{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Information theory: the noisy binary symmetric channel" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Florent Leclercq,
\n", "Imperial Centre for Inference and Cosmology, Imperial College London,
\n", "florent.leclercq@polytechnique.org" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.special import binom\n", "from matplotlib import pyplot as plt\n", "from PIL import Image\n", "np.random.seed(123456)\n", "%matplotlib inline\n", "plt.rcParams.update({'lines.linewidth': 2})\n", "plt.rcParams.update({'font.size': 16})\n", "plt.rcParams.update({'axes.titlesize': 16})\n", "plt.rcParams.update({'axes.labelsize': 16})\n", "plt.rcParams.update({'xtick.labelsize': 16})\n", "plt.rcParams.update({'ytick.labelsize': 16})\n", "plt.rcParams.update({'legend.fontsize': 16})\n", "plt.rcParams.update({'figure.titlesize': 16})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The signal" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Open the image and convert it to an array of black/white pixels\n", "im_data = Image.open('data/correlation.png')\n", "im_grey = im_data.convert('L')\n", "signal = np.array(im_grey, dtype=np.int)\n", "signal[np.where(signal>1)]=1" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(signal,cmap=\"Greys_r\",interpolation=None)\n", "plt.title(\"signal\")\n", "plt.show() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The noisy binary symmetric channel" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The channel flips bits with a probability $f$: the noise level." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def noisy_channel(transmitted,noise_level):\n", " received=np.copy(transmitted)\n", " noise=np.random.uniform(size=received.shape)\n", " received[np.where(noise" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(noisy_signal,cmap=\"Greys_r\",interpolation=None)\n", "plt.title(\"noisy signal\")\n", "plt.show() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The R3 code" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The R3 code is one of the simplest algorithms: the encoder just repeats the signal 3 times. The decoder uses a \"majority vote\" to decide the value of each bit of the decoded signal." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def R3_encoder(signal):\n", " m1=np.copy(signal)\n", " m2=np.copy(signal)\n", " m3=np.copy(signal)\n", " return np.array((m1,m2,m3))\n", "\n", "def R3_decoder(received):\n", " decoded=np.zeros_like(received[0])\n", " decoded[np.where(received[0]+received[1]+received[2]>=2)]=1\n", " return decoded" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "transmitted=R3_encoder(signal)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(transmitted[0],cmap=\"Greys_r\",interpolation=None)\n", "plt.title(\"transmitted (1st)\")\n", "plt.show()\n", "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(transmitted[1],cmap=\"Greys_r\",interpolation=None)\n", "plt.title(\"transmitted (2nd)\")\n", "plt.show()\n", "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(transmitted[2],cmap=\"Greys_r\",interpolation=None)\n", "plt.title(\"transmitted (3rd)\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "received=noisy_channel(transmitted,noise_level)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(received[0],cmap=\"Greys_r\",interpolation=None)\n", "plt.title(\"received (1st)\")\n", "plt.show()\n", "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(received[1],cmap=\"Greys_r\",interpolation=None)\n", "plt.title(\"received (2nd)\")\n", "plt.show()\n", "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(received[2],cmap=\"Greys_r\",interpolation=None)\n", "plt.title(\"received (3rd)\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "decoded=R3_decoder(received)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(decoded,cmap=\"Greys_r\",interpolation=None)\n", "plt.title(\"decoded\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(decoded-signal,cmap=\"bwr_r\",interpolation=None)\n", "plt.imshow(signal,cmap=\"Greys_r\",alpha=0.2,interpolation=None)\n", "plt.title(\"uncorrected errors\")\n", "plt.show() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Uncorrected errors are uncorrelated with the R3 code." