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An Optimization Model for Offline Scheduling Policy of Low-density Parity-check Codes

Dongxu Chang, Zhiming Ma, Guanghui Wang, Guiying Yan, Dawei Yin

TL;DR

The paper tackles decoding latency and complexity in LDPC belief-propagation by introducing an offline scheduling framework that jointly optimizes complexity and decoding performance. It formalizes a complexity–performance paradigm using $NMP$, $AE$, and $GAP$, and defines deformation speeds $\tau_{AE}$ and $\tau_{GAP}$ to guide sequence optimization. The authors propose the Successive-Searching BP (SSBP) algorithm, a CN-centric local-search method with an upper-bound on average search rounds, and demonstrate substantial reductions in decoding complexity (e.g., $>$$20\%$) and improved error-rate performance on 5G NR LDPC codes. This approach offers practical gains for high-throughput systems by enabling faster, more energy-efficient decoding without increasing runtime scheduling overhead, with avenues for further improvement via ML or metaheuristic optimization and theoretical optimality analysis.

Abstract

In this study, an optimization model for offline scheduling policy of low-density parity-check (LDPC) codes is proposed to improve the decoding efficiency of the belief propagation (BP). The optimization model uses the number of messages passed (NMP) as a metric to evaluate complexity, and two metrics, average entropy (AE), and gap to maximum a posteriori (GAP), to evaluate BP decoding performance. Based on this model, an algorithm is proposed to optimize the scheduling sequence for reduced decoding complexity and superior performance compared to layered BP. We validated the proposed algorithm on LDPC codes constructed following 5G New Radio, which resulted in a reduction of decoding complexity of more than 20$\%$ compared to LBP.

An Optimization Model for Offline Scheduling Policy of Low-density Parity-check Codes

TL;DR

The paper tackles decoding latency and complexity in LDPC belief-propagation by introducing an offline scheduling framework that jointly optimizes complexity and decoding performance. It formalizes a complexity–performance paradigm using , , and , and defines deformation speeds and to guide sequence optimization. The authors propose the Successive-Searching BP (SSBP) algorithm, a CN-centric local-search method with an upper-bound on average search rounds, and demonstrate substantial reductions in decoding complexity (e.g., ) and improved error-rate performance on 5G NR LDPC codes. This approach offers practical gains for high-throughput systems by enabling faster, more energy-efficient decoding without increasing runtime scheduling overhead, with avenues for further improvement via ML or metaheuristic optimization and theoretical optimality analysis.

Abstract

In this study, an optimization model for offline scheduling policy of low-density parity-check (LDPC) codes is proposed to improve the decoding efficiency of the belief propagation (BP). The optimization model uses the number of messages passed (NMP) as a metric to evaluate complexity, and two metrics, average entropy (AE), and gap to maximum a posteriori (GAP), to evaluate BP decoding performance. Based on this model, an algorithm is proposed to optimize the scheduling sequence for reduced decoding complexity and superior performance compared to layered BP. We validated the proposed algorithm on LDPC codes constructed following 5G New Radio, which resulted in a reduction of decoding complexity of more than 20 compared to LBP.
Paper Structure (15 sections, 1 theorem, 18 equations, 1 figure, 2 tables, 2 algorithms)

This paper contains 15 sections, 1 theorem, 18 equations, 1 figure, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Basic definitions of LDPC codes
  4. Relative LDPC decoding schemes
  5. Flooding BP
  6. Layered BP (LBP)hocevar2004reduced
  7. The metric to measure the decoding complexity
  8. Two metrics to measure the decoding performance
  9. Average entropy (AE)
  10. Gap to maximum a posteriori (GAP)yin2022message
  11. Scheduling Strategies
  12. SSBP$\textendash$new scheduling strategy
  13. Average-case computational complexity analysis
  14. Simulation Results
  15. Conclusion

Key Result

Proposition 1

The average number of rounds SSBP required is less than $SM^{2h+1}$.

Figures (1)

  • Figure 1: Average entropy (AE), GAP, BER, and BLER vs. NMP for different scheduling policies in (512, 384) BG1 graph, where the number of iterations is fixed to be 5. SSBP has the fastest descent speed and better error-rate performance.

Theorems & Definitions (2)

  • Proposition 1
  • proof