├── AutoEncoderFiber.ipynb ├── LICENSE └── README.md /AutoEncoderFiber.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "nbformat": 4, 3 | "nbformat_minor": 0, 4 | "metadata": { 5 | "colab": { 6 | "name": "AutoEncoderFibercopy.ipynb", 7 | "version": "0.3.2", 8 | "provenance": [], 9 | "collapsed_sections": [], 10 | "include_colab_link": true 11 | }, 12 | "kernelspec": { 13 | "display_name": "Python 3", 14 | "language": "python", 15 | "name": "python3" 16 | } 17 | }, 18 | "cells": [ 19 | { 20 | "cell_type": "markdown", 21 | "metadata": { 22 | "id": "view-in-github", 23 | "colab_type": "text" 24 | }, 25 | "source": [ 26 | "\"Open" 27 | ] 28 | }, 29 | { 30 | "metadata": { 31 | "id": "GuDJI6Q5meSB", 32 | "colab_type": "text" 33 | }, 34 | "cell_type": "markdown", 35 | "source": [ 36 | "# Auto-encoder for a memoryless fiber-optic channel\n", 37 | "\n", 38 | "This script uses an auto-encoder (AE) for end-to-end learning of a non-linear memoryless fiber channel. The determines a good constellation and a good receiver. The achievable information rate is also computed. \n", 39 | "\n", 40 | "The system is of the form:\n", 41 | "$$\n", 42 | "x_{k+1}=x_k \\exp (j \\gamma L / K |x_k|^2) + n_k, k=0,..,K-1\n", 43 | "$$\n", 44 | "where $x_0$ is the input (a complex symbol), $\\gamma$ is the fiber nonlinearity parameter (typically around 1.2), $L$ is the fiber length, and $K$ is the number of amplification stages. The channel output is $x_K$. Finally, $n_k$ is white Gaussian noise. \n", 45 | "\n", 46 | "\n", 47 | "This code was is based on the paper\n", 48 | "\n", 49 | "Shen Li, Christian Häger, Nil Garcia, and Henk Wymeersch, \"Achievable Information Rates for Nonlinear Fiber Communication via End-to-end Autoencoder Learning,\" in *Proc. European Conference on Optical Communication* (2018) [arXiv:1804.07675](https://arxiv.org/pdf/1804.07675.pdf). \n", 50 | "\n", 51 | "The code was written by Christian Häger. Parts were provided by Shen Li. Integration and polishing by Henk Wymeersch. \n", 52 | "\n", 53 | "Remaining issues:\n", 54 | "* returns NaN for too high input power\n", 55 | "\n", 56 | "\n" 57 | ] 58 | }, 59 | { 60 | "metadata": { 61 | "id": "DTSyKzaDmeSN", 62 | "colab_type": "code", 63 | "colab": {} 64 | }, 65 | "cell_type": "code", 66 | "source": [ 67 | "import tensorflow as tf\n", 68 | "import numpy as np\n", 69 | "import matplotlib.pyplot as plt\n", 70 | "import scipy.io as sio\n", 71 | "import math\n", 72 | "import time\n", 73 | "import sys\n", 74 | "import matplotlib.cm as cm" 75 | ], 76 | "execution_count": 0, 77 | "outputs": [] 78 | }, 79 | { 80 | "metadata": { 81 | "id": "IzWYJH3lmeSp", 82 | "colab_type": "code", 83 | "colab": {} 84 | }, 85 | "cell_type": "code", 86 | "source": [ 87 | "def tf_print(tmp_var):\n", 88 | " init = tf.global_variables_initializer()\n", 89 | " sess = tf.Session()\n", 90 | " sess.run(init)\n", 91 | " print(sess.run(tmp_var))\n" 92 | ], 93 | "execution_count": 0, 94 | "outputs": [] 95 | }, 96 | { 97 | "metadata": { 98 | "id": "sQzoQ8lumeS3", 99 | "colab_type": "code", 100 | "colab": {} 101 | }, 102 | "cell_type": "code", 103 | "source": [ 104 | "## START: these are the main parameters to set\n", 105 | "P_in_dBm=-2 # input power in dBm\n", 106 | "gamma = 1.27 # fiber nonlinearity (set to 0 zero for AWGN or 1.27 for a nonlinear channel)\n", 107 | "M = 16 # constellation size\n", 108 | "\n", 109 | "# main network parameters and optimization parameters (to be modified for performance improvements)\n", 110 | "neurons_per_layer = 50 \n", 111 | "tx_layers = 2\n", 112 | "rx_layers = 3\n", 113 | "learning_rate = 0.001\n", 114 | "iterations = 50000\n", 115 | "stacks = 20\n", 116 | "minibatch_size = stacks*M\n", 117 | "## END: these are the main parameters to set\n", 118 | "\n", 119 | "\n", 120 | "# derived channel parameters\n", 121 | "channel_uses = 2 # this should be 2: the fiber code will break otherwise\n", 122 | "assert(channel_uses==2), \"channel uses should be 2\"\n", 123 | "L=2000 # fiber total length\n", 124 | "K=20 # number of amplification stages (more layers requires more time)\n", 125 | "sigma = 3.8505e-4*np.sqrt(2) # N0= h*v*nsp*(G-1) sigma**2 = BW*N0 \n", 126 | "sigma2tot=K*sigma**2\n", 127 | "P_in=10**(P_in_dBm/10)*0.001\n", 128 | "Ess=np.sqrt(P_in)\n", 129 | "SNR=Ess**2/(sigma2tot)\n", 130 | "SNR_dB=10*np.log(SNR)" 131 | ], 132 | "execution_count": 0, 133 | "outputs": [] 134 | }, 135 | { 136 | "metadata": { 137 | "id": "8RbjEuy4LNYG", 138 | "colab_type": "code", 139 | "colab": {} 140 | }, 141 | "cell_type": "code", 142 | "source": [ 143 | "#=====================================================#\n", 144 | "# Define the components of the computation graph\n", 145 | "#=====================================================#\n", 146 | "initializer = tf.contrib.layers.xavier_initializer()\n", 147 | "# transmitter\n", 148 | "W_tx = {}\n", 149 | "b_tx = {}\n", 150 | "for NN in range(tx_layers):\n", 151 | " if NN == 0:\n", 152 | " in_neurons = M\n", 153 | " else:\n", 154 | " in_neurons = neurons_per_layer\n", 155 | " if NN == tx_layers - 1:\n", 156 | " out_neurons = channel_uses\n", 157 | " else:\n", 158 | " out_neurons = neurons_per_layer\n", 159 | " W_tx[NN] = tf.Variable(initializer([in_neurons, out_neurons]))\n", 160 | " b_tx[NN] = tf.Variable(initializer([1, out_neurons]))\n", 161 | " \n", 162 | "# receiver\n", 163 | "W_rx = {}\n", 164 | "b_rx = {}\n", 165 | "for NN in range(rx_layers):\n", 166 | " if NN == 0:\n", 167 | " in_neurons = channel_uses+1\n", 168 | " else:\n", 169 | " in_neurons = neurons_per_layer\n", 170 | " if NN == rx_layers - 1:\n", 171 | " out_neurons = M\n", 172 | " else:\n", 173 | " out_neurons = neurons_per_layer\n", 174 | " W_rx[NN] = tf.Variable(initializer([in_neurons, out_neurons]))\n", 175 | " b_rx[NN] = tf.Variable(initializer([1, out_neurons])) \n", 176 | "\n", 177 | "# the encoder\n", 178 | "def encoder(x):\n", 179 | " for NN in range(tx_layers-1):\n", 180 | " x = tf.nn.tanh(tf.matmul(x, W_tx[NN]) + b_tx[NN])\n", 181 | " x = tf.matmul(x, W_tx[tx_layers-1]) + b_tx[tx_layers-1]\n", 182 | " return x\n", 183 | "\n", 184 | "# the decoder\n", 185 | "def decoder(x):\n", 186 | " for NN in range(rx_layers-1):\n", 187 | " x = tf.nn.tanh(tf.matmul(x, W_rx[NN]) + b_rx[NN])\n", 188 | " x = tf.nn.softmax(tf.matmul(x, W_rx[rx_layers-1]) + b_rx[rx_layers-1])\n", 189 | " return x\n", 190 | "\n", 191 | "# the non-dispersive fiber channel \n", 192 | "def fiber_channel(x):\n", 193 | " xr=x[:,0]\n", 194 | " xi=x[:,1]\n", 195 | " for segments in range(1,K+1): \n", 196 | " s=gamma*(xr**2+xi**2)*L/K \n", 197 | " xr=xr*tf.cos(s)-xi*tf.sin(s)\n", 198 | " xi=xi*tf.cos(s)+xr*tf.sin(s)\n", 199 | " xr=tf.add(xr,tf.random_normal(tf.shape(xr), mean=0.0, stddev=sigma))\n", 200 | " xi=tf.add(xi,tf.random_normal(tf.shape(xi), mean=0.0, stddev=sigma)) \n", 201 | " z=tf.stack([xr,xi,xr**2+xi**2]) \n", 202 | " z=tf.transpose(z) \n", 203 | " return z\n", 204 | "\n", 205 | "# average transmit power constraint\n", 206 | "def normalization(x): # E[|x|^2] = Es\n", 207 | " return Ess*x / tf.sqrt(2*tf.reduce_mean(tf.square(x)))" 208 | ], 209 | "execution_count": 0, 210 | "outputs": [] 211 | }, 212 | { 213 | "metadata": { 214 | "id": "_rlBVxfWmeTH", 215 | "colab_type": "code", 216 | "colab": {} 217 | }, 218 | "cell_type": "code", 219 | "source": [ 220 | "#=====================================================#\n", 221 | "# build the computation graph\n", 222 | "#=====================================================#\n", 223 | "X_tilde = tf.placeholder('float', [minibatch_size, M]) # one-hot vectors\n", 224 | "\n", 225 | "#grid coordinates for visulazing decision regions\n", 226 | "resolution=1000\n", 227 | "G = tf.placeholder('float', [resolution**2, channel_uses+1])\n", 228 | "\n", 229 | "X1=encoder(X_tilde)\n", 230 | "X = normalization(X1) # minibatch_size x channel_uses\n", 231 | "Y = fiber_channel(X)\n", 232 | "Z = decoder(Y)\n", 233 | "D = decoder(G)\n", 234 | "epsilon = 0.000001\n", 235 | "loss = -tf.reduce_mean(X_tilde*tf.log(Z+epsilon))\n", 236 | "MI=(np.log(M)-loss*M)/np.log(2)\n", 237 | "optimizer = tf.train.AdamOptimizer(learning_rate)\n", 238 | "train = optimizer.minimize(loss)" 239 | ], 240 | "execution_count": 0, 241 | "outputs": [] 242 | }, 243 | { 244 | "metadata": { 245 | "id": "cYP38e2pmeTa", 246 | "colab_type": "code", 247 | "outputId": "fd6864b6-6478-4bba-8b1a-99fb70d925e8", 248 | "colab": { 249 | "base_uri": "https://localhost:8080/", 250 | "height": 920 251 | } 252 | }, 253 | "cell_type": "code", 254 | "source": [ 255 | "#=====================================================#\n", 256 | "# parameter training\n", 257 | "#=====================================================#\n", 258 | "start_time = time.time()\n", 259 | "unitmatrix = np.eye(M) \n", 260 | "training_set = np.tile(unitmatrix, [stacks, 1])\n", 261 | "init_op = tf.global_variables_initializer()\n", 262 | "sess = tf.Session()\n", 263 | "sess.run(init_op)\n", 264 | "MI_tmp=0\n", 265 | "totalloss=[]\n", 266 | "for i in range(1, iterations+1):\n", 267 | " _, loss_tmp, MI_tmp = sess.run([train, loss, MI], feed_dict={X_tilde: training_set})\n", 268 | " totalloss=np.append(totalloss, loss_tmp)\n", 269 | " if i%1000==0 or i==1:\n", 270 | " print('iteration ', i, ': loss = ', loss_tmp, '; Mutual information [bits] = ', MI_tmp) \n", 271 | "elapsed = time.time() - start_time\n", 272 | "print(\"{0:.2f} seconds\".format(elapsed))" 273 | ], 274 | "execution_count": 6, 275 | "outputs": [ 276 | { 277 | "output_type": "stream", 278 | "text": [ 279 | "iteration 1 : loss = 0.17885368 ; Mutual information [bits] = -0.12850097\n", 280 | "iteration 1000 : loss = 0.028006202 ; Mutual information [bits] = 3.3535295\n", 281 | "iteration 2000 : loss = 0.011281811 ; Mutual information [bits] = 3.7395804\n", 282 | "iteration 3000 : loss = 0.0055578933 ; Mutual information [bits] = 3.8717065\n", 283 | "iteration 4000 : loss = 0.005900917 ; Mutual information [bits] = 3.8637884\n", 284 | "iteration 5000 : loss = 0.004730115 ; Mutual information [bits] = 3.890814\n", 285 | "iteration 6000 : loss = 0.005254518 ; Mutual information [bits] = 3.878709\n", 286 | "iteration 7000 : loss = 0.0032975976 ; Mutual information [bits] = 3.923881\n", 287 | "iteration 8000 : loss = 0.0026089507 ; Mutual information [bits] = 3.9397771\n", 288 | "iteration 9000 : loss = 0.001929207 ; Mutual information [bits] = 3.9554677\n", 289 | "iteration 10000 : loss = 0.0034735291 ; Mutual information [bits] = 3.9198198\n", 290 | "iteration 11000 : loss = 0.0020205784 ; Mutual information [bits] = 3.9533587\n", 291 | "iteration 12000 : loss = 0.0019302426 ; Mutual information [bits] = 3.955444\n", 292 | "iteration 13000 : loss = 0.0027602636 ; Mutual information [bits] = 3.9362845\n", 293 | "iteration 14000 : loss = 0.001349867 ; Mutual information [bits] = 3.9688408\n", 294 | "iteration 15000 : loss = 0.0029932146 ; Mutual information [bits] = 3.9309072\n", 295 | "iteration 16000 : loss = 0.0007508879 ; Mutual information [bits] = 3.9826672\n", 296 | "iteration 17000 : loss = 0.0019698858 ; Mutual information [bits] = 3.9545288\n", 297 | "iteration 18000 : loss = 0.0018588252 ; Mutual information [bits] = 3.9570923\n", 298 | "iteration 19000 : loss = 0.0028716298 ; Mutual information [bits] = 3.9337137\n", 299 | "iteration 20000 : loss = 0.002332374 ; Mutual information [bits] = 3.9461615\n", 300 | "iteration 21000 : loss = 0.00052453595 ; Mutual information [bits] = 3.9878922\n", 301 | "iteration 22000 : loss = 0.0005966529 ; Mutual information [bits] = 3.9862273\n", 302 | "iteration 23000 : loss = 0.00065423944 ; Mutual information [bits] = 3.984898\n", 303 | "iteration 24000 : loss = 0.0022190292 ; Mutual information [bits] = 3.9487777\n", 304 | "iteration 25000 : loss = 0.0005131921 ; Mutual information [bits] = 3.9881537\n", 305 | "iteration 26000 : loss = 0.001012143 ; Mutual information [bits] = 3.9766364\n", 306 | "iteration 27000 : loss = 0.0011796795 ; Mutual information [bits] = 3.9727693\n", 307 | "iteration 28000 : loss = 0.0016018931 ; Mutual information [bits] = 3.9630234\n", 308 | "iteration 29000 : loss = 0.0016618859 ; Mutual information [bits] = 3.9616385\n", 309 | "iteration 30000 : loss = 0.00021583195 ; Mutual information [bits] = 3.995018\n", 310 | "iteration 31000 : loss = 0.0019067747 ; Mutual information [bits] = 3.9559858\n", 311 | "iteration 32000 : loss = 0.0012141239 ; Mutual information [bits] = 3.9719744\n", 312 | "iteration 33000 : loss = 0.0009799392 ; Mutual