Perturbed Adaptive Belief Propagation Decoding for High-Density Parity-Check Codes

TL;DR

This paper introduces a Perturbed Adaptive Belief Propagation (P-ABP) decoding method that improves error correction and convergence for high-density parity-check codes by incorporating unstable bits with large LLRs into the decoding process.

Contribution

The paper proposes a novel P-ABP decoding algorithm that enhances traditional ABP by perturbing the sparsification process to include unstable bits, along with improved scheduling strategies.

Findings

P-ABP outperforms traditional ABP in error correction.

Faster convergence rates achieved with P-ABP.

Improved performance demonstrated through simulations.

Abstract

Algebraic codes such as BCH code are receiving renewed interest as their short block lengths and low/no error floors make them attractive for ultra-reliable low-latency communications (URLLC) in 5G wireless networks. This paper aims at enhancing the traditional adaptive belief propagation (ABP) decoding, which is a soft-in-soft-out (SISO) decoding for high-density parity-check (HDPC) algebraic codes, such as Reed-Solomon (RS) codes, Bose-Chaudhuri-Hocquenghem (BCH) codes, and product codes. The key idea of traditional ABP is to sparsify certain columns of the parity-check matrix corresponding to the least reliable bits with small log-likelihood-ratio (LLR) values. This sparsification strategy may not be optimal when some bits have large LLR magnitudes but wrong signs. Motivated by this observation, we propose a Perturbed ABP (P-ABP) to incorporate a small number of unstable bits with large LLRs into the sparsification operation of the parity-check matrix. In addition, we propose to apply partial layered scheduling or hybrid dynamic scheduling to further enhance the performance of P-ABP. Simulation results show that our proposed decoding algorithms lead to improved error correction performances and faster convergence rates than the prior-art ABP variants.