[Discuss-gnuradio] GSoC 2013 Status : Project - LDPC codes and more FEC in GNU Radio

[Manu T S]

Hi,

I'm Manu, one of the 5 GSoC students. I am working on LDPC codes, in parallel with Tracie, mentored by Jens. Going on is the 4th week of GSoC.

Given below is a description of current status of the project.

I'm glad to inform that I was successful in making an out of tree module (in python) gr-ldpc which which implements encoding and decoding of LDPC codes.

Some performance statistics is available here.

The codes are available here.

The code used to generate the above mentioned performance statistics is available as an example in gr-ldpc/examples/ folder.

Encoder operation.
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Encoder takes an LDPC matrix as parameter, and reduces the matrix into form [I P].

The codewords is the set of x which satisfy [I P]x = 0.

A vector of length = # of columns of P is taken as data-word. Entries of data-word form the systematic part of the codeword, filling the entries corresponding to the columns of P.

The entries of x corresponding to I form the parity check matrix and are formed by back-substitution.

Decoder operation

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Decoder takes an LDPC matrix as parameter.

Decoder implements sum product algorithm.

A decoder with likelihood messages[1] is implemented.

A decoder with log-likelihood messages[2] is also implemented.

On testing against predefined codes available in good error correction is observed.

LDPC Code construction
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Option to read LDPC code defined as "alist" file[3] is provided.
Thus many predefined codes can be used with the encoder and decoder.

Construction of LDPC codes based on Reed Solomon codes[4] is implemented

It did not produce similar performance as the predefined code.

Goals to be achieved before midterm evaluation.

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Next some algorithms for construction of LDPC codes will be implemented.

Namely progressive edge growth algorithm will be implemented.

References

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[1]. http://www.cs.utoronto.ca/~radford/ftp/LDPC-2012-02-11/decoding.html

[2]. "Modern Coding Theory"
[3]. http://www.inference.phy.cam.ac.uk/mackay/codes/alist.html

[4]. "A class of Low-Density Parity-Check codes constructed based on Reed-Solomon codes with Two information symbols", IEEE communications letters, July 2003.

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Manu T S

PS. I very much want to talk to you all in the coming developers call, but the proxy in my university seems to be blocking hangout.

I'm working on resolving this issue.