Automorphism Ensemble Decoding of Quasi-Cyclic LDPC Codes by Breaking Graph Symmetries

TL;DR

This paper introduces a method to improve belief propagation decoding of quasi-cyclic LDPC codes by breaking graph symmetries through small modifications, leading to better error correction and significantly reduced latency.

Contribution

The paper proposes a novel symmetry-breaking technique for automorphism ensemble decoding of QC-LDPC codes that enhances performance without increasing decoding latency.

Findings

Gains of 0.2 to 0.3 dB over conventional BP decoding.

Reduces average decoding latency by over eight times compared to SBP.

Effective on codes from CCSDS, 802.11n, and 5G standards.

Abstract

We consider automorphism ensemble decoding (AED) of quasi-cyclic (QC) low-density parity-check (LDPC) codes. Belief propagation (BP) decoding on the conventional factor graph is equivariant to the quasi-cyclic automorphisms and therefore prevents gains by AED. However, by applying small modifications to the parity-check matrix at the receiver side, we can break the symmetry without changing the code at the transmitter. This way, we can leverage a gain in error-correcting performance using an ensemble of identical BP decoders, without increasing the worst-case decoding latency. The proposed method is demonstrated using LDPC codes from the CCSDS, 802.11n and 5G standards and produces gains of 0.2 to 0.3 dB over conventional BP decoding. Compared to the similarly performing saturated BP (SBP), the proposed algorithm reduces the average decoding latency by more than eight times.