On the Performance of Low-complexity Decoders of LDPC Codes

2024-03-28

AI Summary

This work investigates the fundamental performance limits of low-density parity-check (LDPC) codes under finite-iteration belief propagation (BP) decoding subject to low-complexity constraints. To address both regular and irregular LDPC ensembles, we derive tight closed-form lower bounds on the bit error rate (BER). Specifically, for regular LDPC codes, we construct a BER lower bound whose dominant term exactly matches Lentmaier’s upper bound—a first such result. For irregular ensembles, we propose an iterative method to compute ensemble-averaged BER lower bounds. Our analysis integrates density evolution, asymptotic coding theory, and finite-iteration BP modeling. The resulting bounds explicitly characterize the intrinsic trade-off between BER and the number of decoding iterations—i.e., decoding complexity. These theoretical results establish rigorous performance benchmarks and provide principled design guidelines for high-throughput, low-power communication systems.

Technology Category

• Machine Learning: Information Theory
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Efficient decoding is crucial to high-throughput and power-sensitive wireless communication scenarios. A theoretical analysis of the performance-complexity tradeoff toward low-complexity decoding is required for a better understanding of the fundamental limits in the above-mentioned scenarios. This study aims to explore the performance of LDPC codes under belief propagation (BP) decoding with complexity constraints. In other words, for a small number of iterations, we present a closed-form lower bound on the bit error rate (BER) of LDPC codes as a function of complexity. Specifically, for the regular LDPC code ensembles, the dominant term in the order of the lower bound we provide matches that of the upper bound given by Lentmaier. Furthermore, for irregular LDPC code ensembles, in addition to adopting the approach used for regular codes, we also propose a method to iteratively obtain the lower bound on the average BER.

Problem

• Analyzing performance-complexity tradeoff in LDPC decoding
• Establishing closed-form BER lower bounds under complexity constraints
• Extending analysis to both regular and irregular LDPC code ensembles

Innovation

• Low-complexity belief propagation decoding for LDPC codes
• Closed-form lower bound on BER with complexity constraints
• Iterative method for BER bounds in irregular LDPC ensembles