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Diffstat (limited to 'Digital_Communications_by_S._Haykin/Chapter2.ipynb')
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diff --git a/Digital_Communications_by_S._Haykin/Chapter2.ipynb b/Digital_Communications_by_S._Haykin/Chapter2.ipynb new file mode 100644 index 00000000..49325463 --- /dev/null +++ b/Digital_Communications_by_S._Haykin/Chapter2.ipynb @@ -0,0 +1,394 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2 Fundamental Limit On Performance" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.1 page 18" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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BhGUGvgN+Ez33e+De6Pb2wMdA0+riiMptFP3bLHp8o5T31ze6fTVw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\nIlKBEoOIiFSgxCAiIhX8P5fhJpLBkGXZAAAAAElFTkSuQmCC\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7f4de4a3d1d0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import arange, zeros\n", + "from math import log\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,xlabel,ylabel,title,show\n", + "\n", + "Po = arange(0,1+0.01,0.01)\n", + "H_Po = zeros(len(Po))\n", + "for i in range(1,len(Po)-1):\n", + " H_Po[i]=-Po[(i)]*log(Po[(i)],2)-(1-Po[(i)])*log(1-Po[(i)],2)\n", + "\n", + "#plot\n", + "#plot2d(Po,H_Po)\n", + "plot(Po,H_Po)\n", + "xlabel('Symbol Probability, Po')\n", + "ylabel('H(Po)')\n", + "title('Entropy function H(Po)')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.2 page 19" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Entropy of Discrete Memoryless Source\n", + "bits : 1.5\n", + "Table 2.1 Alphabet Particulars of Second-order Extension of a Discrete Memoryless Source\n", + "_________________________________________________________________________________\n", + "Sequence of Symbols of ruo2:\n", + " S0*S0 S0*S1 S0*S2 S1*S0 S1*S1 S1*S2 S2*S0 S2*S1 S2*S2\n", + "Probability p(sigma), i =0,1.....8 : [0.0625, 0.0625, 0.125, 0.0625, 0.0625, 0.125, 0.125, 0.125, 0.25]\n", + "_________________________________________________________________________________\n", + " \n", + "H(Ruo_Square)= 3.0 bits\n", + "H(Ruo_Square) = 2*H(Ruo)\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import log\n", + "P0 = 1/4# #probability of source alphabet S0\n", + "P1 = 1/4# #probability of source alphabet S1\n", + "P2 = 1/2# #probability of source alphabet S2\n", + "H_Ruo = P0*log(1/P0,2)+P1*log(1/P1,2)+P2*log(1/P2,2)\n", + "print 'Entropy of Discrete Memoryless Source'\n", + "print 'bits : ',H_Ruo\n", + "#Second order Extension of discrete Memoryless source\n", + "P_sigma = [P0*P0,P0*P1,P0*P2,P1*P0,P1*P1,P1*P2,P2*P0,P2*P1,P2*P2]#\n", + "print 'Table 2.1 Alphabet Particulars of Second-order Extension of a Discrete Memoryless Source'\n", + "print '_________________________________________________________________________________'\n", + "print 'Sequence of Symbols of ruo2:'\n", + "print ' S0*S0 S0*S1 S0*S2 S1*S0 S1*S1 S1*S2 S2*S0 S2*S1 S2*S2'\n", + "print 'Probability p(sigma), i =0,1.....8 : ',P_sigma\n", + "print '_________________________________________________________________________________'\n", + "print ' '\n", + "H_Ruo_Square =0\n", + "for i in range(0,len(P_sigma)):\n", + " H_Ruo_Square=(H_Ruo_Square+P_sigma[i]*log(1/P_sigma[i],2))\n", + "print 'H(Ruo_Square)=', H_Ruo_Square,' bits'\n", + "print 'H(Ruo_Square) = 2*H(Ruo)'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.3 page 20" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Average code-word Length L 2.2 bits\n", + "Entropy of Huffman coding result H 2.12 bits\n", + "Average code-word length L exceeds the entropy H(Ruo) by only 3.679 %\n", + "Varinace of Huffman code : 0.16\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import log\n", + "\n", + "# (a)Average code-word length 'L'\n", + "#(b)Entropy 'H'\n", + "P0 = 0.4# #probability of codeword '00'\n", + "L0 = 2# #length of codeword S0\n", + "P1 = 0.2# #probability of codeword '10'\n", + "L1 = 2# #length of codeword S1\n", + "P2 = 0.2# #probility of codeword '11'\n", + "L2 = 2# #length of codeword S2\n", + "P3 = 0.1# #probility of codeword '010'\n", + "L3 = 3# #length of codeword S3\n", + "P4 =0.1# #probility of codeword '011'\n", + "L4 = 3# #length of codeword S4\n", + "L = P0*L0+P1*L1+P2*L2+P3*L3+P4*L4#\n", + "H_Ruo = P0*log(1/P0,2)+P1*log(1/P1,2)+P2*log(1/P2,2)+P3*log(1/P3,2)+P4*log(1/P4,2)\n", + "print 'Average code-word Length L',L,'bits'\n", + "print 'Entropy of Huffman coding result H %0.2f'%H_Ruo, 'bits'\n", + "print 'Average code-word length L exceeds the entropy H(Ruo) by only %0.3f'%(((L-H_Ruo)/H_Ruo)*100),'%'\n", + "sigma_1 = P0*(L0-L)**2+P1*(L1-L)**2+P2*(L2-L)**2+P3*(L3-L)**2+P4*(L4-L)**2\n", + "print 'Varinace of Huffman code : ',sigma_1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example2.4 page 20" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Average code-word Length L : 2.2 bits\n", + "Entropy of Huffman coding result H : 2.12 bits\n", + "Varinace of Huffman