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

2026-05-11

AI Summary

Min-Sum decoding for quantum LDPC codes suffers from performance limitations due to a fixed scaling factor that fails to adapt to varying check-node degrees and noise levels. This work proposes a syndrome-adaptive gain control mechanism that dynamically adjusts message gains during decoding based on the proportion of unsatisfied stabilizers, eliminating the need for offline parameter tuning tailored to specific code structures or channel conditions. To the best of our knowledge, this is the first adaptive Min-Sum decoder that operates without offline optimization while achieving frame error rate performance on generalized bicycle quantum LDPC codes that matches or exceeds that of conventional scaled Min-Sum with offline-tuned parameters. In certain regimes, the proposed method even approaches or surpasses belief propagation, all while preserving the low computational complexity inherent to Min-Sum decoding.

Abstract

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.

Problem

• Quantum LDPC codes
• Min-Sum decoding
• message magnitude overestimation
• scaling factor
• syndrome adaptation

Innovation

• Syndrome Adaptive Gain
• Min-Sum Decoding
• Quantum LDPC Codes
• Dynamic Scaling
• Low-Complexity Decoding