Layered Normalized Min-Sum Decoding with Bit Flipping for FDPC Codes

2025-10-01

AI Summary

To address the limited decoding performance of high-rate finite-dimensional parity-check (FDPC) codes in 5G scenarios, this paper proposes a layered normalized min-sum (LNMS) decoding algorithm integrating conflict-graph coloring scheduling and syndrome-guided refinement. The method introduces a novel LLR-syndrome joint reliability metric, enforces conflict-free inter-layer message passing, and—upon decoding failure—dynamically identifies the most unreliable bits, performs bit-flipping guided by the minimum-weight syndrome, and re-decodes candidate sequences. Experimental results demonstrate that, for the FDPC(256,192) code, the proposed algorithm achieves a 0.5 dB SNR gain over standard LNMS decoding. Moreover, at identical blocklength and code rate, it attains 0.75–1.5 dB coding gain over both 5G LDPC and polar codes, significantly enhancing the practical competitiveness of high-rate FDPC codes in 5G applications.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Algorithm Configuration
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Fair-density parity-check (FDPC) codes have been recently introduced demonstrating improved performance compared to low-density parity-check (LDPC) codes standardized in 5G systems particularly in high-rate regimes. In this paper, we introduce a layered normalized min-sum (LNMS) message-passing decoding algorithm for the FDPC codes. We also introduce a syndrome-guided bit flipping (SGBF) method to enhance the error-correction performance of our proposed decoder. The LNMS decoder leverages conflict graph coloring for efficient layered scheduling, enabling faster convergence by grouping non-conflicting check nodes and updating variable nodes immediately after each layer. In the event of decoding failure, the SGBF method is activated, utilizing a novel reliability metric that combines log-likelihood ratio (LLR) magnitudes and syndrome-derived error counts to identify the least reliable bits. A set of candidate sequences is then generated by performing single-bit flips at these positions, with each candidate re-decoded via LNMS. The optimal candidate is selected based on the minimum syndrome weight. Extensive simulation results demonstrate the superiority of the proposed decoder. Numerical simulations on FDPC$(256,192)$ code with a bit-flipping set size of $T = 128$ and a maximum of $5$ iterations demonstrate that the proposed decoder achieves approximately a $0.5,mathrm{dB}$ coding gain over standalone LNMS decoding at a frame error rate (FER) of $10^{-3}$, while providing coding gains of $0.75-1.5,mathrm{dB}$ over other state-of-the-art codes including polar codes and 5G-LDPC codes at the same length and rate and also under belief propagation decoding.

Problem

• Enhancing error-correction performance for FDPC codes
• Developing layered normalized min-sum decoding with efficient scheduling
• Improving decoding reliability through syndrome-guided bit flipping

Innovation

• Layered normalized min-sum decoding with conflict graph coloring
• Syndrome-guided bit flipping using LLR and syndrome metrics
• Hybrid decoding combining LNMS with selective bit flipping