5G LDPC Codes as Root LDPC Codes via Diversity Alignment

2026-01-30

AI Summary

This work addresses the challenge that 5G NR protograph-based QC-LDPC codes fail to guarantee full diversity for information bits over non-ergodic block-fading channels. To overcome this limitation, the authors propose a Diversity Evolution (DivE) approach, which introduces Boolean functions to model the evolution of variable nodes affected by channel fading during belief propagation decoding. A greedy block-mapping search algorithm is designed to optimize the assignment of variable nodes to fading blocks, thereby achieving full diversity for information bits without altering the underlying 5G base graph structure. Experimental results demonstrate that the proposed mapping significantly improves block error rate performance at high signal-to-noise ratios, yielding a steeper error-rate decay slope.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This paper studies the diversity of protographbased quasi-cyclic low-density parity-check (QC-LDPC) codes over nonergodic block-fading channels under iterative beliefpropagation decoding. We introduce diversity evolution (DivE), a Boolean-function-based analysis method that tracks how the fading dependence of belief-propagation messages evolves across decoding iterations. Under a Boolean approximation of block fading, DivE derives a Boolean fading function for each variable node (VN) output (i.e., the a-posteriori reliability after iterative decoding), from which the VN diversity order can be directly determined. Building on this insight, we develop a greedy blockmapping search that assigns protograph VNs to fading blocks so that all information VNs achieve full diversity, while including the minimum additional parity VNs when full diversity is infeasible at the nominal rate. Numerical results on the 5G New Radio LDPC codes show that the proposed search finds block mappings that guarantee full diversity for all information bits without modifying the base-graph structure, yielding a markedly steeper high-SNR slope and lower BLER than random mappings.

Problem

• QC-LDPC codes
• block-fading channels
• diversity order
• 5G LDPC codes
• full diversity

Innovation

• Diversity Evolution
• QC-LDPC codes
• block-fading channels
• belief-propagation decoding
• 5G New Radio