Dynamic Weighted Bit-Flipping Decoding Algorithms for LDPC Codes

TL;DR

This paper introduces novel dynamic weighted bit-flipping algorithms for LDPC decoding, enhancing performance and complexity tradeoffs by updating checksum weights and selection rules based on node reliabilities.

Contribution

It proposes new flipping functions, selection rules, and update schedules that improve decoding performance while maintaining low complexity.

Findings

New decoders outperform traditional BF algorithms.

Performance comparable to normalized min-sum algorithm.

Reduced complexity with minimal performance loss.

Abstract

Bit-flipping (BF) decoding of low-density parity-check codes is of low complexity but gives inferior performance in general. To improve performance and provide new BF decoder options for complexity-performance tradeoffs, we propose new designs for the flipping function (FF), the flipped bit selection (FBS) rule and the checksum weight updating schedule. The new FF adjusts the checksum weights in every iteration while our FBS rules take more information into account. These two modifications represent efforts to track more closely the evolutions of both check and variable nodes' reliabilities. Two selective update schedules are proposed to offer more performance and complexity tradeoffs. The combinations of the new FBS rule and known FFs result in new BF decoders with improved performance and a modest complexity increase. On the other hand, combining the new FF and FBS rule gives a new decoder with performance comparable to that of the normalized min-sum algorithm while if we use a much simpler FBS rule instead, the decoder suffers little performance loss with reduced complexity. We also present a simple decision-theoretical argument to justify the new checksum weight formula and a time-expanded factor graph model to explain the proposed selective weight-updating schedules.