",
        "    def save(self, filename):\n",
        "        '''Save the current model'''\n",
        "        return self.saver.save(self.sess, filename)  \n",
        "    \n",
        "    def test_step(self, batch_size, ebnodb):\n",
        "        '''Compute the BLER over a single batch and Eb/No'''\n",
        "        bler = self.sess.run(self.vars['bler'], feed_dict=self.gen_feed_dict(batch_size, ebnodb, lr=0))\n",
        "        return bler\n",
        "    \n",
        "    def transmit(self, s, noise_std):\n",
        "        '''Returns the transmitted sigals corresponding to message indices'''\n",
        "        return self.sess.run(self.vars['x'], feed_dict={self.vars['s']: s, self.vars['noise_std']: noise_std})\n",
        "\n",
        "    def end2end(self, batch_size, ebnodb, input_s):\n",
        "        '''Returns the transmitted sigals corresponding to message indices'''\n",
        "        return self.sess.run(self.vars['correct_s_hat'], feed_dict=self.gen_e2e_feed_dict(batch_size, ebnodb, input_s, lr=0)) \n",
        "        #print(self.sess.run(self.vars['correct_s_hat'], feed_dict={self.vars['s']: input_s}))     \n",
        "\n",
        "    #print(self.sess.run(self.vars['s_hat'], feed_dict={self.vars['s']: s}))\n",
        "    def end2end_bler(self, batch_size, ebnodb, input_s):\n",
        "        '''Returns the transmitted sigals corresponding to message indices'''\n",
        "        return self.sess.run(self.vars['bler'], feed_dict=self.gen_e2e_feed_dict(batch_size, ebnodb, input_s, lr=0)) \n",
        "\n",
        "\n",
        "    def train(self, training_params, validation_params):  \n",
        "        \n",
        "        '''Training and validation loop'''\n",
        "        for index, params in enumerate(training_params):            \n",
        "            s,batch_size, lr, ebnodb, iterations = params            \n",
        "            print('\\nBatch Size: ' + str(batch_size) +\n",
        "                  ', Learning Rate: ' + str(lr) +\n",
        "                  ', EbNodB: ' + str(ebnodb) +\n",
        "                  ', Iterations: ' + str(iterations))\n",
        "            \n",
        "            val_size, val_ebnodb, val_steps = validation_params[index]\n",
        "            \n",
        "            for i in range(iterations):\n",
        "                self.train_step(s,batch_size, ebnodb, lr)    \n",
        "                if (i%val_steps==0):\n",
        "                    #bler = self.sess.run(self.vars['bler'], feed_dict=self.gen_new_feed_dict(val_size, val_ebnodb, lr, s_input))\n",
        "                    bler = self.sess.run(self.vars['bler'], feed_dict=self.gen_feed_dict(val_size, val_ebnodb, lr))\n",
        "                    print(bler)                           \n",
        "        return       \n",
        "    \n",
        "    def train_step(self,s, batch_size, ebnodb, lr):\n",
        "        '''A single training step'''\n",
        "        #self.sess.run(self.vars['train_op'], feed_dict=self.gen_new_feed_dict(batch_size, ebnodb, lr, s_input))\n",
        "        self.sess.run(self.vars['train_op'], feed_dict={self.vars['s']: s, self.vars['batch_size']: batch_size,  self.vars['noise_std']: self.EbNo2Sigma(ebnodb), self.vars['lr']: lr})\n",
        "        return \n",
        "    \n",
        "    def weight_variable(self, shape):\n",
        "        '''Xavier-initialized weights optimized for ReLU Activations'''\n",
        "        (fan_in, fan_out) = shape\n",
        "        low = np.sqrt(6.0/(fan_in + fan_out)) \n",
        "        high = -np.sqrt(6.0/(fan_in + fan_out))\n",
        "        return tf.Variable(tf.random_uniform(shape, minval=low, maxval=high, dtype=tf.float32))\n",
        "    \n",
        "    def bler_sim(self, ebnodbs, batch_size, iterations):\n",
        "        '''Monte Carlo simulations of BLER for a range of Eb/No\n",
        "           Sometimes we to compute statistics for batch sizes that do not fit into the GPUs memory.\n",
        "           You can average over multiple batches with small size instead.           \n",
        "        '''\n",
        "        BLER = np.zeros_like(ebnodbs)\n",
        "        for i in range(iterations):\n",
        "            bler = np.array([self.sess.run(self.vars['bler'],\n",
        "                            feed_dict=self.gen_feed_dict(batch_size, ebnodb, lr=0)) for ebnodb in ebnodbs])\n",
        "            BLER = BLER + bler/iterations\n",
        "        return BLER\n",
        "\n",
        "\n",
        "\n",
        "    def bler_sim1(self,s,  ebnodbs, batch_size, iterations):\n",
        "        '''Monte Carlo simulations of BLER for a range of Eb/No\n",
        "           Sometimes we to compute statistics for batch sizes that do not fit into the GPUs memory.\n",
        "           You can average over multiple batches with small size instead.           \n",
        "        '''\n",
        "        BLER = np.zeros_like(ebnodbs)\n",
        "        for i in range(iterations):\n",
        "          #for ebnodb in ebnodbs:\n",
        "            #print(s, batch_size, ebnodb) \n",
        "          bler = np.array([self.sess.run(self.vars['bler'],\n",
        "                            feed_dict=self.gen_e2e_feed_dict(batch_size, np.transpose(np.tile(np.ones(1000)*ebnodb, (2,2,1))), s, lr=0)) for ebnodb in ebnodbs])\n",
        "                                        \n",
        "          BLER = BLER + bler/iterations\n",
        "        return BLER   \n",
        "    \n",
        "    def plot_bler(self, EbNodB, BLER):\n",
        "        '''Plot a BLER curve'''\n",
        "        image = plt.figure(figsize=(10,8))\n",
        "        plt.plot(EbNodB, BLER, '-r', linewidth=2.0)\n",
        "        plt.yscale('log')\n",
        "        plt.xlabel('EbNo (dB)', fontsize=18)\n",
        "        plt.ylabel('Block-error rate', fontsize=18)\n",
        "        plt.grid(True)\n",
        "        plt.ylim([1e-5,1])\n",
        "        return image"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bANUdLIsf7hM"
      },
      "source": [
        "## Training parameters"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YeHghWVRf7hO",
        "outputId": "35e7375a-b6b2-4545-88d4-4e355de2fd95"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Tensor(\"embedding_lookup/Identity:0\", shape=(?, 256), dtype=float32)\n",
            "Tensor(\"Reshape:0\", shape=(?, 2, 2), dtype=float32)\n",
            "Tensor(\"dense_4/BiasAdd:0\", shape=(10000, 256), dtype=float32)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-24-a5adff64427c>:110: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  x = tf.layers.dense(x, self.M, activation=None)\n",
            "<ipython-input-24-a5adff64427c>:111: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  x = tf.layers.dense(x, self.n, activation=None)\n",
            "<ipython-input-24-a5adff64427c>:126: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  y = tf.layers.dense(y, self.M, activation=None)\n",
            "<ipython-input-24-a5adff64427c>:127: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  y = tf.layers.dense(y, self.M, activation=None)\n",
            "<ipython-input-24-a5adff64427c>:128: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  y = tf.layers.dense(y, self.M, activation=None)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Batch Size: 10000, Learning Rate: 0.01, EbNodB: [[[11.5866756  11.5866756 ]\n",
            "  [11.5866756  11.5866756 ]]\n",
            "\n",
            " [[ 8.84328163  8.84328163]\n",
            "  [ 8.84328163  8.84328163]]\n",
            "\n",
            " [[30.32286404 30.32286404]\n",
            "  [30.32286404 30.32286404]]\n",
            "\n",
            " ...\n",
            "\n",
            " [[27.91724122 27.91724122]\n",
            "  [27.91724122 27.91724122]]\n",
            "\n",
            " [[18.64031196 18.64031196]\n",
            "  [18.64031196 18.64031196]]\n",
            "\n",
            " [[14.40389224 14.40389224]\n",
            "  [14.40389224 14.40389224]]], Iterations: 10000\n",
            "0.9727\n",
            "0.07190001\n",
            "0.08069998\n",
            "0.0808\n",
            "0.08590001\n",
            "0.08789998\n",
            "0.08350003\n",
            "0.07859999\n",
            "0.07459998\n",
            "0.076900005\n",
            "Tensor(\"embedding_lookup/Identity:0\", shape=(?, 256), dtype=float32)\n",
            "Tensor(\"Reshape:0\", shape=(?, 2, 2), dtype=float32)\n",
            "Tensor(\"dense_4/BiasAdd:0\", shape=(10000, 256), dtype=float32)\n"
          ]
        }
      ],
      "source": [
        "train_EbNodB = ad_noise_SNR\n",
        "val_EbNodB = train_EbNodB\n",
        "\n",
        "lr = 0.01\n",
        "\n",
        "epoch = [10000]\n",
        "\n",
        "training_params = [\n",
        "    #batch_size, lr, ebnodb, iterations\n",
        "    [s, batch_size , 0.01, train_EbNodB, 10000]\n",
        "#    [10000 , 0.001, train_EbNodB, 10000]    \n",
        "    ]\n",
        "\n",
        "validation_params = [\n",
        "    #batch_size, ebnodb, val_steps \n",
        "    [batch_size, val_EbNodB, 1000],\n",
        "    [batch_size, val_EbNodB, 1000],\n",
        "    [batch_size, val_EbNodB, 1000]\n",
        "    ]\n",
        "\n",
        "model_file_uw = 'models/ae_k_{}_n_{}'.format(k,n)\n",
