## Sunday, June 8, 2008

### Information on Cyclic Code

Posted by Lionel at 4:01 AM 1 comments

### Information on Convolutional Code

Satellite communications systems commonly use a convolutional code to protect all data carried on the link.

Posted by Lionel at 4:00 AM 1 comments

### Linear Block Code

% Aim: Implementation Of linear Block Code

clc;

clear all;

% Input Generator Matrix

g=input('Enter The Generator Matrix: ')

disp ('G = ')

disp ('The Order of Linear block Code for given Generator Matrix 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 Codewords 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 Received Code Word:')

p = [g(:,n-k+2:n)];

h = [transpose(p),eye(n-k)];

disp('Hammimg Code')

ht = transpose(h)

disp('Syndrome of a Given Codeword is :')

s = rem(r*ht,2)

for i = 1:1:size(ht)

if(ht(i,1:3)==s)

r(i) = 1-r(i);

break;

end

end

disp('The Error is in bit:')

i

disp('The Corrected Codeword is :')

r

%******************** OUTPUT *******************

Enter The Generator Matrix: [1 0 0 0 1 0 1;0 1 0 0 1 1 1;0 0 1 0 1 1 0;0 0 0 1 0 1 1]

g =

1 0 0 0 1 0 1

0 1 0 0 1 1 1

0 0 1 0 1 1 0

0 0 0 1 0 1 1

G =

The Order of Linear block Code for given Generator Matrix is:

n =

7

k =

4

The Possible Codewords are :

c =

0 0 0 0 0 0 0

0 0 0 1 0 1 1

0 0 1 0 1 1 0

0 0 1 1 1 0 1

0 1 0 0 1 1 1

0 1 0 1 1 0 0

0 1 1 0 0 0 1

0 1 1 1 0 1 0

1 0 0 0 1 0 1

1 0 0 1 1 1 0

1 0 1 0 0 1 1

1 0 1 1 0 0 0

1 1 0 0 0 1 0

1 1 0 1 0 0 1

1 1 1 0 1 0 0

1 1 1 1 1 1 1

The Minimum Hamming Distance dmin for given Block Code is=

d_min =

3

Enter the Received Code Word:[1 0 0 0 1 0 0]

r =

1 0 0 0 1 0 0

Hammimg Code

ht =

1 0 1

1 1 1

1 1 0

0 1 1

1 0 0

0 1 0

0 0 1

Syndrome of a Given Codeword is :

s =

0 0 1

The Error is in bit:

i =

7

The Corrected Codeword is :

r =

1 0 0 0 1 0 1

Posted by Lionel at 3:51 AM 5 comments