Finite Alphabet Iterative Decoders, Part II: Improved Guaranteed Error Correction of LDPC Codes via Iterative Decoder Diversity

TL;DR

This paper introduces a novel scheme using multiple finite alphabet iterative decoders (FAIDs) to enhance guaranteed error correction in LDPC codes by leveraging decoder diversity and trapping set knowledge.

Contribution

It proposes a systematic method to select diverse FAIDs that collectively improve error correction beyond individual capabilities on LDPC codes.

Findings

Significant increase in guaranteed error correction with decoder diversity.

Method effectively targets harmful trapping sets.

Demonstrated on (155,64) Tanner code with improved correction capability.

Abstract

Recently, we introduced a new class of finite alphabet iterative decoders (FAIDs) for low-density parity-check (LDPC) codes. These decoders are capable of surpassing belief propagation in the error floor region on the Binary Symmetric channel with much lower complexity. In this paper, we introduce a a novel scheme to further increase the guaranteed error correction capability from what is achievable by a FAID on column-weight-three LDPC codes. The proposed scheme uses a plurality of FAIDs which collectively correct more error patterns than a single FAID on a given code. The collection of FAIDs utilized by the scheme is judiciously chosen to ensure that individual decoders have different decoding dynamics and correct different error patterns. Consequently, they can collectively correct a diverse set of error patterns, which is referred to as decoder diversity. We provide a systematic method to generate the set of FAIDs for decoder diversity on a given code based on the knowledge of the most harmful trapping sets present in the code. Using the well-known column-weight-three $(155,64)$ Tanner code with $d_{min}$ = 20 as an example, we describe the method in detail and show that the guaranteed error correction capability can be significantly increased with decoder diversity.