{
 "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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mq9z92coHGzRo0M+3S0pKKCkpyWiww4fDwQdDmza1lxURqY8TT4Q//QkWLID2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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": 1,
   "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": 2,
   "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": 3,
   "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": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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lUW1EWzPbvoj5lov+pgGLzGxvoODnn6C2bXuSUDZHmlnr6G+b6DOqa95bgN+Y2ZbRzTQ9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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f94d28b5310>"
      ]
     },
     "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": 1,
   "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 0x7f1bfe6cf890>"
      ]
     },
     "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 '_______________________________________________________________'"
   ]
  }
 ],
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   "language": "python",
   "name": "python2"
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  "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"
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 },
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