information [bits] = 3.9773798\n", 313 | "iteration 34000 : loss = 0.0015597316 ; Mutual information [bits] = 3.9639964\n", 314 | "iteration 35000 : loss = 0.0021589745 ; Mutual information [bits] = 3.9501643\n", 315 | "iteration 36000 : loss = 0.0018438756 ; Mutual information [bits] = 3.9574378\n", 316 | "iteration 37000 : loss = 0.0011696611 ; Mutual information [bits] = 3.9730003\n", 317 | "iteration 38000 : loss = 0.0013336143 ; Mutual information [bits] = 3.969216\n", 318 | "iteration 39000 : loss = 0.00085040426 ; Mutual information [bits] = 3.9803698\n", 319 | "iteration 40000 : loss = 0.0018855694 ; Mutual information [bits] = 3.9564753\n", 320 | "iteration 41000 : loss = 0.0006585914 ; Mutual information [bits] = 3.9847977\n", 321 | "iteration 42000 : loss = 0.0019125761 ; Mutual information [bits] = 3.9558516\n", 322 | "iteration 43000 : loss = 0.0027832282 ; Mutual information [bits] = 3.9357545\n", 323 | "iteration 44000 : loss = 0.000286943 ; Mutual information [bits] = 3.9933765\n", 324 | "iteration 45000 : loss = 0.0020027482 ; Mutual information [bits] = 3.9537704\n", 325 | "iteration 46000 : loss = 0.001009146 ; Mutual information [bits] = 3.9767056\n", 326 | "iteration 47000 : loss = 0.0018047865 ; Mutual information [bits] = 3.95834\n", 327 | "iteration 48000 : loss = 0.0005892061 ; Mutual information [bits] = 3.9863992\n", 328 | "iteration 49000 : loss = 0.002877311 ; Mutual information [bits] = 3.9335828\n", 329 | "iteration 50000 : loss = 0.0008200977 ; Mutual information [bits] = 3.9810696\n", 330 | "132.48 seconds\n" 331 | ], 332 | "name": "stdout" 333 | } 334 | ] 335 | }, 336 | { 337 | "metadata": { 338 | "id": "jasr9ooGmeTw", 339 | "colab_type": "code", 340 | "outputId": "6da1268b-b77f-4168-eef8-338c2a80d7cf", 341 | "colab": { 342 | "base_uri": "https://localhost:8080/", 343 | "height": 660 344 | } 345 | }, 346 | "cell_type": "code", 347 | "source": [ 348 | "#=====================================================#\n", 349 | "# Visualization\n", 350 | "#=====================================================#\n", 351 | "#x,y grids\n", 352 | "x = np.arange(-0.1, 0.1, 0.0002)\n", 353 | "xx, yy = np.meshgrid(x, x)\n", 354 | "xg = xx.reshape(1000000,1)\n", 355 | "yg = yy.reshape(1000000,1)\n", 356 | "r = xg**2+yg**2\n", 357 | "xygrids = np.concatenate((xg, yg, r), axis=1)\n", 358 | "\n", 359 | "\n", 360 | "[constellation,receive_points,decision_regions] = sess.run([X,Y,D],feed_dict={X_tilde:training_set, G: xygrids})\n", 361 | "x = constellation[:, 0]\n", 362 | "y = constellation[:, 1]\n", 363 | "\n", 364 | "receive_x = receive_points[:, 0]\n", 365 | "receive_y = receive_points[:, 1]\n", 366 | "\n", 367 | "# plotting\n", 368 | "fig=plt.figure(figsize=(7, 7))\n", 369 | "ax = fig.add_subplot(2, 1, 1)\n", 370 | "plt.plot(totalloss)\n", 371 | "plt.xlabel('iteration')\n", 372 | "plt.ylabel('loss')\n", 373 | "\n", 374 | "fig = plt.figure(figsize=(7, 7))\n", 375 | "ax1 = fig.add_subplot(111)\n", 376 | "plt.xlabel('X')\n", 377 | "plt.ylabel('Y')\n", 378 | "ax1.scatter(x, y, c='b', marker='o')\n", 379 | "plt.axis('equal')\n", 380 | "xmax = max(abs(x))\n", 381 | "ymax = max(abs(y))\n", 382 | "max_axis = 1.2 * max(xmax, ymax)\n", 383 | "plt.xlim(-max_axis, max_axis)\n", 384 | "plt.ylim(-max_axis, max_axis)\n", 385 | "plt.show()\n" 386 | ], 387 | "execution_count": 7, 388 | "outputs": [ 389 | { 390 | "output_type": "display_data", 391 | "data": { 392 | "image/png": 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405 | "text/plain": [ 406 | "" 407 | ] 408 | }, 409 | "metadata": { 410 | "tags": [] 411 | } 412 | } 413 | ] 414 | }, 415 | { 416 | "metadata": { 417 | "id": "ATtx6VedmeUY", 418 | "colab_type": "code", 419 | "outputId": "72aa76c9-3f60-4307-cc85-8e1ac55cbedb", 420 | "colab": { 421 | "base_uri": "https://localhost:8080/", 422 | "height": 428 423 | } 424 | }, 425 | "cell_type": "code", 426 | "source": [ 427 | "#=====================================================#\n", 428 | "# Decision regions\n", 429 | "#=====================================================#\n", 430 | "import matplotlib.cm as cm\n", 431 | "fig=plt.figure(figsize=(7, 7))\n", 432 | "plt.xlim(-max_axis, max_axis)\n", 433 | "plt.ylim(-max_axis, max_axis)\n", 434 | "z = np.argmax(decision_regions, axis=1).reshape(1000, 1000)\n", 435 | "plt.pcolormesh(xx, yy, z)\n", 436 | "cmap = cm.rainbow(np.linspace(0.0, 1.0, M))\n", 437 | "\n", 438 | "for k in range(minibatch_size):\n", 439 | " index = k % M\n", 440 | " plt.scatter(receive_x[k], receive_y[k], c=cmap[index], marker='.',s=50)\n", 441 | "\n", 442 | "plt.show()" 443 | ], 444 | "execution_count": 8, 445 | "outputs": [ 446 | { 447 | "output_type": "display_data", 448 | "data": { 449 | "image/png": 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f/uVfMGvWrIzfh1P67cWoCflSwypbeoacuFLL7wqm7XCMLlPmdwVw7JuDJL1HDWrNjVR8\naxqNWvzN8ge4WZjp96GoUtuxYwcOHTqENWvW4MCBA1i0aBHWrFkTe/6BBx7AypUrMXToUDQ0NODK\nK6+E3+/H559/jjVr1uDUqVO45pprJIUa2YeeB7P1CrFEN954o27BlmzfLBlx+Dn7QggXRDpStdhX\n00JWB7E5/V9zZgo0QGGoNTU1YcaMGQCAUaNG4fTp0+js7ERpaSmam5tRXl6O6upqAMC0adPQ1NSE\nf/zHf4xVc2VlZejp6UEoFILLZf+Wb4rQ+mC2UUGWSM+lycR9s2TEy5ThAhec/SGE3S7N9tXE1FiK\nVHwQmzRntkADFLb0+/1+DBo0KPa4srISPp8PAODz+VBZWTngOZfLheLiYgDA+vXrcdlllzHQcoxW\n7f7nnHOOaQJN7MYbb4wFnJES2/uHv9+K6r+0ab70GJV1u/9Xe2Whd9sGLj1q2LJP1qRKo4icbbk/\n/elPWL9+PZ5//nk1vjVpRIu9LzXb/c0YYqnouSSZTPJlSotVO8mWEdWYIMKxWoqZsUoDFFZqXq8X\nfr8/9rilpQVVVVVJnztx4gS8Xi8A4N1338Wzzz6L5557Dh6PJ5vrJg1F976e/qQYd35Qin1t6p3R\nr6kI44bRfYoDzaxVWSZGVmzdlfnwn1eCQLFxsxa0OJwteYJIqmqO93lTzKyBBigMtbq6Orz11lsA\ngL1798Lr9aK0tBQAMHz4cHR2duLIkSMIBoNobGxEXV0dOjo68Oijj+J3v/sdKioq1PsJSHVq3QRU\nTVYNMzEjgq27Mh/7r6jCyW+UwV9Thv3f8ao6SUQOtYNNONQTO4+Wcq8tTXBxrJYyZg40QOHy46RJ\nkzBu3DjMmzcPDocDixcvxoYNG+DxeDBz5kzcf//9WLBgAQBg9uzZGDlyZKzr8Y477oh9ziOPPIKz\nzjpLnZ+EVKPWTUCzYfUAS0UcbHosSbZXFyFUfOY/81CRK2XHo9pT/ZNRdQiyhKHH6Ton2YAin9kD\nDcjinJpeeE7NGEadJwPsG2jJaB1s0UotGmyunhBG/0/LgNCSc+ZNDbpNHcl0xk3hnpoV/nBXm1V+\nZoYamUYuhZmYHsEWnSIy+EBX0rA6Pq4Mx755Zlug+i9tGLa3XdH3klrt6RlsajeDWOUPeLVY6efl\nmCwyXK6GWZTW59qKWwM4p7Ut7WvUmAsp9x5uus2J5AHsnMJQI139+Mc/jnu8detWYy6E4kidTpKO\n3FmURFpgqJGmEkNMDxMBzATwNoC/6v7dlTPDebZsQkiPuwCQ/qy09AhwT41UoiS8tKjSJgLYCGA4\ngCMArkb6YDNrAJrh1jaA/I5IpR2URt6HTQmr/UGvlBV/TlZqlBWllZhWy44zEQk0fPXPmUgdVuIA\n/AUyB6CetKrauivzcXJUCQQBGPJF8qYR8Wvl7JEB2Vd7ZB5WDDRA4eFroh//+MeGLC1m8jYiFRq+\n+ufbaV6bLADNRO3D2t2V+dj/HS/8NWU4+Y0y7L+iKu1B7GR7ZFrRYuII5SZWaiSLGYNM7K+IVFxS\nlhTfRqRCiy5VpgtAO2ivLkKo6MwQ8VBx+mYOvffIjLxrNsWzapUGcE+NJFIzzMzU8ZhsT81s+2xq\nLUNGK7VosLm6gxi9Jf2Soh5TRsSsEmpW/kM/E6v/bAw1SkuLyixTqBkZKnIbTfSiVrCd/FoR/GM8\nyOsMonpfR9ZBpUXoWSHYrP4HfzpW/9kYahRH6+VFKYGWTajIDcTE198N4BHR878B8KiM76+lbIMt\n8Q7Yw7e3YvBB5UuKWo7WMnOwWf0P/XTs8LOxUYQA6NP4IWXZMZvmjWggPvLVPycqeL2cRpN0n3u3\nhO+vt8Q7YB+5uDKrif1aNpKwcUR/dgg0gKGW88zWxZhNqMgNxFTt/1cjUqEpWXqUG6xyZNsNWXas\nB86+UOxx2O3KKogS76jNw9ZkBgy1HKZnmEltDskmVOQGYqrX/xWRJUcle2laHxPIJtiKWwMYvr0V\nzv5IsGUbRNHRWtV/adNkqv/27dtV/TzKDWzpz0FmqsyS+SuUBYqcdn4lr49Kt28nPiZwGoDZdoQH\nH+xBUXuLKs0d4oPcWhEH25QpU7T7Rio5lJeHvW43xvX349xg0OjLkcwuS48AG0VyilFhZqYW/kwy\nNZrMB/A0gAqkbmSR8ppsGT1GS8nxALnefPPNpF83OtxSBcChvDwsq6hAm8uFilAIv2hrs0yw2SnU\nWKnZnNFVmdUCLd3YrIkAngFQ/tXjVGO4RiASaOleky21x2jJbc2Xe5BbTdHqzehwS7TX7UabK/I7\naXO5sNfttkSo2SnQAO6p2ZrRgWY1mfbDZuJMoAFAG5Lv26nRQamnaGv+sW9W4IvL04/Oiio71gNX\nz5mmE1e3/o0i27dvN9W+27j+flSEIr+TilAI4/r7Db6izOwWaACXH23JLGFmpSoNyHxGTvz8aQC3\nAnglzWfpcYBcjWpN6V2v5QxHlivV0mM6elVu6YLAantqdgw1Lj/aiFnCTC9qB0emxhE5jSVKm12M\noHTGY2Qif/o7autp+/bthi9JnhsMWiLMAHsGGsBKzRbMGmZaVmpmHWdlBDWqNb1nPGaipFIT0yrc\n7BQEdvpZxLinZnFmDTStqXkeLJsJIGadHiJXcWsAw/a2Jw207sp8HB9XltX0Eb2Zaa/NjOwaaAAr\nNcuxSohpvZ+mVtt8NhWfmapFrVr8tZzvmEq2VVoiNas2O4SBHX6GdLinZgFWCTK9TERk4kcFIg0b\nd0N5mMi5U7aa77WKZPMdzbA8KYcZ9tpIP1x+NDGzzWWUSusqTRwm5YicC1Mqm/Z7q7XuK6H3fEe1\nq7QoLkdG2L1KA1ipmY7WITa6wonJw/Kw83gQ+9vCmn4vtSR2Oap5x2qlo7IS39uMM/t6yT7DbDce\nlSo639FMTSRKZXtoOxcCwQ4YaiagVzU2usKJJZcWo6rYhWtHh7DovW7Vg03tKi3VlA+lQZRMtP0+\n2vQh5zOjr8s0iSTd82YXad23bpglytXlyFwJZYaaAYxaUpw8LA9VxZExPlXFLkwelof9beaeepBq\n30rtc2DZBE+mvbVc2HtTg1ZLj2ZhtYPZVsU9NZ1E98eM3CPbeTwIX3dkjI+vO4Sdx+P/wxpd4cS8\nsW6MrjDPvxZ67Vtlc0Qg0zXq8TPU1tZq8Kn2pdce26G8PLxZXIz3CwqwrKICGzweLKuowKE81hNa\nYUu/SqzS0JFqT028NOnrVrY0qVWDiB77Udm252e6Ri1+hr1796Z9/oMPPlDpO8kn9zC30VVapuVI\nJUt34qn9haEQel1nBkBf29GB2d3dsj8zG1x+pLSsEmKJ9reF45YcoyE3pNBp2qVJPUZO/RWR/bQf\nAXhRwffLdI1q/gyZwiyqtrbWkGATn23zd5VmPNtmdKAB2uyziaf297pcKAyH0et0GjLsOFcCDWCo\nSWb2EFPS1Siuzlp7QmjtCaOyyJl0aTITqw0vThQ9+zYcwHgAn8Cc+15SAy0quiypZ7hZ9WxbqmBT\nGgjj+vuxJRSK3V9tTkcHWl0u7qlpjKGWhNkDLJHSrkZx40hlkQvrP+vFyV7BUu3+arFCM4fcQBPT\ns2qTMyDZDFWamJoV27nBIH7R1mZ4c0guVWkAQw2A9UIskdKuxp3Hg7h2dAhVxS509ofxsT+IxiOh\njO+zIzXPvqktmzAT0yvYtD7bds5gJy4Y4cae5n4cPqn+X77EwZZtIFhpar9dKA61JUuWYPfu3XA4\nHFi0aBEuvPDC2HPbtm3D448/DpfLhcsuuwy33347AOCzzz7DbbfdhhtvvBENDQ3ZX70CVg+wZMTh\nJGXpULxU+czfevDryUUodbtw64QiNHeap0FET2qffVOLWoEWpddypFZn284Z7MQdV3lQWerCjAsK\n8MQfOzQJNrIuRaG2Y8cOHDp0CGvWrMGBAwewaNEirFmzJvb8Aw88gJUrV2Lo0KFoaGjAlVdeibPO\nOgv/9m//pmopbMeAUmJ/WxiL3uuWtKeWuFT5zpEASt3mbBDRmxnugaZ2iKUiPgJgRDOJ0mXHC0a4\nUVn61ZJ5qQsXjHDj8MleNS8NQKRau+OOO1T/3Ci9zqzl2tIjoDDUmpqaMGPGDADAqFGjcPr0aXR2\ndqK0tBTNzc0oLy9HdXU1AGDatGloamrC/Pnz8dxzz+G5556T9b0YXNIkdjWKiSuzxKVKByJn16RW\neaQdvQItkVFdkkrsae7HjAsKUFnqQmtnCHuarfcXMHGr/5ZQCL9oa+MSpYoUnbL1+/0YNGhQ7HFl\nZSV8Ph8AwOfzobKycsBzeXl5KCwszPJySa5oZfYvFxZhyaXFONEZijuAvelgPxa9143ffdhjqrNp\nucaoQIvS8/B2Ns0hh0+G8cQfO7D2/W7Nlx6feOIJTT5X3Orf5nJhr9utyffJxSoNUKlRxOTnt3Na\nYmU2tNSVdKkyV5ccjWZ0mInpsd+mRrfj4ZNhTZYc9ZLY6q/3mTW7UxRqXq8Xfr8/9rilpQVVVVVJ\nnztx4gS8Xm+Wl0lKJWsiSbdUaQdDhgyJeyz+99EszBRmibRajjRb+74eku2dmaXV364UhVpdXR2W\nLVuGefPmYe/evfB6vSgtLQUADB8+HJ2dnThy5AiGDRuGxsZGLF26VNWLJunkNJFYRWJoqfV6PcJP\nTpjt63fh/f58XOwOoMat71ELtau2XA20VHtnWrf65+rSI6Aw1CZNmoRx48Zh3rx5cDgcWLx4MTZs\n2ACPx4OZM2fi/vvvx4IFCwAAs2fPxsiRI7Fnzx488sgj+PLLL5GXl4e33noLy5YtQ0VFhao/EMW7\nfLgLV36tAG8d7DP9bWai5IaWnt9XSfApqcr29bvwq9Nl8IVdWNMTwn+Ut+sebIA64ZaLgQYk3zvT\noyrL5UADLDDQ+PLLLzf6EkxJylisy4e7cO/FJXA5HQiFBTz4fpeqh6vVDDWjgiwbmQIumyXG33cW\n4qmu0tjjn5d04qZSY/eRlASb1QMtm7Z+caVWoWOXY66HGieKWJDUsVhXfq0ALqcDAOByOnDl1wrQ\neETfyeDpWDHIxMTXLw44NfbLLnYHsKYnBF/YhSpnCBe7jZ+dqGXrv9ZTQozAvTNjmOfGWSRZsrFY\nybx1sA+hcKQQD4UFvHWwT7drzMTqgZZoyJAhGDJkiGoNIDXuyJLjz0s68R/l7QAi1du+fleGdw60\nr9+l+L2JamtrJbf/S63SolNCrr+4GHdc5cE5g633x1L0vmmJ90k7NxjE7O5u3QIt16s0gJWaJaUb\niyVelmw8EgLe74rtqRk919FuQaa1GncINe5QVvtrWu3Npava5C45Sp0SYtZqTovD1LxLtnIMNQtK\n1dGYbFmy8UjI8CVHhll23u/Phy8c+UPfF450REoNpmzem0myJhIle2hSpoSYeeaj2g0hnDiSHYaa\nRSU7a6Z0Wr8WGGTqyWZ/TY+9udraWvz2t79V/P7olJB0VZheMx+VUPswtVFdk3bBUDMhJTf8BORP\n69cKA01d0f01JWfWsnmvnjJNCTHzzEe1G0I4cSQ7DDWTUXrDT8D4g9Zahtn4fAemFzmwtUfARwFT\nn0LRRHR/Te/3moWUas5Iah6mZtdkdhhqJpPtEqIRI7C0rszG5zvw0rA8nJXnxE+CYTQcD+ZksCll\n5GQSNVlx5qPShg8lIcnOxwjr9c7a3M7jwbgp+ma+FUy0jV1r04scOCsv8q/qWXlOTC9yaP49rUzc\nwh/tfnyqqxS/Ol2mSls/SRNt+Njg8WBZRcWAdn/SBn/LJmP0EqIZbe0R8JNgGGflOXE0GMbWHlZp\nqSS28F9e0KdZ9yOlx4YPYzDUTMgKU/T37Nmj2/f6KCCg4Xgwp/fUpEps4YcgoMpprskkRjDijJue\nDR9cejyDoUay6RloUR8F7BFmWu9viVv4SxDC+Pwgxud34o3eQny3sDcnqzSjzrix4cMYDDWTUdrO\nr/R9pB89Ju/XuEP415JOPNzhQRdceLyzFIIAtMGFA6E8jMwzZtq/kYw846b1LWZoIDaKmEi0nf9f\nLizCkkuLMbpC2v97lL5PCSOqNLtINt1DCyfCLnR99Z/2KcGFNmj/PfV0zmAnZk8olDwjck9zP1o7\nI0FutjNuauDSYzyGmolIGVQ8usKJeWPdccEldcBxthho6b3zzjtpn7/YHUCVM/KHq5b7W+Lv40EI\nQGTZ1gEBnwRclu6AVDL8OHqfV27JAAAgAElEQVTGbe373aYar0XaYKiZSKZ2/lQVmZWOAeSyxMn7\nWi0Dir/PVYW9ACJHIAQ48Kf+Iku39icuJV46piDu+VRV3OGTYbz5t17TBVqq6f6kHH+TJpKpnT/V\nwWytjwGMHTsWgDGVmt0mieg13UM84b+xvzC27AkMbO230uHsPc39mDW+ABUlkZ9nymg33vu0D4dP\nhlVvCMnmBqGJkh3Cfr+gAC+VlaHX6eTgYhUx1EwmVTv/6AonhhQ60doTQmXRwNmOWhwDiIaZUcbn\nO7BmWD6q8hy4NShg7vGALYJNT9GqbWNvATb3FKANLgxyhNAScuDN7nx8FMjD232FOCVo17yipsMn\nw9hxoA+zLiwGAJQXn2n8MOvQ42RT9wHgJY8Hvc5IRan0HBv30wZiqFmAeB5ka08Y6z/rxVsHA5p2\nORoVaOLKbF6pE1V5kaWzqjwH5pU6gc6wrSo3PUSqtm5cXdgXC7e1vSVY3ysgjDPTWcx6ODvxjNl7\nn/Zj8nkDhxubdehxskPYANDrOlM9F4bDHFysEoaaBYiXHSuLnDjZK2gWaEZWZ4kzHrd1x//hWukU\nOAMyjUzLiDXuEN7vD8e6IcWBBmjbvKJUqiXFZMONzTr0ONUh7OjXCkMhNHR0sEpTCUPNAvS6pYzR\ny42JMx5bw2G0BMPw5jnREgyjNTxwBmSyULPbPpwUUs/AiQ9nOxGp1CoQwqyiPlxd2Ge6Ki3VkmKq\n4cZmHHqc6hA2D2Zrg6FmAXrMgzQ60ICBMx5Xd0b+LxpQAPC90vQzIHN1or/UO1yL76821BnCibBL\n8waRbEZUGbWkqGaTCJD8EDYPZmuDoWYRVpgHma1UMx7FoZRqBmS0OhvqgqRqTm2ZzqhpTc4druM7\nMLVdbsy2I9GsS4qZKL3lDGWPoWYiRoy6MkOFJpZqxqN4SXFZexjj8x34RZkzVq1FqzNfUIgtWebS\nRH8j73D929/+NuVzqZYP5VRvZlxSTCdZt6Pawcb9tNQYaiaRzR2v7S5xSfH+k0HcP/jM4//uDMWq\ns6o8B1a0hXA8FMqpPTUg/mza7zsLTXHuLNnyoVEDhvXCW84Yi6FmEtne8VoJM1Vp6Zo7EhtIri91\nxT12IIyjCXtxuRRmYskaRgAYdrg6cfkQAOZMKTbleTK1VIZCKAyF0KvRLWdYpaXHMVkmkcujrqKV\n2P8ZnI+XhuVhfH58q/nWHgFHg5G/yR8NhrG2MxT3eHVnpCHk/54M5ExjSJT4LtfAwIaRjT1uw+98\nHR1RBQB3XOXBhee4EQpH/n+Urvkj0+BiuYON9XAoLw/rPR70ulwoDIcxR0GrPmWHlZpJ6H3HazNV\naYmV2NxSBz46JcRVb4kNIvsD6RtK9GRUk0iyqiyxYQQOh2nufC3eX3M5HfjwcD/Wb+9OuvSYaYnS\nrEuY4qXHXqcTrS5rzti0MvP8FYewvy2M1Z/051SgAZFKrCV45me+tjQP1xTHV28AsKw9HBdg4se5\nKFUbv3ho8tWFfbrcGUCKxFvArN/eDQBJq61kDSbpnr90TPzz2cimnX9cfz8qQpGfUeu7XVNyrNRy\njNkCDYgE1B86w/hZxZlmj8R9M71a860kVRt/4tBko7oiEyXbX0tVbWU6n3ayI4hQWIDLGVmqvnh0\nAd771PiWf63vds39tMwYamQKqzvDcQer13aG8I0CR9qD1rlOaht/9OvRG4QaHWzRppDZEwpTNoxk\nOp822JMXCzQAKCtWp+FEjUPXPFRtLIZaDjHDkOJU1Vayg9fJ9s3MxuhD11JuZSN1hJbeMlVj6c6n\n7Wnux5UXFqD8q47hti5zDDDmoWvjMdRyhJGBJnVsVfTr04scscdmDTMrkTpCS2/JliNnTyiUPDlk\n+/4+lBY60NmL2D3VjKTHoWvKjI0ipKnEzsZoYCWTqbXfjM477zzJr01sv9fLxe6AaZpFEiW2+19/\ncTHuuMqTtk0/2vk468JijD3LrVqg3XHHHVndiTrVLWYS8W7X2lIcakuWLMHcuXMxb948fPjhh3HP\nbdu2DXPmzMHcuXOxfPlySe/JVaMrnJg31o3RFdr9/UKPKi06tirTGbN0e2NyAtBozc3NaG5uBiAt\n2KJLgEacF0vsiFSzSks3IkuK6FmzS8ek73YUy9QZqVS00trg8WBZRYXs0JHS+ZjN92CTiDSK/qqw\nY8cOHDp0CGvWrMGBAwewaNEirFmzJvb8Aw88gJUrV2Lo0KFoaGjAlVdeidbW1rTvyUV6jMbSK9BS\nLTEm2ytLtceWOKXfjM0h0SBLFA22L774IunzRi8BStl7AzLfk01N4rNmbV0hnO4Oobw48zR+LSb3\n33HHHXgzy/FWUjoflY7QYqBJpyjUmpqaMGPGDADAqFGjcPr0aXR2dqK0tBTNzc0oLy9HdXU1AGDa\ntGloampCa2tryvfkKiNGY2khWYUlDivx3pjcADSLVGEmlZwp+kbRu6FEXHFVlLiw+cMetHULGffU\n1J7cH+14THUzTzkydT6q8T0oPUVrXn6/H4MGDYo9rqyshM/nAwD4fD5UVlYOeC7de3KVXUZjqbnE\nKOdQdaolT7XJCbRUS5FaLgGqJVk1qaXEw9jvfdqHN//WKymkontxajaHRCutazs6NGvy0ON75DpV\ndioFQf7fqJW8x26SjcYy4vYzUs2ZMwfr168f8HU5FZZaS4x63AxUaXV23nnnJV2GlLoEaBS51WS2\n+2lmuFda4rk0Pc6Yyf0eXHqUR1Goeb1e+P3+2OOWlhZUVVUlfe7EiRPwer3Iz89P+Z5cJr75p5Vv\nPyO1/V6tJcZMS57Zyna5MVWwmZkR92Sz2r3SyPwULT/W1dXhrbfeAgDs3bsXXq83tjc2fPhwdHZ2\n4siRIwgGg2hsbERdXV3a91BEsj22bJhxJBagztxGOUuecoi7GrMlp93fLGrcIdxU2mvqilItakwP\nIfNR9KfmpEmTMG7cOMybNw8OhwOLFy/Ghg0b4PF4MHPmTNx///1YsGABAGD27NkYOXIkRo4cOeA9\nFG/n8SCuHR1CVbEr6z02swaaWtRuKlEryBJl6ookY1gl0Lj0KJ9DMPnm1uWXX270JehKrT01rUIt\n2Z6a1WkVaInsFGzZ7qcZzQqhxkBThkfaTUa8x0ba0yvQiIxwbBdwYDMwahZQPcnoq9EHx2TZkJZL\nj3PmzNHss/Wk5t6ZVOedd54l99lIf2pUacd2Aa98H/ifeyL/PLZLhQuzAIYamY7W58+Mrs4YbMay\nwtKjGg5sBjqORv53x9HI41zAULMZqzeIXFPswGvV+ZYaaqyElYPNyvtpVgg0tfbSRs0CPGdF/rfn\nrMjjXMBQI9MYn+/A0iF5KHdFgkyLocZGV2liVg42Mr/qScD8/wa+81Dkn7myp8ZGERvRq0pLNVkk\nW9OLHChznfl71umQoOr5MzNiy79+cqlKi6qelDthFsVKjUxDfKC6PRTGXf6AKlNCzBpoYlao2g4e\nPIiDBw/ihhtuMPpSZNM70HjPNOPwN06mocWUfr0C7f3NDmzf7MKUWSFcPEvZdZt1tNbBgwcHfC0a\nbKtWrcr6888Z7JQ9/zF0jhfhb5wH58dfwHW4Je1rjQg0M94BO1fa+xlqNmH1BpEoqTMkpdAz0F54\nMB+C4MC+D5wAArYItmRhluiGG27IKtjE91SbcUEBnvhjR8ZgC53jRf8v5gCVZUDrJLiXrc8YbHId\nystLe1+0dIy6Z1q60Iq293ccBXYss/ceG5cfSRGzn1fTc8lx+2YXBCHS0CIIkYotG0YuRUaXGKUE\nWtQNN9wQ+z+5lNzFOvyN8yKBBgCVZZHHKSip0vS4A7YSx3YB7z2c/LyZ+EzaS/8AvPmL+NflUns/\nQ41sR0mgHfrUgU0vOXHoU/ndllNmheBwRCozh0PAlFnZDwPWM9iUBFkqcsMt8Z5qUu5i7fz4C6C1\nPfKgtT3yWEXJKi05lNwzLVOVlukgtTi0un3AB0/Fvy6X2vs5+9EGjFp6NOMcSKWB9vQ9eWjzO1Ex\nJIzbHgri3DHy/rNQY08tFTWXI+UGl68kD82DCjDiVB+qupTvC6VbotRqT03pXpp4T6xChz0xKcuO\n7z0cCbSo7zwEXLrwzGPx8qKY+HXcUyPKEfs+cKDNH1m0aPM7se8Dh+xQu3iWgItnafMHnxpt/0qq\nMF9JHv54QSW6C1zY0xfCVXtaFQebuHpLDDgl91RzHW5RfR8tKlppKd1Tk0PqPtqoWZG9sI6jySut\n6Jm0v/0e2LMa6PYPfF2utPcz1Mg2lO6j1dQKaNwQjlVqNbXSA+3Qpw7s+8CBmlpBdhBqLdvlxOZB\nBeguiCzDdRe40DyoIKtqLSpdwKkl245HPe6ALUc0tNJVWtHQmnBTblRkqXD50Qa4/Jh9Y4iScDr0\nqQP/31356GxzoLRCwL/+e0DzYMtUramxLxYlrtSKs6zUpFIj5KxwyBrgrWW0wkqNLE+NTsdzx8ir\ntA596sAr/+FCZ1uksaSzzYFtbzpx7hht7xidquVfzTCLquoK4qo9rarsqUllxYPdZC7sfiTFzN7W\nr5VoY8nfP05s3RfiXqO0mzKT6B6bml2LqVR1BTHpSJfqgeYrycOu4SXwleTm36tZpWmHoWZxdjl0\nLdeQIUMwZMgQQ0ZgiRtLokrLw5g6OxJq0dB7bUU+nr4nT5Ng0zLItBZd1txxXhn+eEGl6sF26tQp\nVT9PbQw0bTHUKCt6VmvRIBsyZIhu3zPRoU8dOOVzoLQ80npeWh7G9GuC+NelZ44BJHZT/uE5lybB\nZlXJGlAovXQHrylebtb+NpELVZqRAZZIfJ6ttELA9GsCmDp74F6cuJvS4RDw8Q4Xjn7hUHT+LZkt\nW7Zk/RlKST23lu51I071YU9fKNaAMuJUn9aXHSebEVjZUlKlic+gvbsE+O4zwIX/pMHF2QQrNTIl\noyuyZMQVWGebA4OqkDSkzh0j4LaHgvjGt0Kx8VnR829WJnXZMNProg0o3/qiXbOOylRLkNmOwDKC\neFpIfwfwxm2s2NJhqFHW1FqCVLK8OHHiRFW+txQ1tQIqhkSWHcXn2ZI1hZw7RsAPfxpK+nqrkrps\nKOV1WjWgZJLtCKxsKN1LGzULcHvOPO5vjwQdlySTM/9fU8j2zFaRpRKtwMTn2cRLko0b4kdsJXu9\nlUldNjR6eTGdcf392BIKxUZgqTVsOJNsmkOqJ0WWHN+4LRJonrOAshG5M3VfLh6+tigz7qdJPYyt\ndoj99a9/VfXz5Nj0khOvrciPPb7mZwH8Q4O0+YVKGLmfBqizp6aXQYMGJf263ntqanU7imc3Htic