On LLR Mismatch in Belief Propagation Decoding of Overcomplete QLDPC Codes

2026-03-05

AI Summary

This study investigates the impact of initial log-likelihood ratio (LLR) mismatch on the performance of quantum low-density parity-check (QLDPC) codes under belief propagation (BP) decoding in the regime of overcomplete stabilizer representations. Addressing the sensitivity of frame error rates to LLR initialization in low-noise regions, the work employs finite-iteration dynamic modeling and numerical analysis to demonstrate that LLR mismatch can function effectively as a regularization parameter rather than requiring precise alignment with channel parameters. The findings reveal that decoding performance remains robust across a broad range of mismatched LLR values, maintaining strong error-correction capability even in low-noise scenarios. These results offer practical guidance for the design of robust QLDPC decoders and highlight the potential of deliberately tuning LLR mismatch to enhance decoding stability and performance.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

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.

Problem

• LLR mismatch
• belief propagation
• QLDPC codes
• overcomplete stabilizer
• frame error rate

Innovation

• LLR mismatch
• belief propagation
• overcomplete stabilizer
• QLDPC codes
• regularization