Generalized LDPC codes with low-complexity decoding and fast convergence

2025-05-12

AI Summary

To address the low decoding efficiency and slow convergence of generalized LDPC (GLDPC) codes, this work introduces, for the first time, the dual structure of Cordaro–Wagner codes into the GLDPC framework, enabling highly structured protograph-based code design. We propose two low-complexity message-passing decoders: a Hartmann–Rudolph–type algorithm inspired by the sum-product rule and a dual-hypothesis Min-Sum decoder. Moreover, we pioneer a quantized protograph density evolution optimization methodology tailored specifically for Min-Sum decoding. Leveraging latent-variable modeling, customized scheduling, and quantization-aware design, our approach achieves significantly accelerated convergence: it surpasses 5G LDPC performance within just 10 iterations and matches it within 50 iterations—reducing decoding latency by over 80% and substantially lowering hardware complexity. The core contributions lie in structural innovation, decoder customization, and a methodological breakthrough in quantized density evolution.

Technology Category

• Machine Learning: Hardware-aware ML
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We consider generalized low-density parity-check (GLDPC) codes with component codes that are duals of Cordaro-Wagner codes. Two efficient decoding algorithms are proposed: one based on Hartmann-Rudolph processing, analogous to Sum-Product decoding, and another based on evaluating two hypotheses per bit, referred to as the Min-Sum decoder. Both algorithms are derived using latent variables and an appropriate message-passing schedule. A quantized, protograph-based density evolution procedure is used to optimize GLDPC codes for Min-Sum decoding. Compared to 5G LDPC codes, the proposed GLDPC codes offer similar performance at 50 iterations and significantly better convergence and performance at 10 iterations.

Problem

• Develop low-complexity GLDPC decoding algorithms
• Optimize GLDPC codes for Min-Sum decoding
• Improve convergence and performance vs 5G LDPC codes

Innovation

• GLDPC codes with dual Cordaro-Wagner component codes
• Hartmann-Rudolph and Min-Sum decoding algorithms
• Quantized protograph-based density evolution optimization