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The (7,4) Hamming code" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The (7,4) Hamming code transmits the information by blocs of 4 bits $s_1$, $s_2$, $s_3$, $s_4$. For each block of 4 bits, 3 parity-checks bits $t_5$, $t_6$ and $t_7$ are also transmitted.\n", "The syndrome matrix allows to decode." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "Hamming_matrix=np.array([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,1,1,0],[0,1,1,1],[1,0,1,1]])\n", "syndrome_matrix=np.array([[1,1,1,0,1,0,0],[0,1,1,1,0,1,0],[1,0,1,1,0,0,1]])\n", "\n", "# This function splits the full signal into 4-bit blocks, adding dummy bits at the end if necessary\n", "def split_signal_4bits_blocks(signal):\n", " split=signal.reshape(signal.shape[0]*signal.shape[1])\n", " N_dummy_bits=-len(split)%4\n", " split=np.concatenate((split,np.zeros(N_dummy_bits)))\n", " return np.split(split,len(split)/4)\n", "\n", "# This is the Hamming encoder: transmitted = Hamming_matrix.dot(signal) for each 4-bit block\n", "def Hamming_encoder(signal):\n", " split_signal=split_signal_4bits_blocks(signal)\n", " transmitted=np.zeros((len(split_signal),7),dtype=np.int)\n", " for i in range(len(split_signal)):\n", " signal_block=split_signal[i]\n", " transmitted_block=Hamming_matrix.dot(signal_block)\n", " transmitted[i]=transmitted_block\n", " return np.mod(transmitted,2)\n", "\n", "# This function computes the syndrome: syndrome = syndrome_matrix.dot(received) for each 7-bit block\n", "def compute_syndrome(received_block):\n", " return np.mod(syndrome_matrix.dot(received_block),2)\n", "\n", "# This function corrects the error in a received block, given its syndrome\n", "def correct_block(received_block):\n", " syndrom=compute_syndrome(received_block)\n", " corrected_block=np.copy(received_block)\n", " if np.array_equal(syndrom,np.array((0,0,1))):\n", " corrected_block[6]+=1\n", " elif np.array_equal(syndrom,np.array((0,1,0))):\n", " corrected_block[5]+=1\n", " elif np.array_equal(syndrom,np.array((0,1,1))):\n", " corrected_block[3]+=1\n", " elif np.array_equal(syndrom,np.array((1,0,0))):\n", " corrected_block[4]+=1\n", " elif np.array_equal(syndrom,np.array((1,0,1))):\n", " corrected_block[0]+=1\n", " elif np.array_equal(syndrom,np.array((1,1,0))):\n", " corrected_block[1]+=1\n", " elif np.array_equal(syndrom,np.array((1,1,1))):\n", " corrected_block[2]+=1\n", " return np.mod(corrected_block,2)\n", "\n", "# This function translates corrected 7-bits blocks into 4-bit decoded blocks and removes dummy bits at the end \n", "def reshape_corrected_7bits_blocks(corrected,signal_shape):\n", " decoded=np.zeros((corrected.shape[0],4))\n", " \n", " # for each 7-bits block, keep only the 4 decoded bits\n", " for i in range(corrected.shape[0]):\n", " corrected_block=corrected[i]\n", " decoded[i]=np.array((corrected_block[0],corrected_block[1],corrected_block[2],corrected_block[3])\n", " ,dtype=np.int)\n", " decoded=decoded.flatten()\n", " signal_length=signal_shape[0]*signal_shape[1]\n", " \n", " # remove dummy bits at the end if necessary\n", " N_dummy_bits=-signal_length%4\n", " decoded=decoded[:-N_dummy_bits]\n", " decoded=decoded.reshape(signal_shape[0],signal_shape[1]) \n", " return decoded\n", "\n", "def reshape_parity_7bits_blocks(corrected,signal_shape):\n", " parity=np.zeros((corrected.shape[0],3))\n", "\n", " # for each 7-bits block, keep only the 4 decoded bits\n", " for i in range(corrected.shape[0]):\n", " corrected_block=corrected[i]\n", " parity[i]=np.array((corrected_block[4],corrected_block[5],corrected_block[6]),dtype=np.int)\n", " \n", " # reshape the array of parity bits to plot it as an image. dimensions are arbitrary here\n", " parity=parity.flatten()\n", " j=1\n", " d=1\n", " while(j" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(signal,cmap=\"Greys_r\",interpolation=None)\n", "plt.title(\"transmitted image\")\n", "plt.show()\n", "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(transmitted_parity,cmap=\"Greys_r\",interpolation=None)\n", "plt.title(\"transmitted parity