Hybrid LDPC codes and iterative decoding methods - i3s

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Hybrid LDPC codes and iterative decoding methods - i3s

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Abstract

This thesis is dedicated to the analysis and the design of sparse-graph codes for channel

coding. The aim is to construct coding schemes having high performance both in the

waterfall and in the error-floor regions under iterative decoding.

In the first part, a new class of LDPC codes, named hybrid LDPC codes, is introduced.

Their asymptotic analysis for memoryless symmetric channel is performed, and leads to

code parameter optimization for the binary input Gaussian channel. Additionally to a

better waterfall region, the resulting codes have a very low error-floor for code rate onehalf

and codeword length lower than three thousands bits, thereby competing with multiedge

type LDPC. Thus, hybrid LDPC codes allow to achieve an interesting trade-off

between good error-floor performance and good waterfall region with non-binary coding

techniques.

In the second part of the thesis, we have tried to determine which kind of machine

learning methods would be useful to design better LDPC codes and better decoders in

the short code length case. We have first investigated how to build the Tanner graph of

a code by removing edges from the Tanner graph of a mother code, using a machine

learning algorithm, in order to optimize the minimum distance. We have also investigated

decoder design by machine learning methods in order to perform better than BP which is

suboptimal as soon as there are cycles in the graph.

In the third part of the thesis, we have moved towards quantized decoding in order

to address the same problem: finding rules to decode difficult error configurations. We

have proposed a class of two-bit decoders. We have derived sufficient conditions for a

column-weight four code with Tanner graph of girth six to correct any three errors. These

conditions show that decoding with the two-bit rule allows to ensure weight-three error

correction capability for higher rate codes than the decoding with one bit.

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