        "ae = AE(k,n,seed)\n",
        "ae.train(training_params, validation_params)\n",
        "ae.save(model_file_uw);\n",
        "ae = AE(k,n,seed, filename=model_file_uw)\n",
        "  #ae.plot_constellation();\n",
        "  #ae.end2end(tr)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VKoeXIMOcpbJ"
      },
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Wl3hENsvf7hW"
      },
      "source": [
        "## Create and train model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lzqpcwGaf7hm"
      },
      "source": [
        "## Evaluate trained model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "id": "Y33vV4xKf7hn",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3530c290-7935-43ca-8d7a-ad0d6d3aecf5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Tensor(\"embedding_lookup/Identity:0\", shape=(?, 256), dtype=float32)\n",
            "Tensor(\"Reshape:0\", shape=(?, 2, 2), dtype=float32)\n",
            "Tensor(\"dense_4/BiasAdd:0\", shape=(10000, 256), dtype=float32)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-24-a5adff64427c>:110: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  x = tf.layers.dense(x, self.M, activation=None)\n",
            "<ipython-input-24-a5adff64427c>:111: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  x = tf.layers.dense(x, self.n, activation=None)\n",
            "<ipython-input-24-a5adff64427c>:126: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  y = tf.layers.dense(y, self.M, activation=None)\n",
            "<ipython-input-24-a5adff64427c>:127: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  y = tf.layers.dense(y, self.M, activation=None)\n",
            "<ipython-input-24-a5adff64427c>:128: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  y = tf.layers.dense(y, self.M, activation=None)\n"
          ]
        }
      ],
      "source": [
        "ae_uw = AE(k,n,seed, filename=model_file_uw) #Load a pretrained model that you have saved if needed"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "id": "fasS-Rz1lapW"
      },
      "outputs": [],
      "source": [
        "\n",
        "class AE_Weighted(object):\n",
        "    def __init__(self, k, n, seed=None, filename=None):\n",
        "        assert (n%2 == 0), \"Channel only allows complex symbols -> n must be a multiple of 2\"\n",
        "        self.k = k \n",
        "        self.n = n\n",
        "        self.n_complex = int(self.n/2)\n",
        "        self.bits_per_symbol = self.k/self.n_complex\n",
        "        self.M = 2**self.k\n",
        "        self.seed = seed if (seed is not None) else int(time.time())           \n",
        "        self.graph = None\n",
        "        self.sess = None   \n",
        "        self.vars = None\n",
        "        self.saver = None   \n",
        "        self.constellations = None\n",
        "        self.blers = None\n",
        "        self.create_graph()\n",
        "        self.create_session()\n",
        "        if filename is not None:    \n",
        "            self.load(filename)       \n",
        "        return\n",
        "\n",
        "    \n",
        "    def create_graph(self):\n",
        "        '''This function creates the computation graph of the autoencoder'''\n",
        "        self.graph = tf.Graph()        \n",
        "        with self.graph.as_default():    \n",
        "            tf.set_random_seed(self.seed)\n",
        "            batch_size = tf.placeholder(tf.int32, shape=())\n",
        "            \n",
        "            # Transmitter\n",
        "            s = (tf.random_uniform(shape=[batch_size], minval=0, maxval=self.M, dtype=tf.int64))\n",
        "\n",
        "            ad_noise_std = tf.random_uniform(shape=[batch_size], minval=0, maxval=M, dtype=tf.int64)\n",
        "            ones = tf.ones([2,2,1],dtype=tf.int64)\n",
        "            ad_noise_std = tf.transpose(ad_noise_std*ones)\n",
        "            x = self.encoder(s) \n",
        "\n",
        "                         \n",
        "            \n",
        "            # Channel\n",
        "            #noise_std = tf.placeholder(tf.float32, shape=())\n",
        "            noise_std = tf.placeholder(tf.float32, shape=[10000,2,2])\n",
        "            noise = tf.random_normal(tf.shape(x), mean=0.0, stddev=noise_std) \n",
        "\n",
        "            fade = tf.random.normal(shape=tf.shape(x))\n",
        "            sparr1,sparr2 = tf.split(fade,num_or_size_splits=2, axis=2)\n",
        "            complex_fade = tf.complex(sparr1, sparr2)\n",
        "            fade = tf.abs(complex_fade)\n",
        "            #fade = tf.math.sqrt(1/2)*fade\n",
        "\n",
        "            fade = 1\n",
        "            y = tf.multiply(x,fade) + noise\n",
        "            #y = x + noise\n",
        "            #fade = 1            \n",
        "           \n",
        "            # Receiver\n",
        "            s_hat = self.decoder(y)\n",
        "            correct_s_hat = tf.argmax(tf.nn.softmax(s_hat), axis=1)\n",
        "\n",
        "            \n",
        "            # Loss function\n",
        "            #cross_entropy = tf.losses.sparse_softmax_cross_entropy(labels=s, logits=s_hat)\n",
        "            #cross_entropy = tf.losses.sparse_softmax_cross_entropy(labels=s, logits=s_hat)\n",
        "            cross_entropy = tf.losses.sparse_softmax_cross_entropy(labels=s, logits=s_hat, weights= (s+1)**(1))\n",
        "      \n",
        "           # Performance metrics\n",
        "            #correct_predictions_0 = tf.equal(tf.argmax(tf.nn.softmax([s_hat[x] for x in s_ind_0]), axis=1), [s[x] for x in s_ind_0])\n",
        "\n",
        "            correct_predictions = tf.equal(tf.argmax(tf.nn.softmax(s_hat), axis=1), s)\n",
        "            accuracy = tf.reduce_mean(tf.cast(correct_predictions, tf.float32))\n",
        "            bler = 1-accuracy\n",
        "\n",
        "            lr = tf.placeholder(tf.float32, shape=()) # We can feed in any desired learning rate for each step     \n",
        "            train_op = tf.train.AdamOptimizer(lr).minimize(cross_entropy)\n",
        "            #train_op_0 = tf.train.AdamOptimizer(lr).minimize(cross_entropy_0)\n",
        "            #lr = tf.train.exponential_decay(1e-10, global_step=cross_entropy, decay_steps=100, decay_rate=1.30)\n",
        "\n",
        "            # References to graph variables we need to access later \n",
        "            self.vars = {\n",
        "                'accuracy': accuracy,\n",
        "                'batch_size': batch_size,\n",
        "                'bler': bler,\n",
        "                'cross_entropy': cross_entropy,\n",
        "                'init': tf.global_variables_initializer(),\n",
        "                'lr': lr,\n",
        "                'noise_std': noise_std,\n",
        "                'train_op': train_op,\n",
        "                's': s,\n",
        "                's_hat': s_hat,\n",
        "                'correct_s_hat': correct_s_hat,\n",
        "                'x': x,\n",
        "            }            \n",
        "            self.saver = tf.train.Saver()\n",
        "        return\n",
        "    \n",
        "    \n",
        "    def create_session(self):\n",
        "        '''Create a session for the autoencoder instance with the compuational graph'''\n",
        "        self.sess = tf.Session(graph=self.graph)        \n",
        "        self.sess.run(self.vars['init'])\n",
        "        return\n",
        "    \n",
        "    def encoder(self, input):\n",
        "        '''The transmitter'''\n",
        "        self.weight_var_rec = self.weight_variable((self.M,self.M)) # shape = (8,8)\n",
        "        self.embedding_lookup_rec = tf.nn.embedding_lookup(self.weight_var_rec, input)\n",
        "        print(self.embedding_lookup_rec)\n",
        "        x = tf.nn.elu(self.embedding_lookup_rec)\n",
        "        #x = tf.layers.dense(self.embedding_lookup_rec, self.M, activation=tf.nn.relu)\n",
        "        x = tf.layers.dense(x, self.M, activation=None)\n",
        "        x = tf.layers.dense(x, self.n, activation=None)\n",
        "        #x = tf.layers.dense(x, self.n, activation=None)\n",
        "        #x = tf.layers.dense(x, self.n, activation=None)\n",
        "        #x = tf.layers.dense(x, self.n, activation=None)\n",
        "        #x = tf.layers.dense(x, self.n, activation=None)\n",
        "        x = tf.reshape(x, shape=[-1,self.n_complex,2])\n",
        "        print(x);\n",
        "        #Average power normalization\n",
        "        x = x/tf.sqrt(2*tf.reduce_mean(tf.square(x))) \n",
        "        return x\n",
        "    \n",
        "    def decoder(self, input):\n",
        "        '''The Receiver'''\n",
        "        #input = self.flip_decoder(input)\n",
        "        y = tf.reshape(input, shape=[-1,self.n])\n",
        "        y = tf.layers.dense(y, self.M, activation=None)\n",
        "        y = tf.layers.dense(y, self.M, activation=None)\n",
        "        y = tf.layers.dense(y, self.M, activation=None)\n",
        "        #y = tf.layers.dense(y, self.M, activation=None)\n",
        "        #y = tf.layers.dense(y, self.M, activation=None)\n",
        "        #y = tf.layers.dense(y, self.M, activation=None)\n",
