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

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 article 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.

Automated summary

This article introduces enhancements to traditional adaptive belief propagation (ABP) decoding technique for high-density parity-check (HDPC) algebraic codes, aiming to improve performance by incorporating unstable bits with large LLRs and applying partial layered scheduling or hybrid dynamic scheduling. Simulation results demonstrate that the proposed Perturbed ABP (P-ABP) decoding algorithms lead to improved error correction performances and faster convergence rates compared to prior-art ABP variants.