On LLR Mismatch in Belief Propagation Decoding of Overcomplete QLDPC Codes

Fuente: arXiv
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Main Authors: Cordova, Hernan, Balatsoukas-Stimming, Alexios, Liga, Gabriele, Gültekin, Yunus Can, Alvarado, Alex
Format: Preprint
Published: 2026
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author Cordova, Hernan
Balatsoukas-Stimming, Alexios
Liga, Gabriele
Gültekin, Yunus Can
Alvarado, Alex
author_facet Cordova, Hernan
Balatsoukas-Stimming, Alexios
Liga, Gabriele
Gültekin, Yunus Can
Alvarado, Alex
contents Belief propagation (BP) decoding of quantum low density parity check (QLDPC) codes is often implemented using overcomplete stabilizer (OS) representations, where redundant parity checks are introduced to improve finite length performance. Decoder behavior for such representations is governed primarily by finite iteration dynamics rather than asymptotic code properties. These dynamics are known to critically depend on the initialization of the decoder. In this paper, we investigate the impact of mismatched log likelihood ratios (LLRs) used for BP initialization on the performance of QLDPC codes with OS representations. Our results demonstrate that initial LLR mismatch has a strong influence on the frame error rate (FER), particularly in the low noise regime. We also show that the optimal performance is not sharply localized: the FER remains largely insensitive over an extended region of mismatched LLRs. This behavior motivates an interpretation of LLR mismatch as a regularization control parameter rather than a quantity that must be precisely matched to the quantum channel.
format Preprint
id arxiv_https___arxiv_org_abs_2603_04991
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On LLR Mismatch in Belief Propagation Decoding of Overcomplete QLDPC Codes
Cordova, Hernan
Balatsoukas-Stimming, Alexios
Liga, Gabriele
Gültekin, Yunus Can
Alvarado, Alex
Information Theory
Belief propagation (BP) decoding of quantum low density parity check (QLDPC) codes is often implemented using overcomplete stabilizer (OS) representations, where redundant parity checks are introduced to improve finite length performance. Decoder behavior for such representations is governed primarily by finite iteration dynamics rather than asymptotic code properties. These dynamics are known to critically depend on the initialization of the decoder. In this paper, we investigate the impact of mismatched log likelihood ratios (LLRs) used for BP initialization on the performance of QLDPC codes with OS representations. Our results demonstrate that initial LLR mismatch has a strong influence on the frame error rate (FER), particularly in the low noise regime. We also show that the optimal performance is not sharply localized: the FER remains largely insensitive over an extended region of mismatched LLRs. This behavior motivates an interpretation of LLR mismatch as a regularization control parameter rather than a quantity that must be precisely matched to the quantum channel.
title On LLR Mismatch in Belief Propagation Decoding of Overcomplete QLDPC Codes
topic Information Theory
url https://arxiv.org/abs/2603.04991