        "        #y = tf.layers.dense(y, self.M, activation=None)\n",
        "        #y = tf.layers.dense(y, self.M, activation=None)\n",
        "        print(y);\n",
        "        return y\n",
        "    \n",
        "    def EbNo2Sigma(self, ebnodb):\n",
        "        '''Convert Eb/No in dB to noise standard deviation'''\n",
        "        ebno = 10**(ebnodb/10)\n",
        "        return 1/np.sqrt(2*self.bits_per_symbol*ebno)\n",
        "    \n",
        "    def gen_feed_dict(self, batch_size, ebnodb, lr):\n",
        "        '''Generate a feed dictionary for training and validation'''        \n",
        "        return {\n",
        "            self.vars['batch_size']: batch_size,\n",
        "            self.vars['noise_std']: self.EbNo2Sigma(ebnodb),\n",
        "            self.vars['lr']: lr,\n",
        "        }\n",
        "\n",
        "    def gen_e2e_feed_dict(self, batch_size, ebnodb, s_input, lr):\n",
        "        '''Generate a feed dictionary for training and validation'''        \n",
        "        return {\n",
        "            self.vars['batch_size']: batch_size,\n",
        "            self.vars['noise_std']: self.EbNo2Sigma(ebnodb),\n",
        "            self.vars['s']: s_input,\n",
        "            self.vars['lr']: lr,\n",
        "        }    \n",
        "    \n",
        "    def load(self, filename):\n",
        "        '''Load an pre_trained model'''\n",
        "        return self.saver.restore(self.sess, filename)\n",
        "        \n",
        "    def plot_constellation(self,noise_std, maxrange=None):\n",
        "        '''Generate a plot of the current constellation'''\n",
        "        x = self.transmit(range(self.M), noise_std)\n",
        "        if (maxrange is None):\n",
        "            maxrange = np.max(np.abs(x))\n",
        "        for k in range(self.n_complex):\n",
        "            image = plt.figure(figsize=(6,6))\n",
        "            plt.grid(True)\n",
        "            plt.xlim(-maxrange,maxrange)\n",
        "            plt.ylim(-maxrange,maxrange)\n",
        "            for i in range(self.M):       \n",
        "              if (i <=150):\n",
        "                plt.scatter(x[i,k,0],x[i,k,1],c=\"black\")\n",
        "                #plt.annotate(i, (x[i,k,0],x[i,k,1]))  \n",
        "              if (i > 150):\n",
        "                plt.scatter(x[i,k,0],x[i,k,1],c=\"red\")\n",
        "                #plt.annotate(i, (x[i,k,0],x[i,k,1]))      \n",
        "                #plt.scatter(x[i,k,0],x[i,k,1],c=\"black\",marker='x')   \n",
        "            image.axes[0].set_xticks(np.array([-2,-1,0,1,2]))\n",
        "            image.axes[0].set_yticks(np.array([-2,-1,0,1,2]))\n",
        "            image.suptitle('%d. complex symbol' % (k+1))\n",
        "            plt.xlabel('Re')\n",
        "            plt.ylabel('Im')\n",
        "        return x, image\n",
        "    \n",
        "    def save(self, filename):\n",
        "        '''Save the current model'''\n",
        "        return self.saver.save(self.sess, filename)  \n",
        "    \n",
        "    def test_step(self, batch_size, ebnodb):\n",
        "        '''Compute the BLER over a single batch and Eb/No'''\n",
        "        bler = self.sess.run(self.vars['bler'], feed_dict=self.gen_feed_dict(batch_size, ebnodb, lr=0))\n",
        "        return bler\n",
        "    \n",
        "    def transmit(self, s, noise_std):\n",
        "        '''Returns the transmitted sigals corresponding to message indices'''\n",
        "        return self.sess.run(self.vars['x'], feed_dict={self.vars['s']: s, self.vars['noise_std']: noise_std})\n",
        "\n",
        "    def end2end(self, batch_size, ebnodb, input_s):\n",
        "        '''Returns the transmitted sigals corresponding to message indices'''\n",
        "        return self.sess.run(self.vars['correct_s_hat'], feed_dict=self.gen_e2e_feed_dict(batch_size, ebnodb, input_s, lr=0)) \n",
        "        #print(self.sess.run(self.vars['correct_s_hat'], feed_dict={self.vars['s']: input_s}))     \n",
        "\n",
        "    def end2end_bler(self, batch_size, ebnodb, input_s):\n",
        "        '''Returns the transmitted sigals corresponding to message indices'''\n",
        "        return self.sess.run(self.vars['bler'], feed_dict=self.gen_e2e_feed_dict(batch_size, ebnodb, input_s, lr=0)) \n",
        "\n",
        "    def train(self, training_params, validation_params):  \n",
        "        \n",
        "        '''Training and validation loop'''\n",
        "        for index, params in enumerate(training_params):            \n",
        "            s,batch_size, lr, ebnodb, iterations = params            \n",
        "            print('\\nBatch Size: ' + str(batch_size) +\n",
        "                  ', Learning Rate: ' + str(lr) +\n",
        "                  ', EbNodB: ' + str(ebnodb) +\n",
        "                  ', Iterations: ' + str(iterations))\n",
        "            \n",
        "            val_size, val_ebnodb, val_steps = validation_params[index]\n",
        "            \n",
        "            for i in range(iterations):\n",
        "                self.train_step(s,batch_size, ebnodb, lr)    \n",
        "                if (i%val_steps==0):\n",
        "                    #bler = self.sess.run(self.vars['bler'], feed_dict=self.gen_new_feed_dict(val_size, val_ebnodb, lr, s_input))\n",
        "                    bler = self.sess.run(self.vars['bler'], feed_dict=self.gen_feed_dict(val_size, val_ebnodb, lr))\n",
        "                    print(bler)                           \n",
        "        return       \n",
        "    \n",
        "    def train_step(self,s, batch_size, ebnodb, lr):\n",
        "        '''A single training step'''\n",
        "        #self.sess.run(self.vars['train_op'], feed_dict=self.gen_new_feed_dict(batch_size, ebnodb, lr, s_input))\n",
        "        self.sess.run(self.vars['train_op'], feed_dict={self.vars['s']: s, self.vars['batch_size']: batch_size,  self.vars['noise_std']: self.EbNo2Sigma(ebnodb), self.vars['lr']: lr})\n",
        "        return \n",
        "    \n",
        "    def weight_variable(self, shape):\n",
        "        '''Xavier-initialized weights optimized for ReLU Activations'''\n",
        "        (fan_in, fan_out) = shape\n",
        "        low = np.sqrt(6.0/(fan_in + fan_out)) \n",
        "        high = -np.sqrt(6.0/(fan_in + fan_out))\n",
        "        return tf.Variable(tf.random_uniform(shape, minval=low, maxval=high, dtype=tf.float32))\n",
        "    \n",
        "    def bler_sim(self, ebnodbs, batch_size, iterations):\n",
        "        '''Monte Carlo simulations of BLER for a range of Eb/No\n",
        "           Sometimes we to compute statistics for batch sizes that do not fit into the GPUs memory.\n",
        "           You can average over multiple batches with small size instead.           \n",
        "        '''\n",
        "        BLER = np.zeros_like(ebnodbs)\n",
        "        for i in range(iterations):\n",
        "            bler = np.array([self.sess.run(self.vars['bler'],\n",
        "                            feed_dict=self.gen_feed_dict(batch_size, ebnodb, lr=0)) for ebnodb in ebnodbs])\n",
        "            BLER = BLER + bler/iterations\n",
        "        return BLER\n",
        "\n",
        "\n",
        "\n",
        "    def bler_sim1(self,s,  ebnodbs, batch_size, iterations):\n",
        "        '''Monte Carlo simulations of BLER for a range of Eb/No\n",
        "           Sometimes we to compute statistics for batch sizes that do not fit into the GPUs memory.\n",
        "           You can average over multiple batches with small size instead.           \n",
        "        '''\n",
        "        BLER = np.zeros_like(ebnodbs)\n",
        "        for i in range(iterations):\n",
        "          #for ebnodb in ebnodbs:\n",
        "            #print(s, batch_size, ebnodb) \n",
        "          bler = np.array([self.sess.run(self.vars['bler'],\n",
        "                            feed_dict=self.gen_e2e_feed_dict(batch_size, np.transpose(np.tile(np.ones(1000)*ebnodb, (2,2,1))), s, lr=0)) for ebnodb in ebnodbs])\n",
        "                                        \n",
        "          BLER = BLER + bler/iterations\n",
        "        return BLER        \n",
        "    \n",
        "    def plot_bler(self, EbNodB, BLER):\n",
        "        '''Plot a BLER curve'''\n",
        "        image = plt.figure(figsize=(10,8))\n",
        "        plt.plot(EbNodB, BLER, '-r', linewidth=2.0)\n",
        "        plt.yscale('log')\n",
        "        plt.xlabel('EbNo (dB)', fontsize=18)\n",
        "        plt.ylabel('Block-error rate', fontsize=18)\n",
        "        plt.grid(True)\n",
        "        plt.ylim([1e-5,1])\n",
        "        return image"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "id": "rjh_J3MIlyrF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "81b15622-b670-45cc-fc1f-e3de27e38b99"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Tensor(\"embedding_lookup/Identity:0\", shape=(?, 256), dtype=float32)\n",
            "Tensor(\"Reshape:0\", shape=(?, 2, 2), dtype=float32)\n",
            "Tensor(\"dense_4/BiasAdd:0\", shape=(10000, 256), dtype=float32)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-27-5f02ca401e59>:110: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  x = tf.layers.dense(x, self.M, activation=None)\n",