code = 1.36\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import log\n", + "\n", + "def log2(x):\n", + " return log(x,2)\n", + "\n", + "# Calculation of (a)Average code-word length 'L' (b)Entropy 'H'\n", + "P0 = 0.4# #probability of codeword '1'\n", + "L0 = 1# #length of codeword S0\n", + "P1 = 0.2# #probability of codeword '01'\n", + "L1 = 2# #length of codeword S1\n", + "P2 = 0.2# #probility of codeword '000'\n", + "L2 = 3# #length of codeword S2\n", + "P3 = 0.1# #probility of codeword '0010'\n", + "L3 = 4# #length of codeword S3\n", + "P4 =0.1# #probility of codeword '0011'\n", + "L4 = 4# #length of codeword S4\n", + "L = P0*L0+P1*L1+P2*L2+P3*L3+P4*L4#\n", + "H_Ruo = P0*log2(1/P0)+P1*log2(1/P1)+P2*log2(1/P2)+P3*log2(1/P3)+P4*log2(1/P4)#\n", + "print 'Average code-word Length L :',L,'bits'\n", + "print 'Entropy of Huffman coding result H : %0.2f bits'%H_Ruo\n", + "sigma_2 = P0*(L0-L)**2+P1*(L1-L)**2+P2*(L2-L)**2+P3*(L3-L)**2+P4*(L4-L)**2\n", + "print 'Varinace of Huffman code = %0.2f'%sigma_2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example2.5 page 20" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "probility of 0 receiving if a 0 is sent = probility of 1 receiving if a 1 is sent= 0.4\n", + "Transition probility\n", + "probility of 0 receiving if a 1 is sent = probility of 1 receiving if a 0 is sent= 0.6\n" + ] + } + ], + "source": [ + "p = 0.4# #probability of correct reception\n", + "pe = 1-p##probility of error reception (i.e)transition probility\n", + "print 'probility of 0 receiving if a 0 is sent = probility of 1 receiving if a 1 is sent=',p\n", + "print 'Transition probility'\n", + "print 'probility of 0 receiving if a 1 is sent = probility of 1 receiving if a 0 is sent=',pe" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example2.6 page 21" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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tUWCY+lWvQ9eu8OijcPLJ4fKiiIhIFijhyhgzO9nMxgIbmtnY2N8k4L2Uw2sS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\nM2ubtA0A7j4eWGBmq5hZtZldZWZvAKe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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f4e00050f10>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import arange\n", + "from math import log\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,title,show,xlabel,ylabel\n", + "\n", + "\n", + "\n", + "def log2(x):\n", + " return log(x,2)\n", + "\n", + "\n", + "p = arange(0,0.5+0.01,0.01)\n", + "C=[]\n", + "for i in range(0,len(p)):\n", + " if(i!=0):\n", + " C.append(1+p[i]*log2(p[i])+(1-p[i])*log2((1-p[i])))\n", + " elif(i==0):\n", + " C.append(1)\n", + " elif(i==len(p)):\n", + " C.append(0)\n", + " \n", + "\n", + "plot(p,C)\n", + "xlabel('Transition Probility, p')\n", + "ylabel('Channel Capacity, C')\n", + "title('Figure 2.10 Variation of channel capacity of a binary symmetric channel with transition probility p')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example2.7 page 21" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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WtDkFpvsws/8lHVxdeLJyrv49/DAcfTQMHQr77JN2NC4J5ZishprZsZIqKZys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\nVM4VYAaXXALXXgujR8PGG6c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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f4de45b5e10>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Table 2.3 Average Probility of Error for Repetition Code\n", + "_______________________________________________________________\n", + "Average Probility of Error, Pe =\n", + "0.01\n", + "0.000298\n", + "9.8506e-06\n", + "3.416698e-07\n", + "Code Rate, r =1/n = \n", + "1.00\n", + "0.33\n", + "0.20\n", + "0.14\n", + "_______________________________________________________________\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,title,show,xlabel,ylabel,legend\n", + "\n", + "\n", + "#Average Probility of Error of Repetition Code\n", + "p =10**-2#\n", + "pe_1 =p# #Average Probility of error for code rate r = 1\n", + "pe_3 = 3*p**2*(1-p)+p**3##probility of error for code rate r =1/3\n", + "pe_5 = 10*p**3*(1-p)**2+5*p**4*(1-p)+p**5##error for code rate r =1/5\n", + "pe_7 = ((7*6*5)/(1*2*3))*p**4*(1-p)**3+(42/2)*p**5*(1-p)**2+7*p**6*(1-p)+p**7##error for code rate r =1/7\n", + "r = [1,1/3,1/5,1/7]#\n", + "pe = [pe_1,pe_3,pe_5,pe_7]#\n", + "plot(r,pe)\n", + "xlabel('Code rate, r')\n", + "ylabel('Average Probability of error, Pe')\n", + "title('Figure 2.12 Illustrating significance of the channel coding theorem')\n", + "#xgrid(1)\n", + "show()\n", + "print 'Table 2.3 Average Probility of Error for Repetition Code'\n", + "print '_______________________________________________________________'\n", + "print 'Average Probility of Error, Pe ='\n", + "for pp in pe: print pp\n", + "print 'Code Rate, r =1/n = '\n", + "for rr in r:print '%0.2f'%rr\n", + "print '_______________________________________________________________'" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |