5G LDPC Codes as Root LDPC Codes via Diversity Alignment

TL;DR

This paper introduces a novel diversity evolution analysis method for protograph-based QC-LDPC codes over nonergodic channels, enabling optimized block mappings that ensure full diversity and improve error performance in 5G LDPC codes.

Contribution

It develops the diversity evolution (DivE) method and a greedy block-mapping search to guarantee full diversity for all information bits without altering the base graph.

Findings

Proposed block mappings guarantee full diversity for all information bits.

Mapped codes show steeper high-SNR slope and lower BLER.

Method applies to 5G LDPC codes with improved error performance.

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.