Hi, I am trying to make a parity check matrix from non-systematic to systematic. Hence I am attaching my code below. Somewhat it is correct, but there are some problems. It would be really great if someone could help me in this. Thanks

Information theory and coding. I am working on LDPC coding and decoding. Please check the code below

[Walter Roberson]

Do we get some hints about what the problems are ?

[sb]

For e.g.

This is my H matrix

H =

   1     0     1     1     0
   0     0     1     0     1
   1     0     0     1     0
   1     0     1     1     1

I want to have an identity matrix inside the matrix. the dimension on H matrix here is (mxn) which is (4x5).

I should have matrix as this in the result:

Hsys =

   0     1     0     0     0
   0     0     1     0     0
   1     0     0     1     0
   0     0     0     0     1

I should have an identity matrix of dimension 'm'

Answer 1

[freebil]

You have to do gauss jordan elimination to convert a parity check matrix to upper triangular form. For example,

H=[1 1 0 1 1 0 0 1 0 0;
   0 1 1 0 1 1 1 0 0 0;
   0 0 0 1 0 0 0 1 1 1;
   1 1 0 0 0 1 1 0 1 0;
   0 0 1 0 0 1 0 1 0 1];

There is rref() in matlab and you have to do it in GF(2). So,

HH = mod(rref(H),2)

gives

HH = 1     0     0     0     0     0     1     1     1     0
     0     1     0     0     0     1     0     1     0     0
     0     0     1     0     0     1     0     1     0     1
     0     0     0     1     0     0     0     1     1     1
     0     0     0     0     1     1     1     0     0     1

[Aitor López Hernández]

Hello there,

Wouldn't the systematic form of a parity check matrix be of the form H = [A In-k]?

[SP22]

This might help you to get parity check matrix in form H=[A In-k].

temp=HH(:,1:5) %Access the identity matrix through column

temp2=HH(:,6:10) %Acces the parity through column

Hsyst=horzcat(temp2,temp) %Actual systematic matrix in the form H((n-k)*n)=[P' :I(n-k)]