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```Hi, I'm a new poster to comp.dsp.  Recently I've been digging in to LDPCs
out of general curiosity and after reading several papers and trying out
some techniques, I have a question about encoding LDPCs.  There are two
methods that seem to have the most general application, but I have not had
success with either method.

Both methods involve taking the original parity check matrix and
manipulating it so that the square parity portion of the matrix is upper
triangular (or nearly so) or decomposing the square parity portion of the
matrix into complete upper and lower triangular matrices.

The second decomposition is preferred to the first because the decoder
becomes well defined performing back substitution to calculate the parity
bits.  The first manipulation (also in Richardson and Urbanke's book Modern
Coding Theory) results in some submatrices and the encoder is more
complicated.

My difficulty is in manipulating the check matrix so that the parity
portion is non-singular.  I've tried several different regular code
generation techniques and LU decomposition techniques which involve
permuting the H matrix and none of the algorithms converge to a solution so
that the parity portion is non-singular.  Is this a problem that involves
extensive trial and error to find an H-matrix that will yield a
non-singular parity portion or are there algorithms available that yield a
higher probability of success?

Of course my troubles so far do not even get into the question of whether
or not the codes I have been generating are good codes.  I'm just trying to
come up with the encoder!

Thanks.
Jim

```
 0
Reply ChinookPass 11/24/2009 8:44:57 PM

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```ChinookPass <james.a.laudolff@saic.com> wrote:

>I have a question about encoding LDPCs.  There are two
>methods that seem to have the most general application, but I have not had
>success with either method.

>Both methods involve taking the original parity check matrix and
>manipulating it so that the square parity portion of the matrix is upper
>triangular (or nearly so) or decomposing the square parity portion of the
>matrix into complete upper and lower triangular matrices.

>The second decomposition is preferred to the first because the decoder
>becomes well defined performing back substitution to calculate the parity
>bits.  The first manipulation (also in Richardson and Urbanke's book Modern
>Coding Theory) results in some submatrices and the encoder is more
>complicated.

>My difficulty is in manipulating the check matrix so that the parity
>portion is non-singular.  I've tried several different regular code
>generation techniques and LU decomposition techniques which involve
>permuting the H matrix and none of the algorithms converge to a solution so
>that the parity portion is non-singular.  Is this a problem that involves
>extensive trial and error to find an H-matrix that will yield a
>non-singular parity portion or are there algorithms available that yield a
>higher probability of success?

>Of course my troubles so far do not even get into the question of whether
>or not the codes I have been generating are good codes.  I'm just trying to
>come up with the encoder!

In that case implement a straightforware, dumb, simple encoder and don't
even bother with these decompositions (which in reality may not save
you as many gates as you think).  Then investigate your code
performance.  THEN go back and tweak the logic design...

Steve
```
 0
Reply spope33 11/25/2009 6:18:59 AM

```>In that case implement a straightforware, dumb, simple encoder and don't
>even bother with these decompositions (which in reality may not save
>you as many gates as you think).  Then investigate your code
>performance.  THEN go back and tweak the logic design...
>
>Steve
>
Steve, thanks for the reply.  How do you implement the straightforward
simple encoder?  I know that the generator is a dual code of the check
matrix and this could be used to encode.  How do you derive the generator
matrix from the check matrix?  I know this is straightforward if the check
matrix is systematic (i.e. and identity matrix plus concatenated with
another matrix) but for LDPC, this is not the case.  Or is there some
simpler idea which I am missing?
Thanks,
Jim

```
 0
Reply ChinookPass 11/25/2009 4:28:13 PM

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