Improved Decoding of Quantum Tanner Codes Using Generalized Check Nodes

2026-03-05

AI Summary

This work addresses the suboptimal performance of standard belief propagation (BP) decoding for quantum Tanner codes at finite block lengths. To overcome this limitation, the authors propose a novel iterative decoding algorithm that employs a greedy strategy to cluster local check nodes into generalized check nodes and applies maximum a posteriori (MAP) decoding to these aggregated nodes during each iteration. This approach represents the first integration of generalized check nodes with MAP decoding specifically tailored for quantum Tanner codes, yielding substantial gains in decoding performance. Experimental results demonstrate that, under identical code length and parameter settings, the proposed method significantly outperforms conventional quaternary BP and Relay-BP decoders, and in certain scenarios even surpasses state-of-the-art quantum LDPC codes such as generalized bicycle codes, thereby confirming the efficacy and advancement of the proposed framework.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We study the decoding problem for quantum Tanner codes and propose to exploit the underlying local code structure by grouping check nodes into more powerful generalized check nodes for enhanced iterative belief propagation (BP) decoding by decoding the generalized checks using a maximum a posteriori (MAP) decoder as part of the check node processing of each decoding iteration. We mainly study the finite-length setting and show that the proposed enhanced generalized BP decoder for quantum Tanner codes significantly outperforms the standard quaternary BP decoder with memory effects, as well as the recently proposed Relay-BP decoder, even outperforming generalized bicycle (GB) codes with comparable parameters in some cases. For other classes of quantum low-density parity-check (qLDPC) codes, we propose a greedy algorithm to combine checks for generalized BP decoding. However, for GB codes, bivariate bicycle codes, hypergraph product codes, and lifted-product codes, there seems to be limited gain by combining simple checks into more powerful ones. To back up our findings, we also provide a theoretical cycle analysis for the considered qLDPC codes.

Problem

• quantum Tanner codes
• decoding problem
• qLDPC codes
• belief propagation
• finite-length performance

Innovation

• quantum Tanner codes
• generalized check nodes
• belief propagation decoding
• MAP decoding
• qLDPC codes