\nfhZkLmOlRrrRqiKbOHGiYcFWUyvg7TVhdJ52orTc+kuMmVR1BQeEVLIAS/Y6s9BzBJaa7fuJsxvT\nzYLMZQw1CzJjlZaKlCCrKXWgblA+/nwqgH2d5gyFtGO0HI74f+aAaJCV9gbx/qhyVYYeW4GcKk/L\n82hSZkHmKoYaYYg3D+d8zY3DB/vhb1H+B9KcOXNiS5BSq7KaUgeevqAYwwqd+KfefNy2p9t0wZZu\n32zfB464UVlvvezEOV8XbLGHlop4JmR+MIRA3pmmkE+8Raj6e4fBV6gN8S1ptuhwS5pMcmXqvlzs\nfrShId48TPpWMYZ4M/+dZYg3D9+7dhCmTivD964dJOk9aT9PZvdi3aB8DCuM/Gs4rNCJukH5Gd6h\nv2S3pomqqRViB7EB4C/vuDSbJGL0flqUuLsxkOeCK3hm3uXnQ4vw7kiPLcdfyemcVKNKY3ejMgw1\ni8m09Cg3pM75mhulnsh/qKUeF875WuYW5xFdbZh1/HOM6GqTfuEp/PlUAMd7I6FwvDeMP58KKPoc\nLVv7U7XyA5EOx8lXiBpDbHQuLSpxTuOIU30o7osEWXFfCOeK7oXW73Zh74hSTcZfGW1cfz8qQpGf\nO13npFqBlu5O15Savf6ts5DRFU5MHpaHnceD2N+mXrdcspBKt6R4+GA/LpwUQqnHhc6OEA4fTN/i\nPKKrDbce+ACDAr2Ynn8Qz4yqRXNJBQBg69atsq93X6eA2/Z0m3pPLVNr/tTZYfzt3TMTRATBYYtz\naUD8UuPu/hBGt/Rg7ImeuOn9AHC8ojBWvQHq3n9NqVOnTqXsgFRCys1D1dpHEx+47jgaecylRmkY\nagYYXeHEkkuLUVXswrWjQ1j0XrekYJPSICI3pPwtQby+4ZTkPbWaDh8GBSJ/Mx8U6EVNhy8Wakrt\n6xSwrzP780JadkGmuzWNOPQqvALaWuxxLg2IX2rsc7uwd3gp/l5VhKv2tGLSka7Y667a04pPhhZh\nv7cIfW7znU9TS7rOSTUbQzLd6ZpSY6gZYPKwPFQVR/6gqCp2YfKwPOxvU+cQqNyQir5HaoPIPk8V\npucfxKBAL07lF2KfpyrbS7a8gZ2R1g+zKPFB6qhkVVhVVxBVX3Rg7Ikew8+nGUHtTkd2NyrHUDPA\nzuNBXDs6hKpiF3zdIew8ru5//IkhpVZ3IwA0l1TgmVG1qOnwYZ+nKusqzerSdUbaQXRO4yfeIhwY\nWoTeDFWYmc+naUWr1n12NyrDUDPA/rYwFr3XrcmeWqJo40ipx4ULJ4Xw+oZTqgRbrodZVLLOSDuF\nGvBVUP29A2NbpFVhZpgmohfeG818GGoG2d8WlrXkqPTAtdzGEavTe7pIhVeINYc4HAIqvOYNtGzD\nJlUVJv5cALHGEjMcxla7WUSMgWZOilr6A4EAFixYgPnz56OhoSHp3Yc3btyI6667DvX19Vi3bl3s\n6zt27MAll1yCxsZG5VdNkh0+2I/OjkgbspTGEbOpKXXgJyPcqCk1Z3t8W4sjdnsZQXCgrcWc16nV\n3aYTP/eToUU5cQNQrQKNZ9OypyjUXn/9dZSVleGVV17BLbfcgsceeyzu+e7ubixfvhwvvPACXnzx\nRaxatQptbW04fPgwfv/732PSJC4Uy5HNWKxo48i2d9pVWXpMRUk7fybRaSMLRhXg6QuKTRls6c6w\nmYmad5sWn1tL/FwIiDvDZscOSC0DLXo27YXpwIcva/JtbE9RqDU1NWHmzJkAgKlTp2LXrvi/Vuze\nvRvjx4+Hx+NBYWEhJk2ahF27dqGqqgpPPfUUPB5Pso+lLKWaJOJvCWLXjm7Dlx3lVl1WmDZy7hgB\n19wSuSHoNbdIaxJJdv81rSUemFYaNuLK7I3xlfCXuFDQf+Zzx7b0aH4DUCNpueTIm4GqQ1Go+f1+\nVFZWRj7A6YTD4UC/6HS9+HkAqKyshM/nQ1FREVwu14DPo+xlmiQiZ3SWFpRUXUqnjeh549BDnzrw\n2rN5+HiHC689m3k0VrRbUqtRWqmodbdpcWXW63bhi6ElcAAY19wZ+1yjbgCqNa330FLdDJTkyfgn\n3Lp16+L2xIBIJSaW6ZZsJr9lmy2kawjRogNSrmRVV6YD11aYNiK3+1GPbslUDSFqtNsnO7fW63ah\nJBC2XYiJ6dEUkuxmoDx0LV/GUKuvr0d9fX3c1xYuXAifz4exY8ciEAhAEAS4RcM9vV4v/H5/7HFL\nSwsmTJig4mVTonSTRMzQAfnnUwH8U28k2ORUXWpNG9FKTa2Axg2REVlS9tTkvl4u8VgrLboPY+fW\ncmB6SJSeXY4X/hNQVQP87fd2OsKvL0VrUXV1ddi0aRO+/e1vo7GxEVOmTIl7/qKLLsJ9992H9vZ2\nuFwu7Nq1C4sWLVLlgnON1CaRdJNEpI7OUvOQdiK9qy69WvszzYXM9vVyJWsIUbuCstr0EKVt/Ua2\n7O/bENlf+2QDMONRoL2Zk0WkcggK1gZDoRDuu+8+HDx4EG63Gw8//DCqq6uxYsUK1NbWYuLEidi0\naRNWrlwJh8OBhoYGXH311di6dStWrlyJL774ApWVlaiqqsLzzz+f9ntdfvnlin84O1DrhqCZAku8\nRNnZIX+JUovuRzUYdUdsLUi59Yy4UitWUKnZ9eC03FAzMtDeezjSARnl9kQaRzxnRUZnMdjSUxRq\nesrlUNPzDteTvlWMqdPKYo+3vdOOXTu6Jb+foaY9qfdTUxpM2QaimUkNNTMcqI629nccBdxlkf21\nqO88BFy60LhrswLeT40AWP+Qdip6dkKahdLuQzXPsgED78NmdmYINODMMOPvPAR89+lIhQawcUQq\na/zbloP0rNIAZdP91VRT6jBll+PACfz6vl9P4s7GbJs/tG5YUZNZwgyIVGnRyfzRiqyqhtP65WCo\nUYycW9CoKXqGbVihE//Um4/b9nSrGmxKm0ayncBvtQn+0c5GNfbU9GhYUYPZAi267Lhj2Zn9M07r\nl4fLj2Q4s04OSXamTM/3G0Gtg9NqTTDRyiWXXGJooCWb8ZjsbtckH0PNhLRcehRPFjF6ykiUkskh\nqUZupfq6kr21bOc6WmUupBbUmmCipmi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450 | "text/plain": [ 451 | "" 452 | ] 453 | }, 454 | "metadata": { 455 | "tags": [] 456 | } 457 | } 458 | ] 459 | } 460 | ] 461 | } -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2018 Henk Wymeersch 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Auto-encoder for a memoryless fiber-optical channel 2 | 3 | This script uses an auto-encoder (AE) for end-to-end learning of a non-linear memoryless fiber channel. The determines a good constellation and a good receiver. The achievable information rate is also computed. 4 | 5 | This code was is based on the paper 6 | 7 | Shen Li, Christian Häger, Nil Garcia, and Henk Wymeersch, "Achievable Information Rates for Nonlinear Fiber Communication via End-to-end Autoencoder Learning," in *Proc. European Conference on Optical Communication* (2018) [arXiv:1804.07675](https://arxiv.org/pdf/1804.07675.pdf). 8 | --------------------------------------------------------------------------------