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

TL;DR

This paper introduces the syndrome adaptive gain Min-Sum (SAGMS) decoder for quantum LDPC codes, which adaptively adjusts message gain during decoding to improve performance without code-specific tuning.

Contribution

The paper proposes a novel SAGMS decoder that dynamically adapts gain based on stabilizer satisfaction, eliminating the need for fixed scaling optimization across different degrees.

Findings

SAGMS matches or outperforms offline optimized SMS in simulations.

SAGMS approaches belief propagation performance.

Under certain conditions, SAGMS outperforms BP while maintaining low complexity.

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.