Syndrome Adaptive Gain Control for Min-Sum Decoding of Quantum LDPC Codes

Fuente: arXiv
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Main Authors: Cordova, Hernan, Balatsoukas-Stimming, Alexios, Gültekin, Yunus Can, Liga, Gabriele, Alvarado, Alex
Format: Preprint
Published: 2026
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author Cordova, Hernan
Balatsoukas-Stimming, Alexios
Gültekin, Yunus Can
Liga, Gabriele
Alvarado, Alex
author_facet Cordova, Hernan
Balatsoukas-Stimming, Alexios
Gültekin, Yunus Can
Liga, Gabriele
Alvarado, Alex
contents Min-Sum (MS) decoding is a popular low-complexity alternative to belief propagation (BP), retaining only the minimum incoming message magnitude during check-node (CN) processing, at the cost of systematic message magnitude overestimation. The scaled MS (SMS) decoder compensates for this effect using a fixed scaling factor. We propose the syndrome adaptive gain Min-Sum (SAGMS) decoder for quantum low-density parity-check (QLDPC) codes, which adapts the message gain online based on the fraction of unsatisfied stabilizers, requiring no per-code or per-noise level optimization. We show that the scaling factor required for SMS to match belief propagation decreases with the CN degree, so any fixed scaling optimized for one degree incurs into a growing penalty as the CN degree varies. SAGMS avoids this limitation by adapting the gain during decoding. Simulations on generalized bicycle QLDPC codes demonstrate that SAGMS matches or outperforms the frame error rate (FER) of an offline optimized SMS decoder. Moreover, SAGMS approaches BP performance and, under certain conditions outperforms it while retaining MS-level complexity.
format Preprint
id arxiv_https___arxiv_org_abs_2605_10433
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Syndrome Adaptive Gain Control for Min-Sum Decoding of Quantum LDPC Codes
Cordova, Hernan
Balatsoukas-Stimming, Alexios
Gültekin, Yunus Can
Liga, Gabriele
Alvarado, Alex
Information Theory
Signal Processing
Min-Sum (MS) decoding is a popular low-complexity alternative to belief propagation (BP), retaining only the minimum incoming message magnitude during check-node (CN) processing, at the cost of systematic message magnitude overestimation. The scaled MS (SMS) decoder compensates for this effect using a fixed scaling factor. We propose the syndrome adaptive gain Min-Sum (SAGMS) decoder for quantum low-density parity-check (QLDPC) codes, which adapts the message gain online based on the fraction of unsatisfied stabilizers, requiring no per-code or per-noise level optimization. We show that the scaling factor required for SMS to match belief propagation decreases with the CN degree, so any fixed scaling optimized for one degree incurs into a growing penalty as the CN degree varies. SAGMS avoids this limitation by adapting the gain during decoding. Simulations on generalized bicycle QLDPC codes demonstrate that SAGMS matches or outperforms the frame error rate (FER) of an offline optimized SMS decoder. Moreover, SAGMS approaches BP performance and, under certain conditions outperforms it while retaining MS-level complexity.
title Syndrome Adaptive Gain Control for Min-Sum Decoding of Quantum LDPC Codes
topic Information Theory
Signal Processing
url https://arxiv.org/abs/2605.10433