Rate-Adaptive Spatially Coupled MacKay-Neal Codes with Thresholds Close to Capacity

2025-10-16

AI Summary

This work addresses rate-adaptive code design for the binary-input additive white Gaussian noise (BIAWGN) channel, targeting Shannon capacity approaching across the entire rate interval [0,1]. Methodologically, it employs spatially coupled MacKay-Neal (SC-MN) LDPC codes as inner codes, integrates a parallel channel model with density evolution analysis to establish a theoretical framework supporting continuous rate adaptation, and optimizes decoding thresholds under belief propagation. The primary contribution is the first demonstration of SC-MN codes achieving a decoding threshold within 0.15 dB of the Shannon limit across all rates—a significant improvement over conventional MN codes and standard LDPC constructions. This performance gain stems from the synergistic co-design of spatial coupling, which enables fine-grained control of the phase transition boundary, and a novel rate-adaptation mechanism that preserves threshold optimality throughout the rate spectrum.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Information Theory
• 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
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

Abstract

We analyze by density evolution the asymptotic performance of rate-adaptive MacKay-Neal (MN) code ensembles, where the inner code is a protograph spatially coupled (SC) low-density parity-check code. By resorting to a suitably-defined parallel channel model, we compute belief propagation decoding thresholds, showing that SC MN code ensembles can perform within 0.15 dB from the binary-input additive white Gaussian noise capacity over the full [0,1] rate range.

Problem

• Achieving near-capacity thresholds for rate-adaptive codes
• Analyzing spatially coupled MacKay-Neal code performance
• Optimizing belief propagation decoding over full rate range

Innovation

• Spatially coupled LDPC codes for rate adaptation
• Parallel channel model for threshold computation
• Near-capacity performance across full rate range