bits\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "received=noisy_channel(transmitted,noise_level)\n", "received_image=reshape_corrected_7bits_blocks(received,signal.shape)\n", "received_parity=reshape_parity_7bits_blocks(received,signal.shape)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(received_image,cmap=\"Greys_r\",interpolation=None)\n", "plt.title(\"received noisy image\")\n", "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(received_parity,cmap=\"Greys_r\",interpolation=None)\n", "plt.title(\"received parity bits\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "decoded=Hamming_decoder(received,signal.shape)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(decoded,cmap=\"Greys_r\",interpolation=None)\n", "plt.title(\"decoded\")\n", "plt.show() " ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,4))\n", "plt.axis('off')\n", "plt.imshow(decoded-signal,cmap=\"bwr_r\",interpolation=None)\n", "plt.imshow(signal,cmap=\"Greys_r\",alpha=0.2,interpolation=None)\n", "plt.title(\"uncorrected errors\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are more errors with the (7,4) Hamming code than with the R3 code, which is unsurprising since the *rate of information transfer* is $R = \\frac{4}{7} > \\frac{1}{3}$. Uncorrected errors are correlated, they happen preferentially in blocks of 4 consecutive bits." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Shannon's noisy channel coding theorem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Rate of information transfer $R$ and probability of error $p_\\mathrm{b}$ of repetition codes: for odd $N$:\n", "\\begin{equation}\n", "R=\\frac{1}{N}\n", "\\end{equation}\n", "\\begin{equation}\n", "p_\\mathrm{b}=\\sum_{(N+1)/2}^{N} \\binom{N}{n} \\, f^n (1-f)^{N-n}\n", "\\end{equation}\n", "(MacKay 2003, equation (1.24))" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "R=np.array([1./N for N in range(1,62,2)])\n", "p=np.array([np.sum(np.array([binom(N,n)*noise_level**n*(1-noise_level)**(N-n)\n", " for n in range((N+1)//2,N)])) for N in range(1,62,2)])\n", "p[0]=noise_level" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Binary entropy function*:\n", "\\begin{equation}\n", "H_2(x) \\equiv x \\log \\frac{1}{x} + (1-x)\\log \\frac{1}{1-x}\n", "\\end{equation}\n", "*Capacity* of the noisy channel:\n", "\\begin{equation}\n", "C(f) \\equiv 1 - H_2(f)\n", "\\end{equation}\n", "Shannon limit:\n", "\\begin{equation}\n", "R=\\frac{C(f)}{1-H_2(f)}\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "def H2(f):\n", " return f*np.log2(1./f) + (1-f)*np.log2(1./(1-f))\n", "def capacity(noise_level):\n", " return 1.-H2(noise_level)\n", "def shannon_limit(p,noise_level):\n", " return capacity(noise_level)/(1-H2(p))" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(10,10))\n", "ax = fig.add_subplot(1,1,1)\n", "ax.set_xlim(0,1)\n", "ax.set_xlabel(\"$R$\")\n", "ax.set_xticks([0.0, 0.2, 0.4, 0.6, 0.8, 1.0, capacity(noise_level)])\n", "ax.set_xticklabels([\"0.0\", \"0.2\", \"0.4\", \"0.6\", \"0.8\", \"1.0\", \"$C(f)$\"])\n", "ax.set_yscale('log')\n", "ax.set_ylim([1e-15,1e0])\n", "ax.set_ylabel(\"$p_\\mathrm{b}$\")\n", "ax.scatter(R,p,s=60,marker='.',color='blue',label=\"repetition codes\")\n", "ax.scatter([4./7.],[7e-2],s=60,marker='.',color='red')\n", "p_shannon=np.linspace(noise_level,1e-15,1000)\n", "ax.plot(shannon_limit(p_shannon,noise_level),p_shannon,color='black',lw=2,label=\"Shannon limit\")\n", "ax.fill_betweenx(p_shannon,shannon_limit(p_shannon,noise_level),np.ones_like(p_shannon),\n", " facecolor='grey',alpha=0.3, linewidth=0.)\n", "ax.set_title(\"Error probability versus rate - Shannon's theorem\")\n", "ax.text(0.333, 7e-3, '$R_3$', fontsize=16)\n", "ax.text(0.965, 2e-2, '$R_1$', fontsize=16)\n", "ax.text(0.58, 1e-1, '$H(7,4)$', fontsize=16)\n", "ax.text(0.2, 1e-13, 'achievable', fontsize=16)\n", "ax.text(0.6, 1e-13, 'not achievable', fontsize=16)\n", "plt.legend(frameon=False,loc='center left',bbox_to_anchor=(1, 0.5))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Shannon's noisy-channel coding theorem: rates above the Shannon limit are achievable, rates below the Shannon limit are not achievable.\n", "\n", "Rates up to $R=C(f)$ are achievable with arbitrarily small $p_\\mathrm{b}$. The boundary between achievable and non-achievable points meets the $R$ axis at a *non-zero* value $R=C(f)$." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }