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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 8: Information theory"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8.10_A: SNR.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"clear;\n",
+"W=3000;\n",
+"SNR_db=39;// 10log (SNR_ratio)=SRN_db\n",
+"SNR_ratio=7943; //10^(3.9)\n",
+"\n",
+"C=W*log2(1+SNR_ratio);\n",
+"\n",
+"disp(C,'Capacity (in bits/s) =');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8.1_A: Information_Rate.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"clear;\n",
+"p1=1/8;\n",
+"p2=1/8;\n",
+"p3=5/8;\n",
+"p4=1/8; //Quantization Levels\n",
+"//B is the Bandwidth of the signal\n",
+"\n",
+"H=p1*log2(1/p1)+p2*log2(1/p2)+p3*log2(1/p3)+p4*log2(1/p4);\n",
+"\n",
+"disp(H,'The average Information (in bits/message)=');\n",
+"disp('The Information Rate R=rH =2*B(1.55) =3.1B bits/s');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8.2_A: ShannonFano_and_Huffman_coding.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"clear;\n",
+"m1=0.2;\n",
+"m2=0.3;\n",
+"m3=0.2;\n",
+"m4=0.15;\n",
+"m5=0.15; // probability of 5 source messages \n",
+"\n",
+"H=m1*log2(1/m1)+m2*log2(1/m2)+m3*log2(1/m3)+m4*log2(1/m4)+m5*log2(1/m5);//Average information in bits\n",
+"\n",
+"//a) Shannon-fano coding\n",
+" //coding\n",
+"// m1 0.2 0 0 00\n",
+"// m2 0.3 0 1 01\n",
+"// m3 0.2 1 0 10\n",
+"// m4 0.15 1 1 0 110\n",
+"// m5 0.15 1 1 1 111\n",
+"\n",
+"L=(0.2*2)+(.3*2)+(0.2*2)+(2*0.15*3) //Average code word length(in bits)=probability *coding length\n",
+"\n",
+"n=H/L; \n",
+"\n",
+"disp(n*100,'Coding efficiency for Shannon Fano coding is');\n",
+"\n",
+"//b) Huffman coding\n",
+"\n",
+"// m1 0.2 01\n",
+"// m2 0.3 00 \n",
+"// m3 0.2 11\n",
+"// m4 0.15 010\n",
+"// m5 0.15 110\n",
+"\n",
+"L=(0.2*2)+(.3*2)+(0.2*2)+(2*0.15*3) //Average code word length(in bits)=probability *coding length\n",
+"\n",
+"n=H/L;\n",
+"\n",
+"disp(n*100,'Coding efficiency for Huffman coding is');\n",
+"\n",
+"//change in answer due to rounded off value in text-book"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8.3_A: Gaussian_Channel.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"clear;\n",
+"\n",
+"PSD=10^(-9); //noise PSD in W/Hz\n",
+"Bw=4000;//Wandwidth in Hz\n",
+"\n",
+"//a) \n",
+"E=0.1 //Energy in Joules\n",
+"C=Bw*log2(1+E/(2*PSD*Bw));\n",
+"disp(C,'a) Capacity of the gaussian channel(in bits/s) when E is 0.1J=');\n",
+"\n",
+"//b) \n",
+"E=0.001 //Energy in Joules\n",
+"C=Bw*log2(1+E/(2*PSD*Bw));\n",
+"disp(C,'b) Capacity of the gaussian channel(in bits/s) when E is 0.001J=');\n",
+"\n",
+"//c)\n",
+"Bw=10000;\n",
+"C=Bw*log2(1+E/(2*PSD*Bw));\n",
+"disp(C,'d) Capacity of the gaussian channel(in bits/s) when Bw is 10Khz=');\n",
+"\n",
+"disp('100 times fall in Energy when the BW is increased by 2.5 times');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8.5_A: Throughput_efficiency.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"clear;\n",
+"k=973;\n",
+"n=1023;\n",
+"Pa=0.99;\n",
+"Tw=10*10^(-6);\n",
+"Tl=40*10^(-6);\n",
+"N=4;\n",
+"\n",
+"N_sw=(k/n)*(Pa/(1+Tl/Tw));// efficiency of stop and wait algorithm\n",
+"N_sgpull=(k/n)*(1/(1+N*(1-Pa)/Pa));//efficiency of go-back-N algorithm\n",
+"Nsr=(k/n)*Pa;// efficiency of selective repeat algorithm\n",
+"\n",
+"disp(N_sw,'N s&w');\n",
+"disp(N_sgpull,'Nsgpull');\n",
+"disp(Nsr,'Nsr');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8.6_A: Rate_of_source.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"clear;\n",
+"p1=1/2;\n",
+"p2=1/4;\n",
+"p3=1/8;\n",
+"p4=1/16;\n",
+"p5=1/16;// probabilities\n",
+"\n",
+"H=p1*log2(1/p1)+p2*log2(1/p2)+p3*log2(1/p3)+p4*log2(1/p4)+p5*log2(1/p5);\n",
+"Bw=4000; //Bandwidth in Hz\n",
+"R=2*H*Bw ;\n",
+"\n",
+"disp(R,'Rate of the source ( in bits/s) is');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8.7_A: entropy_of_equiprobable_source.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"clear;\n",
+"\n",
+"// probability of all the events are same\n",
+"syms N;\n",
+"\n",
+"H_X=N*[(-1/N)*log(1/N)]; //H(X)=(-1/N)log(1/N)+(-1/N)log(1/N)+....N times\n",
+"\n",
+"disp(H_X,'H(X)=');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8.8_A: Self_Information.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"clear;\n",
+"P0=2/3; //P(X=0)\n",
+"P1=2/3; //P(Y=0)\n",
+"H_x=0.919;\n",
+"H_y=0.919;\n",
+"H_b=0.919; //Hb(2/3)\n",
+"\n",
+"//since X,Y pair is uniformly distributed on three values\n",
+"H_xy=log2(3); // H(X,Y)\n",
+"\n",
+"H_xdivy=H_xy-H_y; //H(X/Y)=H(X,Y)-H(Y)\n",
+"I_xdivy=H_x-H_xdivy; //I(X,Y)=H(X)-H(X/Y)\n",
+"\n",
+"disp(I_xdivy,'I(X,Y)=');\n",
+"\n",
+""
+ ]
+ }
+],
+"metadata": {
+ "kernelspec": {
+ "display_name": "Scilab",
+ "language": "scilab",
+ "name": "scilab"
+ },
+ "language_info": {
+ "file_extension": ".sce",
+ "help_links": [
+ {
+ "text": "MetaKernel Magics",
+ "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+ }
+ ],
+ "mimetype": "text/x-octave",
+ "name": "scilab",
+ "version": "0.7.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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