LINEAR BLOCKCODES

LINEAR BLOCKCODES

AIM

To detect and correct the error accruing in the transmitted data with the help

of linear block codes.

THEORY

A code is said to be linear if any two code word in the code, can be added in module 2 arithmetic to Produce a third codeword in the code. The (n-k) bits in the remaining portion are computed from the message bits in the accordance with the prescribed encoding rule that determines a mathematical structure of the code, then use frame to get the syndrome calculation.

The hamming weight of the code vector C is defined in the number of non zero elements in the code vector. The minimum distance of the linear block code is defiend in the smallest hamming distance between any pair of code vector in code.

Algorithm

1. Get the generator matrix value.
2. Calculate the order of given matrix.
3. calculate the code word.
4. calculate the minimum ha
5. Get the received code word.
6. Display the hamming code
7. Display the syndrome of the code word.
8. Calculate the error in the bit.
9. Display the correlated code word.
   
   
   PROGRAM
   #######################################
   clc;
   clear all;
   close all;
   %input generator matrix
   g=input('enter the generator matrix:')
   disp('G=')
   disp('the order of linear block code for given generator mathrix is:');
   [n,k]=size(transpose(g))
   for i=1:2^k
       for j=k:-1:1
           if rem(i-1,2^(-j+k+1))>=2^(-j+k)
               u(i,j)=1;
           else
               u(i,j)=0;
           end
       end
   end
   u;
   disp('the possible code word are:');
   c=rem(u*g,2);
   disp('the minimum hamming distance dmin for given block code is:');
   d_min=min(sum((c(2:2^k,:))'))
   %code word
   r=input('enter the recieved code word:');
   p=[g(:,n-k+2:n)];
   h=[transpose(p),eye(n-k)];
   disp('hamming code');
   ht=transpose(h)
   disp('syndrome of a given code word is:');
   s=rem(r*ht,2)
   for i=1:1:size(ht)
       if(ht(i,1:3)==5)
           r(i)=1-r(i);
           break;
       end
   end
   disp('the error is in bit:');
   i;
   disp('the correct codeword is:');
   r;
   
   
   ###########################################################################
   OUTPUT
   Enter the generator matrix:[1000101;0100111;0010110;0001011]
   g =1000101
   0100111
   0010110
   0001011
   G = The order of linear block code for given generator mathrix is:
   n = 7
   k = 4
   The possible code word are:
   0000000
   0001011
   0010110
   0011101
   0000111
   0101100
   0110001
   0111010
   1000100
   1001110
   1010011
   1011000
   1100010
   1101001
   1110100
   1111111
   The minimum hamming distance dmin for given block code is:
   d_min =3
   Enter the received code word:[1000100]
   r=1000100
   Hamming code
   H=
   101
   111
   110
   011
   100
   101
   001
   
   
   Syndrome of t given codeword is:
   s=001
   The error is in bit :
   i=7
   The corrected code word is : r=100010.
   
   
   Result
   Thus the error is detected and corrected n the transmitted code by using linear block codes.