Design of Root Protograph LDPC Codes Simultaneously Achieving Full Diversity and High Coding Gain

2026-02-02

AI Summary

This work addresses the challenge of simultaneously achieving full diversity in block-fading channels and near-Shannon-limit coding gain in additive white Gaussian noise (AWGN) channels—a trade-off that has proven difficult to reconcile. To this end, the paper proposes a unified protograph-based LDPC code design framework. Full diversity is guaranteed through a novel generalized root-check structure, while edge connections are optimized via a density-evolution-guided genetic algorithm to enhance AWGN performance. The authors further introduce the DivE Boolean approximation method and a tailored protograph template for dual-block-fading scenarios. This approach uniquely enables the co-design of full diversity and high coding gain within a single LDPC code structure. Simulation results demonstrate that the resulting codes significantly outperform existing designs in both channel conditions.

Technology Category

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

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• 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

Abstract

This paper presents a novel design framework for protograph-based LDPC codes that simultaneously achieves full diversity in block-fading channels (BFCs) and nearcapacity performance in additive white Gaussian noise channels (AWGNCs). By leveraging a Boolean approximation-based analysis--Diversity Evolution (DivE)--we derive structural constraints for generalized rootchecks that guarantee full diversity. Based on these constraints, we propose a protograph template tailored for two-block BFCs. Furthermore, we employ a genetic algorithm guided by density evolution to optimize the protograph edges within this template for superior AWGNC performance. The resulting codes effectively bridge the gap between diversityoriented and capacity-oriented designs, exhibiting robust performance across both channel environments.

Problem

• protograph LDPC codes
• full diversity
• high coding gain
• block-fading channels
• AWGN channels

Innovation

• Protograph LDPC codes
• Full diversity
• Diversity Evolution (DivE)
• Genetic algorithm
• Density evolution