Improved Decoding of Quantum Tanner Codes Using Generalized Check Nodes
2026-03-05 • Information Theory
Information Theory
AI summaryⓘ
The authors study ways to improve decoding for quantum Tanner codes by grouping small check nodes into stronger combined checks and using a better decoding method called MAP during each iteration. They show that this new approach works better than existing methods for these codes, especially for codes of practical size. For other types of quantum codes, they suggest a greedy method to group checks but find limited improvement for some well-known code families. The authors also provide a theoretical analysis to explain when and why their method helps.
quantum Tanner codesbelief propagation (BP) decodingmaximum a posteriori (MAP) decoderquantum low-density parity-check (qLDPC) codesgeneralized bicycle codesbivariate bicycle codeshypergraph product codeslifted-product codesiterative decodingcycle analysis
Authors
Olai Å. Mostad, Eirik Rosnes, Hsuan-Yin Lin
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.