            "<ipython-input-27-5f02ca401e59>:111: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  x = tf.layers.dense(x, self.n, activation=None)\n",
            "<ipython-input-27-5f02ca401e59>:126: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  y = tf.layers.dense(y, self.M, activation=None)\n",
            "<ipython-input-27-5f02ca401e59>:127: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  y = tf.layers.dense(y, self.M, activation=None)\n",
            "<ipython-input-27-5f02ca401e59>:128: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  y = tf.layers.dense(y, self.M, activation=None)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Batch Size: 10000, Learning Rate: 0.01, EbNodB: [[[11.5866756  11.5866756 ]\n",
            "  [11.5866756  11.5866756 ]]\n",
            "\n",
            " [[ 8.84328163  8.84328163]\n",
            "  [ 8.84328163  8.84328163]]\n",
            "\n",
            " [[30.32286404 30.32286404]\n",
            "  [30.32286404 30.32286404]]\n",
            "\n",
            " ...\n",
            "\n",
            " [[27.91724122 27.91724122]\n",
            "  [27.91724122 27.91724122]]\n",
            "\n",
            " [[18.64031196 18.64031196]\n",
            "  [18.64031196 18.64031196]]\n",
            "\n",
            " [[14.40389224 14.40389224]\n",
            "  [14.40389224 14.40389224]]], Iterations: 10000\n",
            "0.9814\n",
            "0.08819997\n",
            "0.09960002\n",
            "0.099399984\n",
            "0.096899986\n",
            "0.09759998\n",
            "0.09469998\n",
            "0.08759999\n",
            "0.08789998\n",
            "0.08890003\n",
            "Tensor(\"embedding_lookup/Identity:0\", shape=(?, 256), dtype=float32)\n",
            "Tensor(\"Reshape:0\", shape=(?, 2, 2), dtype=float32)\n",
            "Tensor(\"dense_4/BiasAdd:0\", shape=(10000, 256), dtype=float32)\n"
          ]
        }
      ],
      "source": [
        "train_EbNodB = ad_noise_SNR\n",
        "val_EbNodB = train_EbNodB\n",
        "\n",
        "lr = 0.01\n",
        "\n",
        "epoch = [10000]\n",
        "\n",
        "training_params = [\n",
        "    #batch_size, lr, ebnodb, iterations\n",
        "    [s, batch_size , 0.01, train_EbNodB, 10000]\n",
        "#    [10000 , 0.001, train_EbNodB, 10000]    \n",
        "    ]\n",
        "\n",
        "validation_params = [\n",
        "    #batch_size, ebnodb, val_steps \n",
        "    [batch_size, val_EbNodB, 1000],\n",
        "    [batch_size, val_EbNodB, 1000],\n",
        "    [batch_size, val_EbNodB, 1000]\n",
        "    ]\n",
        "\n",
        "model_file = 'models/ae_k_{}_n_{}'.format(k,n)\n",
        "ae_Weighted = AE_Weighted(k,n,seed)\n",
        "ae_Weighted.train(training_params, validation_params)\n",
        "ae_Weighted.save(model_file);\n",
        "ae_Weighted = AE_Weighted(k,n,seed, filename=model_file)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "id": "v3Yddt94DMAO"
      },
      "outputs": [],
      "source": [
        "\n",
        "class AE_Tb(object):\n",
        "    def __init__(self, k, n, seed=None, filename=None):\n",
        "        assert (n%2 == 0), \"Channel only allows complex symbols -> n must be a multiple of 2\"\n",
        "        self.k = k \n",
        "        self.n = n\n",
        "        self.n_complex = int(self.n/2)\n",
        "        self.bits_per_symbol = self.k/self.n_complex\n",
        "        self.M = 2**self.k\n",
        "        self.seed = seed if (seed is not None) else int(time.time())           \n",
        "        self.graph = None\n",
        "        self.sess = None   \n",
        "        self.vars = None\n",
        "        self.saver = None   \n",
        "        self.constellations = None\n",
        "        self.blers = None\n",
        "        self.create_graph()\n",
        "        self.create_session()\n",
        "        if filename is not None:    \n",
        "            self.load(filename)       \n",
        "        return\n",
        "    \n",
        "    \n",
        "    def create_graph(self):\n",
        "        '''This function creates the computation graph of the autoencoder'''\n",
        "        self.graph = tf.Graph()        \n",
        "        with self.graph.as_default():    \n",
        "            tf.set_random_seed(self.seed)\n",
        "            batch_size = tf.placeholder(tf.int32, shape=())\n",
        "            \n",
        "            # Transmitter\n",
        "            s = (tf.random_uniform(shape=[batch_size], minval=0, maxval=self.M, dtype=tf.int64))\n",
        "\n",
        "            ad_noise_std = tf.random_uniform(shape=[batch_size], minval=0, maxval=M, dtype=tf.int64)\n",
        "            ones = tf.ones([2,2,1],dtype=tf.int64)\n",
        "            ad_noise_std = tf.transpose(ad_noise_std*ones)\n",
        "            #ad_noise_std = tf.transpose(tf.tile(ad_noise_std, [2,2,1]))           \n",
        "            x = self.encoder(s)                         \n",
        "            \n",
        "            # Channel\n",
        "            #noise_std = tf.placeholder(tf.float32, shape=())\n",
        "            noise_std = tf.placeholder(tf.float32, shape=[10000,2,2])\n",
        "            noise = tf.random_normal(tf.shape(x), mean=0.0, stddev=noise_std) \n",
        "\n",
        "            fade = tf.random.normal(shape=tf.shape(x))\n",
        "            sparr1,sparr2 = tf.split(fade,num_or_size_splits=2, axis=2)\n",
        "            complex_fade = tf.complex(sparr1, sparr2)\n",
        "            fade = tf.abs(complex_fade)\n",
        "            #fade = tf.math.sqrt(1/2)*fade\n",
        "\n",
        "            fade = 1\n",
        "            y = tf.multiply(x,fade) + noise\n",
        "            #y = x + noise\n",
        "       \n",
        "           \n",
        "            # Receiver\n",
        "            s_hat = self.decoder(y)\n",
        "            correct_s_hat = tf.argmax(tf.nn.softmax(s_hat), axis=1)\n",
        "\n",
        "            \n",
        "            # Loss function\n",
        "            #cross_entropy = tf.losses.sparse_softmax_cross_entropy(labels=s, logits=s_hat)\n",
        "            cross_entropy = tf.losses.sparse_softmax_cross_entropy(labels=s, logits=s_hat)\n",
        "            #cross_entropy_0 = tf.losses.sparse_softmax_cross_entropy(labels=s, logits=s_hat)\n",
        "            #cross_entropy = tf.losses.sparse_softmax_cross_entropy(labels=s, logits=s_hat, weights= (s+1)**(4))\n",
        "      \n",
        "           # Performance metrics\n",
        "            #correct_predictions_0 = tf.equal(tf.argmax(tf.nn.softmax([s_hat[x] for x in s_ind_0]), axis=1), [s[x] for x in s_ind_0])\n",
        "\n",
        "            correct_predictions = tf.equal(tf.argmax(tf.nn.softmax(s_hat), axis=1), s)\n",
        "            accuracy = tf.reduce_mean(tf.cast(correct_predictions, tf.float32))\n",
        "            bler = 1-accuracy\n",
        "\n",
        "            lr = tf.placeholder(tf.float32, shape=()) # We can feed in any desired learning rate for each step     \n",
        "            train_op = tf.train.AdamOptimizer(lr).minimize(cross_entropy)\n",
        "            #train_op_0 = tf.train.AdamOptimizer(lr).minimize(cross_entropy_0)\n",
        "            #lr = tf.train.exponential_decay(1e-10, global_step=cross_entropy, decay_steps=100, decay_rate=1.30)\n",
        "\n",
        "            # References to graph variables we need to access later \n",
        "            self.vars = {\n",
        "                'accuracy': accuracy,\n",
        "                'batch_size': batch_size,\n",
        "                'bler': bler,\n",
        "                'cross_entropy': cross_entropy,\n",
        "                'init': tf.global_variables_initializer(),\n",
        "                'lr': lr,\n",
        "                'noise_std': noise_std,\n",
        "                'train_op': train_op,\n",
        "                #'s': (np.floor(np.random.uniform(0,256, 1000))).astype('int64'),\n",
        "                's': s,\n",
        "                's_hat': s_hat,\n",
        "                'correct_s_hat': correct_s_hat,\n",
        "                'x': x,\n",
        "            }            \n",
        "            self.saver = tf.train.Saver()\n",
        "        return\n",
        "    \n",
        "    def create_session(self):\n",
        "        '''Create a session for the autoencoder instance with the compuational graph'''\n",
        "        self.sess = tf.Session(graph=self.graph)        \n",
        "        self.sess.run(self.vars['init'])\n",
        "        return\n",
        "    \n",
        "    def encoder(self, input):\n",
        "        '''The transmitter'''\n",
        "        self.weight_var_rec = self.weight_variable((self.M,self.M)) # shape = (8,8)\n",
        "        self.embedding_lookup_rec = tf.nn.embedding_lookup(self.weight_var_rec, input)\n",
        "        print(self.embedding_lookup_rec)\n",
        "        x = tf.nn.elu(self.embedding_lookup_rec)\n",
        "        #x = tf.layers.dense(self.embedding_lookup_rec, self.M, activation=tf.nn.relu)\n",
        "        x = tf.layers.dense(x, self.M, activation=None)\n",
        "        x = tf.layers.dense(x, self.n, activation=None)\n",
        "        #x = tf.layers.dense(x, self.n, activation=None)\n",
        "        #x = tf.layers.dense(x, self.n, activation=None)\n",
        "        #x = tf.layers.dense(x, self.n, activation=None)\n",
        "        #x = tf.layers.dense(x, self.n, activation=None)\n",
        "        x = tf.reshape(x, shape=[-1,self.n_complex,2])\n",
        "        print(x);\n",
        "        #Average power normalization\n",
        "        x = x/tf.sqrt(2*tf.reduce_mean(tf.square(x))) \n",
        "        return x\n",
        "    \n",
        "    def decoder(self, input):\n",
        "        '''The Receiver'''\n",
        "        #input = self.flip_decoder(input)\n",
        "        y = tf.reshape(input, shape=[-1,self.n])\n",
        "        y = tf.layers.dense(y, self.M, activation=None)\n",
        "        y = tf.layers.dense(y, self.M, activation=None)\n",
        "        y = tf.layers.dense(y, self.M, activation=None)\n",
        "        #y = tf.layers.dense(y, self.M, activation=None)\n",
        "        #y = tf.layers.dense(y, self.M, activation=None)\n",
        "        #y = tf.layers.dense(y, self.M, activation=None)\n",
        "        #y = tf.layers.dense(y, self.M, activation=None)\n",
        "        #y = tf.layers.dense(y, self.M, activation=None)\n",
        "        print(y);\n",
        "        return y\n",
        "    \n",
        "    def EbNo2Sigma(self, ebnodb):\n",
        "        '''Convert Eb/No in dB to noise standard deviation'''\n",
        "        ebno = 10**(ebnodb/10)\n",
        "        return 1/np.sqrt(2*self.bits_per_symbol*ebno)\n",
        "    \n",
        "    def gen_feed_dict(self, batch_size, ebnodb, lr):\n",
        "        '''Generate a feed dictionary for training and validation'''        \n",
        "        return {\n",
        "            self.vars['batch_size']: batch_size,\n",
        "            self.vars['noise_std']: self.EbNo2Sigma(ebnodb),\n",
        "            self.vars['lr']: lr,\n",
        "        }\n",
        "\n",
        "    def gen_e2e_feed_dict(self, batch_size, ebnodb, s_input, lr):\n",
        "        '''Generate a feed dictionary for training and validation'''        \n",
        "        return {\n",
        "            self.vars['batch_size']: batch_size,\n",
        "            self.vars['noise_std']: self.EbNo2Sigma(ebnodb),\n",
        "            self.vars['s']: s_input,\n",
        "            self.vars['lr']: lr,\n",
        "        }   \n",
        "    \n",
        "    def load(self, filename):\n",
        "        '''Load an pre_trained model'''\n",
        "        return self.saver.restore(self.sess, filename)\n",
        "        \n",
        "    def plot_constellation(self, noise_std, maxrange=None):\n",
        "        '''Generate a plot of the current constellation'''\n",
        "        x = self.transmit(range(self.M), noise_std)\n",
        "        if (maxrange is None):\n",
        "            maxrange = np.max(np.abs(x))\n",
        "        for k in range(self.n_complex):\n",
        "            image = plt.figure(figsize=(6,6))\n",
        "            plt.grid(True)\n",
        "            plt.xlim(-maxrange,maxrange)\n",
        "            plt.ylim(-maxrange,maxrange)\n",
        "            for i in range(self.M):\n",
        "              if (i <=150):\n",
        "                plt.scatter(x[i,k,0],x[i,k,1],c=\"black\")\n",
        "                #plt.annotate(i, (x[i,k,0],x[i,k,1]))  \n",
        "              if (i > 150):\n",
        "                plt.scatter(x[i,k,0],x[i,k,1],c=\"red\")\n",
        "                #plt.annotate(i, (x[i,k,0],x[i,k,1]))      \n",
        "                #plt.scatter(x[i,k,0],x[i,k,1],c=\"black\",marker='x')   \n",
        "            image.axes[0].set_xticks(np.array([-2,-1,0,1,2]))\n",
        "            image.axes[0].set_yticks(np.array([-2,-1,0,1,2]))\n",
        "            image.suptitle('%d. complex symbol' % (k+1))\n",
        "            plt.xlabel('Re')\n",
        "            plt.ylabel('Im')\n",
        "        return x, image\n",
        "    \n",
        "    def save(self, filename):\n",
        "        '''Save the current model'''\n",
        "        return self.saver.save(self.sess, filename)  \n",
        "    \n",
        "    def test_step(self, batch_size, ebnodb):\n",
        "        '''Compute the BLER over a single batch and Eb/No'''\n",
        "        bler = self.sess.run(self.vars['bler'], feed_dict=self.gen_feed_dict(batch_size, ebnodb, lr=0))\n",
        "        return bler\n",
        "    \n",
        "    def transmit(self, s, noise_std):\n",
        "        '''Returns the transmitted sigals corresponding to message indices'''\n",
        "        return self.sess.run(self.vars['x'], feed_dict={self.vars['s']: s, self.vars['noise_std']: noise_std})\n",
        "\n",
        "    def end2end(self, batch_size, ebnodb, input_s):\n",
        "        '''Returns the transmitted sigals corresponding to message indices'''\n",
        "        return self.sess.run(self.vars['correct_s_hat'], feed_dict=self.gen_e2e_feed_dict(batch_size, ebnodb, input_s, lr=0)) \n",
        "        #print(self.sess.run(self.vars['correct_s_hat'], feed_dict={self.vars['s']: input_s}))     \n",
        "\n",
        "    def end2end_bler(self, batch_size, ebnodb, input_s):\n",
        "        '''Returns the transmitted sigals corresponding to message indices'''\n",
        "        return self.sess.run(self.vars['bler'], feed_dict=self.gen_e2e_feed_dict(batch_size, ebnodb, input_s, lr=0))\n",
        "\n",
        "    def train(self, training_params, validation_params):  \n",
        "        \n",
        "        '''Training and validation loop'''\n",
        "        for index, params in enumerate(training_params):            \n",
        "            s,batch_size, lr, ebnodb, iterations = params            \n",
        "            print('\\nBatch Size: ' + str(batch_size) +\n",
        "                  ', Learning Rate: ' + str(lr) +\n",
        "                  ', EbNodB: ' + str(ebnodb) +\n",
        "                  ', Iterations: ' + str(iterations))\n",
        "            \n",
        "            val_size, val_ebnodb, val_steps = validation_params[index]\n",
        "            \n",
        "            for i in range(iterations):\n",
        "                self.train_step(s,batch_size, ebnodb, lr)    \n",
        "                if (i%val_steps==0):\n",
        "                    #bler = self.sess.run(self.vars['bler'], feed_dict=self.gen_new_feed_dict(val_size, val_ebnodb, lr, s_input))\n",
        "                    bler = self.sess.run(self.vars['bler'], feed_dict=self.gen_feed_dict(val_size, val_ebnodb, lr))\n",
        "                    print(bler)                           \n",
        "        return       \n",
        "    \n",
        "    def train_step(self,s, batch_size, ebnodb, lr):\n",
        "        '''A single training step'''\n",
        "        #self.sess.run(self.vars['train_op'], feed_dict=self.gen_new_feed_dict(batch_size, ebnodb, lr, s_input))\n",
        "        self.sess.run(self.vars['train_op'], feed_dict={self.vars['s']: s, self.vars['batch_size']: batch_size,  self.vars['noise_std']: self.EbNo2Sigma(ebnodb), self.vars['lr']: lr})\n",
        "        return \n",
        "    \n",
        "    def weight_variable(self, shape):\n",
        "        '''Xavier-initialized weights optimized for ReLU Activations'''\n",
        "        (fan_in, fan_out) = shape\n",
        "        low = np.sqrt(6.0/(fan_in + fan_out)) \n",
        "        high = -np.sqrt(6.0/(fan_in + fan_out))\n",
        "        return tf.Variable(tf.random_uniform(shape, minval=low, maxval=high, dtype=tf.float32))\n",
        "    \n",
        "    def bler_sim(self, ebnodbs, batch_size, iterations):\n",
        "        '''Monte Carlo simulations of BLER for a range of Eb/No\n",
        "           Sometimes we to compute statistics for batch sizes that do not fit into the GPUs memory.\n",
        "           You can average over multiple batches with small size instead.           \n",
        "        '''\n",
        "        BLER = np.zeros_like(ebnodbs)\n",
        "        for i in range(iterations):\n",
        "            bler = np.array([self.sess.run(self.vars['bler'],\n",
        "                            feed_dict=self.gen_feed_dict(batch_size, ebnodb, lr=0)) for ebnodb in ebnodbs])\n",
        "            BLER = BLER + bler/iterations\n",
        "        return BLER\n",
        "\n",
        "    def bler_sim1(self,s,  ebnodbs, batch_size, iterations):\n",
        "        '''Monte Carlo simulations of BLER for a range of Eb/No\n",
        "           Sometimes we to compute statistics for batch sizes that do not fit into the GPUs memory.\n",
        "           You can average over multiple batches with small size instead.           \n",
        "        '''\n",
        "        BLER = np.zeros_like(ebnodbs)\n",
        "        for i in range(iterations):\n",
        "          #for ebnodb in ebnodbs:\n",
        "            #print(s, batch_size, ebnodb) \n",
        "          bler = np.array([self.sess.run(self.vars['bler'],\n",
        "                            feed_dict=self.gen_e2e_feed_dict(batch_size, np.transpose(np.tile(np.ones(1000)*ebnodb, (2,2,1))), s, lr=0)) for ebnodb in ebnodbs])\n",
