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Layered Normalized Min-Sum Decoding with Bit Flipping for FDPC Codes

Niloufar Hosseinzadeh, Mohsen Moradi, Hessam Mahdavifar

TL;DR

FDPC codes offer advantages over 5G-LDPC in high-rate regimes, motivating advanced decoding. The authors introduce a layered LNMS decoder with conflict-graph scheduling plus a syndrome-guided bit-flipping (SGBF) post-processing that generates candidate decodings by single-bit flips and selects the best by minimum syndrome weight. Across BI-AWGN simulations, the method achieves about $0.5$ dB gains over standalone LNMS at FER=$10^{-3}$ (e.g., FDPC$(256,192)$ with $T=128$ and up to $5$ iterations) and $0.75$–$1.5$ dB gains over polar and 5G-LDPC codes at the same length and rate. The results indicate faster convergence, improved error correction, and practical decoding complexity for short-to-medium block lengths.

Abstract

Fair-density parity-check (FDPC) codes have been recently introduced demonstrating improved performance compared to low-density parity-check (LDPC) codes standardized in 5G systems particularly in high-rate regimes. In this paper, we introduce a layered normalized min-sum (LNMS) message-passing decoding algorithm for the FDPC codes. We also introduce a syndrome-guided bit flipping (SGBF) method to enhance the error-correction performance of our proposed decoder. The LNMS decoder leverages conflict graph coloring for efficient layered scheduling, enabling faster convergence by grouping non-conflicting check nodes and updating variable nodes immediately after each layer. In the event of decoding failure, the SGBF method is activated, utilizing a novel reliability metric that combines log-likelihood ratio (LLR) magnitudes and syndrome-derived error counts to identify the least reliable bits. A set of candidate sequences is then generated by performing single-bit flips at these positions, with each candidate re-decoded via LNMS. The optimal candidate is selected based on the minimum syndrome weight. Extensive simulation results demonstrate the superiority of the proposed decoder. Numerical simulations on FDPC$(256,192)$ code with a bit-flipping set size of $T = 128$ and a maximum of $5$ iterations demonstrate that the proposed decoder achieves approximately a $0.5\,\mathrm{dB}$ coding gain over standalone LNMS decoding at a frame error rate (FER) of $10^{-3}$, while providing coding gains of $0.75-1.5\,\mathrm{dB}$ over other state-of-the-art codes including polar codes and 5G-LDPC codes at the same length and rate and also under belief propagation decoding.

Layered Normalized Min-Sum Decoding with Bit Flipping for FDPC Codes

TL;DR

FDPC codes offer advantages over 5G-LDPC in high-rate regimes, motivating advanced decoding. The authors introduce a layered LNMS decoder with conflict-graph scheduling plus a syndrome-guided bit-flipping (SGBF) post-processing that generates candidate decodings by single-bit flips and selects the best by minimum syndrome weight. Across BI-AWGN simulations, the method achieves about dB gains over standalone LNMS at FER= (e.g., FDPC with and up to iterations) and – dB gains over polar and 5G-LDPC codes at the same length and rate. The results indicate faster convergence, improved error correction, and practical decoding complexity for short-to-medium block lengths.

Abstract

Fair-density parity-check (FDPC) codes have been recently introduced demonstrating improved performance compared to low-density parity-check (LDPC) codes standardized in 5G systems particularly in high-rate regimes. In this paper, we introduce a layered normalized min-sum (LNMS) message-passing decoding algorithm for the FDPC codes. We also introduce a syndrome-guided bit flipping (SGBF) method to enhance the error-correction performance of our proposed decoder. The LNMS decoder leverages conflict graph coloring for efficient layered scheduling, enabling faster convergence by grouping non-conflicting check nodes and updating variable nodes immediately after each layer. In the event of decoding failure, the SGBF method is activated, utilizing a novel reliability metric that combines log-likelihood ratio (LLR) magnitudes and syndrome-derived error counts to identify the least reliable bits. A set of candidate sequences is then generated by performing single-bit flips at these positions, with each candidate re-decoded via LNMS. The optimal candidate is selected based on the minimum syndrome weight. Extensive simulation results demonstrate the superiority of the proposed decoder. Numerical simulations on FDPC code with a bit-flipping set size of and a maximum of iterations demonstrate that the proposed decoder achieves approximately a coding gain over standalone LNMS decoding at a frame error rate (FER) of , while providing coding gains of over other state-of-the-art codes including polar codes and 5G-LDPC codes at the same length and rate and also under belief propagation decoding.

Paper Structure

This paper contains 11 sections, 14 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proposed Decoder
  4. Layered Scheduling via Conflict Graph Coloring
  5. LNMS Message Passing Algorithm
  6. SGBF Method
  7. Numerical Results
  8. Performance Comparison with Standalone LNMS
  9. Impact of Bit-Flipping Set Size on Decoding Performance
  10. Decoding Complexity
  11. Conclusions

Figures (5)

  • Figure 1: FER performance of the FDPC$(128,80)$ codes with LNMS decoding and LNMS with SGBF list correction, compared with the corresponding 5G-LDPC and polar codes.
  • Figure 2: FER performance of the FDPC$(256,164)$ codes with LNMS decoding and LNMS with SGBF list correction, compared with the corresponding 5G-LDPC and polar codes.
  • Figure 3: FER performance of the FDPC$(256,192)$ codes with LNMS decoding and LNMS with SGBF list correction, compared with the corresponding 5G-LDPC and polar codes.
  • Figure 4: FER performance of the FDPC$(1024,844)$ codes with LNMS decoding and LNMS with SGBF list correction, compared with the corresponding 5G-LDPC and polar codes.
  • Figure 5: FER performance of the FDPC$(256,192)$ codes with LNMS with SGBF list correction for different bit-flipping set sizes.