Hybrid LDPC codes and iterative decoding methods - i3s

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Hybrid LDPC codes and iterative decoding methods - i3s

Conclusions and Perspectives

Conclusions

In this thesis, we have first proposed a new class of non-binary LDPC codes, named hybrid

LDPC codes. The asymptotic analysis of this new class has been carried out. Specific

properties of considered hybrid LDPC code ensembles, like the Linear-Map invariance,

have been expressed to be able to derive both stability condition and EXIT charts. The

stability condition of such hybrid LDPC ensembles shows interesting advantages over

non-binary codes. The EXIT charts analysis is performed on the BIAWGN channel. In

order to optimize the distributions of hybrid LDPC ensembles, we have investigated how

to project the message densities on only one scalar parameter using a Gaussian approximation.

The accuracy of such an approximation has been studied, and has led to two

kinds of EXIT charts for hybrid LDPC codes: multi-dimensional and mono-dimensional

EXIT charts. The distribution optimization allows to get finite length codes with very low

connection degrees and better waterfall region than protograph or multi-edge type LDPC

codes. Moreover, hybrid LDPC codes are well fitted for the cycle cancellation presented

in [34], thanks to their specific structure. Additionally to a better waterfall region, the

resulting codes have a very low error-floor for code rate one-half and codeword length

lower than three thousands bits, thereby competing with multi-edge 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 codes techniques.

We have also shown that hybrid LDPC codes can be very good candidates for efficient

low rate coding schemes. For code rate one sixth, they compare very well to

existing Turbo Hadamard or Zigzag Hadamard codes. More particularly, hybrid LDPC

codes exhibit very good minimum distances and error floor properties.

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 pruning away

edges from the Tanner graph of a mother code, using a machine learning algorithm, in

order to optimize the minimum distance. We showed that no relevant cost function can be

found for this problem. Hence, no pruning method could be applied. We have pointed out

that this pruning problem was not a classification problem, and that is why this approach

failed.

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