        "                                        \n",
        "          BLER = BLER + bler/iterations\n",
        "        return BLER   \n",
        "\n",
        "\n",
        "    def plot_bler(self, EbNodB, BLER):\n",
        "        '''Plot a BLER curve'''\n",
        "        image = plt.figure(figsize=(10,8))\n",
        "        plt.plot(EbNodB, BLER, '-r', linewidth=2.0)\n",
        "        plt.yscale('log')\n",
        "        plt.xlabel('EbNo (dB)', fontsize=18)\n",
        "        plt.ylabel('Block-error rate', fontsize=18)\n",
        "        plt.grid(True)\n",
        "        plt.ylim([1e-5,1])\n",
        "        return image"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "id": "OqkN-OmfD1GW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1046b1ef-312b-4254-cd7b-6b97e7864a7d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Tensor(\"embedding_lookup/Identity:0\", shape=(?, 256), dtype=float32)\n",
            "Tensor(\"Reshape:0\", shape=(?, 2, 2), dtype=float32)\n",
            "Tensor(\"dense_4/BiasAdd:0\", shape=(10000, 256), dtype=float32)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-29-2926bb07d458>:110: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  x = tf.layers.dense(x, self.M, activation=None)\n",
            "<ipython-input-29-2926bb07d458>:111: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  x = tf.layers.dense(x, self.n, activation=None)\n",
            "<ipython-input-29-2926bb07d458>:126: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  y = tf.layers.dense(y, self.M, activation=None)\n",
            "<ipython-input-29-2926bb07d458>:127: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  y = tf.layers.dense(y, self.M, activation=None)\n",
            "<ipython-input-29-2926bb07d458>:128: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  y = tf.layers.dense(y, self.M, activation=None)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Batch Size: 10000, Learning Rate: 0.01, EbNodB: [[[15.69862303 15.69862303]\n",
            "  [15.69862303 15.69862303]]\n",
            "\n",
            " [[11.93914594 11.93914594]\n",
            "  [11.93914594 11.93914594]]\n",
            "\n",
            " [[12.19079    12.19079   ]\n",
            "  [12.19079    12.19079   ]]\n",
            "\n",
            " ...\n",
            "\n",
            " [[12.79167711 12.79167711]\n",
            "  [12.79167711 12.79167711]]\n",
            "\n",
            " [[21.35466904 21.35466904]\n",
            "  [21.35466904 21.35466904]]\n",
            "\n",
            " [[14.1014316  14.1014316 ]\n",
            "  [14.1014316  14.1014316 ]]], Iterations: 10000\n",
            "0.9738\n",
            "0.008099973\n",
            "0.0059999824\n",
            "0.008599997\n",
            "0.007099986\n",
            "0.007099986\n",
            "0.008099973\n",
            "0.008300006\n",
            "0.007799983\n",
            "0.008300006\n",
            "Tensor(\"embedding_lookup/Identity:0\", shape=(?, 256), dtype=float32)\n",
            "Tensor(\"Reshape:0\", shape=(?, 2, 2), dtype=float32)\n",
            "Tensor(\"dense_4/BiasAdd:0\", shape=(10000, 256), dtype=float32)\n"
          ]
        }
      ],
      "source": [
        "train_EbNodB = seven_noise_SNR\n",
        "val_EbNodB = train_EbNodB\n",
        "\n",
        "lr = 0.01\n",
        "\n",
        "epoch = [10000]\n",
        "\n",
        "training_params = [\n",
        "    #batch_size, lr, ebnodb, iterations\n",
        "    [s, batch_size , 0.01, train_EbNodB, 10000]\n",
        "    #[s, 1000 , 0.001, train_EbNodB, 10000]\n",
        "    #[1000 , 0.001, train_EbNodB, 10000]    \n",
        "    ]\n",
        "\n",
        "validation_params = [\n",
        "    #batch_size, ebnodb, val_steps \n",
        "    [batch_size, val_EbNodB, 1000],\n",
        "    [batch_size, val_EbNodB, 1000],\n",
        "    [batch_size, val_EbNodB, 1000]\n",
        "    ]\n",
        "\n",
        "model_file_Tb = 'models/ae_k_{}_n_{}'.format(k,n)\n",
        "ae_Tb = AE_Tb(k,n,seed)\n",
        "ae_Tb.train(training_params, validation_params)\n",
        "ae_Tb.save(model_file_Tb);\n",
        "ae_Tb = AE_Tb(k,n,seed, filename=model_file_Tb)  #ae.plot_constellation();\n",
        "  #ae.end2end(tr)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dsoF-I7Rf7hy"
      },
      "source": [
        "### Plot of learned constellations"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "id": "YjGW8S_df7h0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 655
        },
        "outputId": "2b2dc742-c5c1-4f19-e872-c54fb03c94e4"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([[[-0.0163323 ,  0.00277036],\n",
              "         [-0.01411643, -0.00731078]],\n",
              " \n",
              "        [[ 0.13818951, -0.47354332],\n",
              "         [ 0.04462139, -0.12333751]],\n",
              " \n",
              "        [[ 0.16787471, -0.30551293],\n",
              "         [ 0.257487  , -0.38646358]],\n",
              " \n",
              "        ...,\n",
              " \n",
              "        [[-0.1440736 ,  0.30310178],\n",
              "         [ 2.4964206 , -0.04623182]],\n",
              " \n",
              "        [[-0.6690386 , -0.54595906],\n",
              "         [-1.7460378 ,  1.4861658 ]],\n",
              " \n",
              "        [[-1.2080157 , -1.8963437 ],\n",
              "         [ 1.2219166 ,  1.0101628 ]]], dtype=float32), [])"
            ]
          },
          "metadata": {},
          "execution_count": 31
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "import itertools\n",
        "def plot_constellation_2(ae, arr, noise_std,  maxrange=None):\n",
        "        '''Generate a plot of the current constellation'''\n",
        "        x = ae.transmit(arr, noise_std)\n",
        "        #marker = itertools.cycle(('1', '2', '3', '4', '^', '6', '7', '8'))\n",
        "        #weights = [1,4,9,16,25,36,49,64]\n",
        "        #weights = [1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256]\n",
        "        #weights = [1,1,1,1,1,1,1,1]\n",
        "        #weights = [1,8,27,64,125,216,343,512]\n",
        "        #weights = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]\n",
        "        weights = np.arange(M)\n",
        "        #weights = [1,16,81,256,625, 1296, 2401, 4096]\n",
        "        #weights = [1,256,6561,65536, 390625, 1.6, 5.7, 16.7]\n",
        "        #x = ae.transmit(np.ones(ae.M)*n)\n",
        "        #print(ae.M)\n",
        "        if (maxrange is None):\n",
        "            maxrange = np.max(np.abs(x))\n",
        "        for k in range(ae.n_complex):\n",
        "            \n",
        "#            image = plt.figure(figsize=(6,6))\n",
        "            image = plt.plot()\n",
        "            plt.grid(True)\n",
        "            plt.xlim(-2,2)\n",
        "            plt.ylim(-2,2)\n",
        "            #plt.show() \n",
        "            #plt.ion()\n",
        "            xshape = np.shape(x)\n",
        "            for i in range(xshape[0]): \n",
        "              if (i <=150):\n",
        "                plt.scatter(x[i,k,0],x[i,k,1],c=\"black\")\n",
        "                plt.annotate(weights[i], (x[i,k,0],x[i,k,1]))  \n",
        "              if (i > 150):\n",
        "                plt.scatter(x[i,k,0],x[i,k,1],c=\"red\")\n",
        "                plt.annotate(weights[i], (x[i,k,0],x[i,k,1]))     \n",
        "\n",
        "\n",
        "\n",
        "                #plt.show()              \n",
        "                #plt.pause(1)\n",
        "                #plt.hold(True)\n",
        "            #image.axes[0].set_xticks(np.array([-2,-1,0,1,2]))\n",
        "            #image.axes[0].set_yticks(np.array([-2,-1,0,1,2]))\n",
        "            #image.suptitle('%d. complex symbol' % (k+1))\n",
        "            #image.canvas.draw()\n",
        "            #image.canvas.flush_events()\n",
        "            \n",
        "            plt.xlabel('Re')\n",
        "            plt.ylabel('Im')\n",
        "            #time.sleep(0.1)\n",
        "        return x, image\n",
        "\n",
        "plot_constellation_2(ae,range(0,ae.M), const_noise_SNR)\n",
        "#plot_constellation_2(ae_Weighted, range(0, ae_Weighted.M))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qMbROTHNMa79"
      },
      "source": [
        "**THE RMSE Calculations**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "id": "B7-W-Be2auJV",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 388
        },
        "outputId": "5d72eb2b-6e0c-45cc-e4bf-30a2f1c0fea8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
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            "272.53566961139876\n",
            "304.59700208358754\n",
            "2610.9458151426606\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "def rmse(predictions,targets):\n",
        "  return (np.sqrt((np.subtract(predictions,targets) ** 2).mean()))   \n",
        "\n",
        "iter = 10\n",
        "rmse_uw = {}\n",
        "rmse_w = {}\n",
        "rmse_Tb = {}\n",
        "sum_uw = {}\n",
        "sum_w = {}\n",
        "sum_Tb = {}\n",
        "sum_uw[0] = 0\n",
        "#for i in range(1,iter):\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "tr_hat = ae.end2end(len(tr), tr_noise_SNR, tr)\n",
