Hybrid LDPC codes and iterative decoding methods - i3s

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Hybrid LDPC codes and iterative decoding methods - i3s

22 Introduction

◦ Several classification methods have been studied to see whether they might

advantageously substitute the BP decoder. The fundamental reason why this is

not possible is exhibited: those methods are non-parametric machine learning

algorithms where the elements to be classified, must be highly non-uniformly

distributed. However, the channel coding problem corresponds to the opposite

case.

• A class of two-bit message passing decoders for decoding column-weight-four

LDPC codes over the binary symmetric channel is proposed and analyzed.

◦ Thresholds are derived for various decoders in this class.

◦ We consider a specific decoder in this class, and prove sufficient conditions

for a code with Tanner graph of girth six to correct three errors.

◦ A code satisfying the conditions is constructed and numerical assessment of

the code performance is provided via simulation results.

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