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Quasi-BP for BCH Codes and its Optimization

Guangwen Li

Abstract

This paper proposes a quasi-belief propagation decoder for BCH codes that systematically integrates domain knowledge--specifically, channel noise variance, the cyclic property of the codes, and the deliberate redundancy in their parity-check matrices--to enable efficient iterative decoding. We rigorously formalize this parallelizable decoder within an information-theoretic framework by tracking mutual information evolution through the constituent variable and check decoders, thereby validating the use of scattered EXIT charts as a tool for optimizing the decoder's parameters. At each iteration, an input dilation operation expands the set of messages, while a subsequent merging operation accelerates mutual information growth, ensuring rapid convergence. The proposed decoder achieves decoding performance approaching that of LDPC codes with comparable rate and blocklength, effectively pioneering the feasible deployment of BP-like decoding for high-density parity-check codes. The generality and robustness of the scheme are demonstrated through extensive simulations across codes of varying rates and blocklengths.

Quasi-BP for BCH Codes and its Optimization

Abstract

This paper proposes a quasi-belief propagation decoder for BCH codes that systematically integrates domain knowledge--specifically, channel noise variance, the cyclic property of the codes, and the deliberate redundancy in their parity-check matrices--to enable efficient iterative decoding. We rigorously formalize this parallelizable decoder within an information-theoretic framework by tracking mutual information evolution through the constituent variable and check decoders, thereby validating the use of scattered EXIT charts as a tool for optimizing the decoder's parameters. At each iteration, an input dilation operation expands the set of messages, while a subsequent merging operation accelerates mutual information growth, ensuring rapid convergence. The proposed decoder achieves decoding performance approaching that of LDPC codes with comparable rate and blocklength, effectively pioneering the feasible deployment of BP-like decoding for high-density parity-check codes. The generality and robustness of the scheme are demonstrated through extensive simulations across codes of varying rates and blocklengths.

Paper Structure

This paper contains 13 sections, 11 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. BP Variants and Neural Counterparts
  4. EXIT and S-EXIT Charts
  5. Method and Optimization
  6. Quasi-BP Iterative Decoding
  7. EXIT View of Quasi-BP
  8. Selection of $l_{\max}$
  9. Connection Between MI and FER
  10. Selection of $\delta_1$ and $\delta_2$
  11. Simulation and Analysis
  12. Potentials of Quasi-BP
  13. Reflections on Quasi-BP

Figures (5)

  • Figure 1: Comparison of BP and quasi-BP in EXIT view.
  • Figure 2: Association of $I_{_{E,V}}$ and $I_{_{E,C}}$ with $l_{\max}$ optimization and FER estimation under ($l_{\max}$, $\delta_1$, $\delta_2$) = (30, 2, 15) for BCH(127,64) code.
  • Figure 3: Impact of $\delta_1$ and $\delta_2$ on $I_{E,C}$ with respect to iteration index for BCH(127,64) code parameterized by varying SNR.
  • Figure 4: FER/BER of BCH(127,64) and LDPC(128,64) codes.
  • Figure 5: FER/BER for BCH(127,99) and BCH(255,239) codes.