        "tr_hat_w = ae_Weighted.end2end(len(tr), tr_noise_SNR, tr)\n",
        "tr_hat_Tb = ae_Tb.end2end(len(tr), tr_noise_SNR, tr)\n",
        "\n",
        "#print(abs(tr_hat - tr))\n",
        "\n",
        "for j in range(1,M):\n",
        "#    rmse_uw[j,i] = rmse(([tr_hat[x] for x in s_ind[j]]), ([tr[x] for x in s_ind[j]]))\n",
        "  rmse_uw[j] = rmse(([tr_hat[x] for x in s_ind[j]]), ([tr[x] for x in s_ind[j]]))\n",
        "for j in range(1,M):\n",
        " #   rmse_w[j,i] = rmse(([tr_hat_w[x] for x in s_ind[j]]), ([tr[x] for x in s_ind[j]]))\n",
        " rmse_w[j] = rmse(([tr_hat_w[x] for x in s_ind[j]]), ([tr[x] for x in s_ind[j]]))\n",
        "for j in range(1,M):\n",
        "#    rmse_Tb[j,i] = rmse(([tr_hat_Tb[x] for x in s_ind[j]]), ([tr[x] for x in s_ind[j]]))\n",
        "  rmse_Tb[j] = rmse(([tr_hat_Tb[x] for x in s_ind[j]]), ([tr[x] for x in s_ind[j]]))\n",
        "  #sum_uw[i] = sum_uw[i] + sum_uw[i-1]\n",
        "\n",
        "print(rmse_uw)\n",
        "message_factor = (np.arange(1, M))\n",
        "\n",
        "rmse_uwA = []\n",
        "for i in rmse_uw.values():\n",
        "  rmse_uwA.append(i)\n",
        "\n",
        "rmse_wA = []\n",
        "for i in rmse_w.values():\n",
        "  rmse_wA.append(i)\n",
        "\n",
        "rmse_TbA = []\n",
        "for i in rmse_Tb.values():\n",
        "  rmse_TbA.append(i)\n",
        "\n",
        "#rmse_uw = np.log2(np.divide(rmse_uwA,message_factor) +1)\n",
        "#rmse_uw = (np.divide(rmse_uwA,message_factor) +1)\n",
        "rmse_uw = rmse_uwA\n",
        "\n",
        "#rmse_w = np.log2(np.divide(rmse_wA,message_factor) + 1)\n",
        "#rmse_w = (np.divide(rmse_wA,message_factor) + 1)\n",
        "rmse_w = rmse_wA\n",
        "\n",
        "\n",
        "#rmse_Tb = np.log2(np.divide(rmse_TbA,message_factor) +1)\n",
        "#rmse_Tb = (np.divide(rmse_TbA,message_factor))\n",
        "rmse_Tb = rmse_TbA\n",
        "\n",
        "message = np.arange(1,M)\n",
        "\n",
        "print(rmse_uw)\n",
        "plt.plot(message, rmse_uw, '-o');\n",
        "plt.plot(message, rmse_w, '-*');\n",
        "plt.plot(message, rmse_Tb, '-+');\n",
        "plt.xlabel('Distance')\n",
        "plt.ylabel('Absolute RMSE')\n",
        "#plt.ylim([0, 20])\n",
        "#plt.ylabel('log2 Norm RMSE deviation')\n",
        "plt.legend(['Unweighted SPL', 'Weighted(^1) SPL','TB'])\n",
        "\n",
        "\n",
        "print(np.sum(rmse_uw))\n",
        "print(np.sum(rmse_w))\n",
        "print(np.sum(rmse_Tb))\n",
        "#print(np.sum(rmse_uwA))\n",
        "#print(np.sum(rmse_wA))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "id": "AljuBtOiRYMZ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "outputId": "1ffca75c-4186-4e73-8534-9e87c29b6e84"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
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            "32385\n",
            "32385\n",
            "32385\n"
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          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "#print([x for x in s_ind[0]])\n",
        "\n",
        "#for i in range(len(s_ind[253])):\n",
        "#  print(s_ind[253][i])\n",
        "#batch_size = 50000\n",
        "bler_uw = {}\n",
        "bler_w = {}\n",
        "bler_Tb = {}\n",
        "bler_final_uw = {}\n",
        "bler_final_w = {}\n",
        "bler_final_Tb = {}\n",
        "bler_final_uw_val = []\n",
        "bler_final_w_val = []\n",
        "bler_final_Tb_val = []\n",
        "\n",
        "#for j in range(batch_size):\n",
        "#    bler_uw[j] = ae.end2end_bler(len(tr), np.tile(tr_noise_std[j], (batch_size, 1, 1)), tr[j]*np.ones(batch_size))\n",
        "#    bler_w[j] = ae_Weighted.end2end_bler(len(tr), np.tile(tr_noise_std[j], (batch_size, 1, 1)), tr[j]*np.ones(batch_size))\n",
        "#    bler_Tb[j] = ae_Tb.end2end_bler(len(tr), np.tile(tr_noise_std[j], (batch_size, 1, 1)), tr[j]*np.ones(batch_size))\n",
        "#print(bler_uw)  \n",
        "#print(bler_w)\n",
        "#print(bler_Tb)    \n",
        "Beta = {}\n",
        "SNR_var = {}\n",
        "\n",
        "\n",
        "for j in range(1,M-1):\n",
        "    bler_uw[j] = ae.end2end_bler(batch_size, np.tile(const_noise_SNR[j], (batch_size, 1, 1)), j*np.ones(batch_size))\n",
        "    bler_w[j] = ae_Weighted.end2end_bler(batch_size, np.tile(const_noise_SNR[j], (batch_size, 1, 1)), j*np.ones(batch_size))\n",
        "    bler_Tb[j] = ae_Tb.end2end_bler(batch_size, np.tile(const_noise_SNR[j], (batch_size, 1, 1)), j*np.ones(batch_size))\n",
        "print(bler_uw)  \n",
        "print(bler_w)\n",
        "print(bler_Tb)  \n",
        "\n",
        "\n",
        "bler_final_uw = bler_uw\n",
        "bler_final_w = bler_w\n",
        "bler_final_Tb = bler_Tb\n",
        "\n",
        "for i in bler_final_uw.values():\n",
        "  bler_final_uw_val.append(i)\n",
        "#bler_final_uw_val = np.flip(bler_final_uw_val)\n",
        "for i in bler_final_w.values():\n",
        "  bler_final_w_val.append(i)\n",
        "#bler_final_w_val = np.flip(bler_final_w_val)\n",
        "for i in bler_final_Tb.values():\n",
        "  bler_final_Tb_val.append(i)  \n",
        "#bler_final_Tb_val = np.flip(bler_final_Tb_val)  \n",
        "message = np.arange(1,M-1)\n",
        "plt.plot(message, bler_final_uw_val, '-o');\n",
        "plt.plot(message, bler_final_w_val, '-*');\n",
        "plt.plot(message, bler_final_Tb_val, '-+');\n",
        "print(bler_final_Tb_val)\n",
        "plt.xlabel('Distance')\n",
        "plt.ylabel('BLER')\n",
        "plt.legend(['Unweighted SPL', 'Weighted(^2) SPL','TB'])\n",
        "\n",
        "print(sum(bler_uw))\n",
        "print(sum(bler_w))\n",
        "print(sum(bler_Tb))\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "id": "6QIbpnhmnFLO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 392
        },
        "outputId": "b3fba4bd-5088-45f1-a833-08d0e1b8fca5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
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            "1.342391582943309\n",
            "1.1463487813302868\n",
            "8.751900282038084\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "def nsj_bler(predictions,targets):\n",
        "  return 1 - (((np.equal(predictions,targets)).mean()))   \n",
        "\n",
        "iter = 10\n",
        "bler_uw = {}\n",
        "bler_w = {}\n",
        "bler_Tb = {}\n",
        "sum_uw = {}\n",
        "sum_w = {}\n",
        "sum_Tb = {}\n",
        "\n",
        "\n",
        "\n",
        "for j in range(1,M):\n",
        "#    rmse_uw[j,i] = rmse(([tr_hat[x] for x in s_ind[j]]), ([tr[x] for x in s_ind[j]]))\n",
        "  bler_uw[j] = nsj_bler(([tr_hat[x] for x in s_ind[j]]), ([tr[x] for x in s_ind[j]]))\n",
        "for j in range(1,M):\n",
        " #   rmse_w[j,i] = rmse(([tr_hat_w[x] for x in s_ind[j]]), ([tr[x] for x in s_ind[j]]))\n",
        "  bler_w[j] = nsj_bler(([tr_hat_w[x] for x in s_ind[j]]), ([tr[x] for x in s_ind[j]]))\n",
        "for j in range(1,M):\n",
        "#    rmse_Tb[j,i] = rmse(([tr_hat_Tb[x] for x in s_ind[j]]), ([tr[x] for x in s_ind[j]]))\n",
        "  bler_Tb[j] = nsj_bler(([tr_hat_Tb[x] for x in s_ind[j]]), ([tr[x] for x in s_ind[j]]))\n",
        "  #sum_uw[i] = sum_uw[i] + sum_uw[i-1]\n",
        "\n",
        "print(bler_uw)\n",
        "message_factor = (np.arange(1, M))\n",
        "\n",
        "bler_uwA = []\n",
        "for i in bler_uw.values():\n",
        "  bler_uwA.append(i)\n",
        "\n",
        "bler_wA = []\n",
        "for i in bler_w.values():\n",
        "  bler_wA.append(i)\n",
        "\n",
        "bler_TbA = []\n",
        "for i in bler_Tb.values():\n",
        "  bler_TbA.append(i)\n",
        "\n",
        "#rmse_uw = np.log2(np.divide(rmse_uwA,message_factor) +1)\n",
        "#rmse_uw = (np.divide(rmse_uwA,message_factor) +1)\n",
        "bler_uw = bler_uwA\n",
        "\n",
        "#rmse_w = np.log2(np.divide(rmse_wA,message_factor) + 1)\n",
        "#rmse_w = (np.divide(rmse_wA,message_factor) + 1)\n",
        "bler_w = bler_wA\n",
        "\n",
        "\n",
        "#rmse_Tb = np.log2(np.divide(rmse_TbA,message_factor) +1)\n",
        "#rmse_Tb = (np.divide(rmse_TbA,message_factor))\n",
        "bler_Tb = bler_TbA\n",
        "\n",
        "message = np.arange(1,M)\n",
        "\n",
        "print(bler_uw)\n",
        "plt.plot(message, bler_uw, '-o');\n",
        "plt.plot(message, bler_w, '-*');\n",
        "plt.plot(message, bler_Tb, '-+');\n",
        "plt.xlabel('Distance')\n",
        "plt.ylabel('Absolute bler')\n",
        "plt.ylim([0, 1])\n",
        "#plt.ylabel('log2 Norm RMSE deviation')\n",
        "plt.legend(['Unweighted SPL', 'Weighted(^1) SPL','TB'])\n",
        "\n",
        "\n",
        "print(np.sum(bler_uw))\n",
        "print(np.sum(bler_w))\n",
        "print(np.sum(bler_Tb))\n",
        "#print(np.sum(rmse_uwA))\n",
        "#print(np.sum(rmse_wA))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "sxostCb-vY1i",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 845
        },
        "outputId": "736ff310-d866-44a7-dec3-0174425b987f"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "ae.plot_constellation(const_noise_SNR);\n",
        "#plot_constellation_2(ae,range(0,ae.M))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "id": "75eUVLFnq1JO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 845
        },
