Selecting Two-Bit Bit Flipping Algorithms for Collective Error Correction

TL;DR

This paper introduces a method to select effective collections of two-bit bit flipping algorithms for decoding low-density parity-check codes, improving error correction by analyzing trapping set profiles.

Contribution

It proposes a recursive procedure to select algorithms based on trapping set profiles, enhancing parallel decoding performance.

Findings

Effective algorithm collections can correct multiple errors with high probability.

The recursive selection process improves decoding success rates.

The approach reduces the complexity of designing parallel decoders.

Abstract

A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in parallel can offer low error floor decoding for high-speed applications. As the number of two-bit bit flipping algorithms is large, designing such a decoder is not a trivial task. In this paper, we describe a procedure to select collections of algorithms that work well together. This procedure relies on a recursive process which enumerates error configurations that are uncorrectable by a given algorithm. The error configurations uncorrectable by a given algorithm form its trapping set profile. Based on their trapping set profiles, algorithms are selected so that in parallel, they can correct a fixed number of errors with high probability.