[Paper Review] Reliability-Based Windowed Decoding for Spatially-Coupled LDPC Codes

Peng Kang, Yixuan Xie+2 more|arXiv (Cornell University)|May 8, 2018

Error Correcting Code Techniques10 references3 citations

TL;DR

This paper proposes a reliability-based windowed decoding (RBWD) scheme for spatially-coupled LDPC codes that improves error floor performance by reserving only reliable messages from complete variable nodes between decoding windows and applying a partial syndrome check stopping rule. The method achieves bit error rate performance within 0.1 dB of full block decoding with significantly reduced decoding complexity.

ABSTRACT

In this letter, we propose a reliability-based windowed decoding scheme for spatially-coupled (SC) low-density parity-check (LDPC) codes. To mitigate the error propagation along the sliding windowed decoder of the SC LDPC codes, a partial message reservation (PMR) method is proposed where only the reliable messages generated in the previous decoding window are reserved for the next decoding window. We also propose a partial syndrome check (PSC) stopping rule for each decoding window, in which only the complete VNs are checked. Simulation results show that our proposed scheme significantly improves the error floor performance compared to the sliding windowed decoder with the conventional weighted bit-flipping (WBF) algorithm.

Motivation & Objective

• To address the high error floor in sliding windowed decoding of spatially-coupled LDPC codes caused by unreliable message propagation.
• To reduce decoding complexity while maintaining performance close to full block decoding (FBD).
• To improve the reliability of message passing between decoding windows by selectively reserving only reliable messages.
• To introduce a partial syndrome check stopping rule that enhances convergence and reduces error floor.

Proposed method

• Introduces a partial message reservation (PMR) mechanism that retains only messages from variable nodes (VNs) that are fully decoded (i.e., complete VNs) across adjacent decoding windows.
• Applies a partial syndrome check (PSC) stopping rule that validates only parity-check equations involving complete VNs, reducing false convergence.
• Uses a sliding window decoder with a fixed window size W, shifting the window along the Tanner graph to decode the codeword incrementally.
• Employs a hard-decision weighted bit-flipping (WBF) algorithm for low-complexity decoding, with reliability-based message selection to avoid propagating erroneous information.
• Defines 'complete VNs' as those whose all check node neighbors are within the current decoding window, ensuring message reliability.
• Introduces a stopping criterion that checks only the syndrome equations of complete VNs, improving decoding accuracy and reducing error floor.

Experimental results

Research questions

• RQ1 How can message propagation in windowed decoding of SC-LDPC codes be made more reliable to reduce error floor?
• RQ2 Can selective message reservation between decoding windows improve performance without increasing complexity?
• RQ3 Does a partial syndrome check stopping rule based only on complete VNs enhance decoding convergence and reduce error floor?
• RQ4 To what extent can a reliability-based windowed decoding scheme approach the performance of full block decoding?

Key findings

• The proposed RBWD scheme reduces the error floor significantly compared to conventional sliding windowed decoding with WBF.
• The BER performance of RBWD is within 0.1 dB of full block decoding (FBD) across multiple SNR regimes.
• For the length-38024 (7,49) SC-LDPC code, RBWD achieves an average iteration count of only 8 at 6 dB Eb/N0, compared to 17 for MBF-PMR and 18 for SBF-PMR.
• The method maintains high performance across different code structures, including both high-degree and low-degree SC-LDPC codes (e.g., (3,6)-regular).
• The partial syndrome check (PSC) stopping rule further reduces the error floor, especially in the waterfall and error floor regions.
• The scheme achieves a 50% reduction in average number of updates compared to baseline WBF schemes at high SNR, indicating lower decoding complexity.