        "outputId": "2c6ee343-cbe4-46df-8275-2dc0eb00e311"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "ae_Weighted.plot_constellation(const_noise_SNR);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "id": "lFZkk0N3JD48",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 845
        },
        "outputId": "205971d7-c10a-4784-8674-848338e15321"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "ae_Tb.plot_constellation(const_noise_SNR);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {
        "id": "mtoc7OKCUgko"
      },
      "outputs": [],
      "source": [
        "# 8-PSK Modulation\n",
        "#8PSK constellation \n",
        "#Demodulation matrx\n",
        "#Qfunction \n",
        "\n",
        "import numpy as np\n",
        "from scipy import special\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "import subprocess\n",
        "import shlex\n",
        "\n",
        "\n",
        "#Generating constellation points\n",
        "s = np.zeros((8,2))\n",
        "s_comp = np.zeros((8,1))+1j*np.zeros((8,1))\n",
        "for i in range(8):\n",
        "\ts[i,:] = np.array(([np.cos(i*2*np.pi/8),np.sin(i*2*np.pi/8)])) #vector\n",
        "\ts_comp[i] = s[i,0]+1j*s[i,1] #equivalent complex number\n",
        "\n",
        "#Generating demodulation matrix\n",
        "A = np.zeros((8,2,2))\n",
        "A[0,:,:] = np.array(([np.sqrt(2)-1,1],[np.sqrt(2)-1,-1]))\n",
        "A[1,:,:] = np.array(([np.sqrt(2)+1,-1],[-(np.sqrt(2)-1),1]))\n",
        "A[2,:,:] = np.array(([-(np.sqrt(2)+1),1],[np.sqrt(2)+1,1]))\n",
        "A[3,:,:] = np.array(([np.sqrt(2)-1,1],[-(np.sqrt(2)+1),-1]))\n",
        "A[4,:,:] = np.array(([-(np.sqrt(2)-1),-1],[-(np.sqrt(2)-1),1]))\n",
        "A[5,:,:] = np.array(([-(np.sqrt(2)+1),1],[np.sqrt(2)-1,-1]))\n",
        "A[6,:,:] = np.array(([np.sqrt(2)+1,-1],[-(np.sqrt(2)+1),-1]))\n",
        "A[7,:,:] = np.array(([-(np.sqrt(2)-1),-1],[np.sqrt(2)+1,1]))\n",
        "\n",
        "#Gray code\n",
        "gray = np.zeros((8,3))\n",
        "gray[0,:] = np.array(([0,0,0]))\n",
        "gray[1,:] = np.array(([0,0,1]))\n",
        "gray[2,:] = np.array(([0,1,1]))\n",
        "gray[3,:] = np.array(([0,1,0]))\n",
        "gray[4,:] = np.array(([1,1,0]))\n",
        "gray[5,:] = np.array(([1,1,1]))\n",
        "gray[6,:] = np.array(([1,0,1]))\n",
        "gray[7,:] = np.array(([1,0,0]))\n",
        "\n",
        "\n",
        "#Q-function\n",
        "def qfunc(x):\n",
        "\treturn 0.5*special.erfc(x/np.sqrt(2))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "id": "7LDujO11Ulo5"
      },
      "outputs": [],
      "source": [
        "def decode(vec_comp):\n",
        "\tvec = np.zeros((2,1))\n",
        "\tvec[0] = np.real(vec_comp)\n",
        "\tvec[1] = np.imag(vec_comp)\n",
        "\tfor i in range(8):\n",
        "\t\ty = A[i,:,:]@vec\n",
        "\t\tif (y [0] >= 0) and (y[1] >= 0):\n",
        "\t\t\treturn s_comp[i]\n",
        "\n",
        "#Extracting bits from demodulated symbols\n",
        "def detect(vec_comp):\n",
        "\tvec = np.zeros((2,1))\n",
        "\tvec[0] = np.real(vec_comp)\n",
        "\tvec[1] = np.imag(vec_comp)\n",
        "\tfor i in range(8):\n",
        "\t\tif s[i,0]==vec[0] and s[i,1] == vec[1]:\n",
        "\t\t\treturn gray[i,:]\n",
        "\n",
        "#Demodulating symbol stream from received noisy  symbols\n",
        "def rx_symb(mat):\n",
        "\tlen = mat.shape[1]\n",
        "\trx_symb_stream = []\n",
        "\tfor i in range(len):\n",
        "\t\trx_symb_stream.append(decode(mat[:,i]))\n",
        "\treturn rx_symb_stream\n",
        "\n",
        "#Getting received bit stream from demodulated symbols\n",
        "def rx_bit(mat):\n",
        "\tlen = mat.shape[1]\n",
        "\trx_bit_stream = []\n",
        "\tfor i in range(len):\n",
        "\t\trx_bit_stream.append(detect(mat[:,i]))\n",
        "\treturn rx_bit_stream"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "id": "qPu3HX_SUov_"
      },
      "outputs": [],
      "source": [
        "#Generates a bitstream\n",
        "def bitstream(n):\n",
        "\treturn np.random.randint(0,2,n)\n",
        "\n",
        "#Converts bits to 8-PSK symbols using gray code\n",
        "def mapping(b0,b1,b2):\n",
        "\tif (b0 == 0 and b1 == 0 and b2 == 0):\n",
        "\t\treturn s[0,:]\n",
        "\telif (b0 == 0 and b1 == 0 and b2 == 1):\n",
        "\t\treturn s[1,:]\n",
        "\telif (b0 == 0 and b1 == 1 and b2 == 1):\n",
        "\t\treturn s[2,:]\n",
        "\telif (b0 == 0 and b1 == 1 and b2 == 0):\n",
        "\t\treturn s[3,:]\n",
        "\telif( b0 == 1 and b1 == 1 and b2 == 0):\n",
        "\t\treturn s[4,:]\n",
        "\telif(b0==1 and b1 == 1 and b2 == 1):\n",
        "\t\treturn s[5,:]\n",
        "\telif(b0==1 and b1 == 0 and b2 == 1):\n",
        "\t\treturn s[6,:]\n",
        "\telif(b0==1 and b1 == 0 and b2 == 0):\n",
        "\t\treturn s[7,:]\n",
        "\n",
        "\n",
        "#Converts bitstream to 8-PSK symbol stream\n",
        "def symb(bits):\n",
        "\tsymbol =[]\n",
        "\ti = 0\n",
        "\twhile(1):\n",
        "\t\ttry:\n",
        "\t\t\tsymbol.append(mapping(bits[i],bits[i+1],bits[i+2]))\n",
        "\t\t\ti = i+3\n",
        "\t\texcept IndexError:\n",
        "\t\t\treturn symbol\n",
        "\n",
        "#Converts bitstream to 8-PSK complex symbol stream\n",
        "def CompSymb(bits):\n",
        "\tsymbols_lst = symb(bits)\n",
        "\tsymbols = np.array(symbols_lst).T #Symbol vectors\n",
        "\tsymbols_comp = symbols[0,:]+1j*symbols[1,:] #Equivalent complex symbols\n",
        "\treturn symbols_comp"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "id": "FPNtUtWBUryp",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 291
        },
        "outputId": "93ea7211-cc10-46a0-d2e4-e21a4a583377"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "\n",
        "#SNR range\n",
        "snrlen=15\n",
        "\n",
        "#SNR in dB and actual per bit \n",
        "#(Check Proakis for factor of 6)\n",
        "snr_db = np.linspace(0,snrlen,snrlen)\n",
        "snr = 6*10**(0.1*snr_db)\n",
        "\n",
        "#Bitstream size\n",
        "bitsimlen = 99999\n",
        "\n",
        "#Symbol stream size\n",
        "simlen = bitsimlen //3\n",
        "\n",
        "#Generating bitstream\n",
        "bits = bitstream(bitsimlen)\n",
        "\n",
        "#Converting bits to Gray coded 8-PSK symbols\n",
        "#Intermediate steps  required for converting list to\n",
        "#numpy matrix\n",
        "symbols_lst = symb(bits)\n",
        "symbols = np.array(symbols_lst).T #Symbol vectors\n",
        "symbols_comp = symbols[0,:]+1j*symbols[1,:] #Equivalent complex symbols\n",
        "\n",
        "ser =[]\n",
        "ser_anal=[]\n",
        "ber = []\n",
        "\n",
        "#SNRloop\n",
        "for k in range(0,snrlen):\n",
        "\treceived = []\n",
        "\tt=0\n",
        "\t#Complex noise\n",
        "\tnoise_comp = np.random.normal(0,1,simlen)+1j*np.random.normal(0,1,simlen)\n",
        "\t#Generating complex received symbols\n",
        "  #fade_comp = np.random.normal(0,1,simlen)+1j*np.random.normal(0,1,simlen)\n",
        "  #fade_comp = np.abs(fade_comp)\n",
        "  #fade_comp = np.math.sqrt(1/2)*fade_comp\n",
        "\ty_comp = np.sqrt(snr[k])*symbols_comp +noise_comp\n",
        "\tbrx = []\n",
        "\tfor i in range(simlen):\n",
        "\t\tsrx_comp = decode(y_comp[i]) #Received Symbol\n",
        "\t\tbrx.append(detect(srx_comp))  #Received Bits\n",
        "\t\tif symbols_comp[i]==srx_comp:\n",
        "\t\t\tt+=1; #Counting symbol errors\n",
        "\t#Evaluating SER\n",
        "\tser.append(1-(t/33334.0))\n",
        "\tser_anal.append(2*qfunc((np.sqrt(snr[k]))*np.sin(np.pi/8)))\n",
        "\t#Received bitstream\n",
        "\tbrx=np.array(brx).flatten()\n",
        "\t#Evaluating BER\n",
        "\tbit_diff = bits-brx\n",
        "\tber.append(1-len(np.where(bit_diff == 0)[0])/bitsimlen)\n",
        "\n",
        "\n",
        "\n",
        "#Plots\n",
        "plt.semilogy(snr_db,ser_anal,label='SER Analysis')\n",
        "plt.semilogy(snr_db,ser,'o',label='SER Sim')\n",
        "plt.semilogy(snr_db,ber,label='BER Sim')\n",
        "plt.xlabel('SNR$\\\\left(\\\\frac{E_b}{N_0}\\\\right)$')\n",
        "plt.ylabel('$P_e$')\n",
        "plt.legend()\n",
        "plt.grid()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AFZCQNe9f7iD"
      },
      "source": [
        "### BLER Simulations"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {
        "id": "zMl-Rljrf7iR"
      },
      "outputs": [],
      "source": [
        "#IEEE 802.11p Max TX Power 30dBm\n",
        "#Path loss model corresponding: 20log10(d(m))  (We take n=2, FSPL)\n",
        "#0.1W corresponds to 20dBm or -10dB\n",
        "#7dB corresponds to 5W\n",
        "#IEEE 802.11p is an approved amendment to the IEEE 802.11 standard to add wireless access in vehicular environments (WAVE), a vehicular communication system. \n",
        "#IEEE 802.11p standard typically uses channels of 10 MHz bandwidth in the 5.9 GHz band (5.850–5.925 GHz).\n",
        "# Noise Power -100dBm, TX Power is 20dBm and that \\\n",
        "#256m- -94dBm, 128m- -88dBm, 1m\n",
        "#2.8 Path loss exponent, -63dB at 5m, 20dBm TX Power, -95dBm NOise figure, net 52dB SNR at 5m distance"
      ]
    }
  ],
  "metadata": {
    "accelerator": "GPU",
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}