{"paper":{"title":"Multiple-Bases Belief Propagation List Decoding for Quantum LDPC Codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"MBBP-LD improves quantum LDPC decoding by running parallel belief propagation across multiple parity-check bases derived from cycle-free Tanner subtrees.","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hessam Mahdavifar, Sheida Rabeti","submitted_at":"2026-05-13T22:49:35Z","abstract_excerpt":"In this paper, we propose a belief-propagation (BP)-based decoder, termed the Multiple-Bases Belief-Propagation List Decoder (MBBP-LD), for quantum low-density parity-check (QLDPC) codes. The key idea is to generate \\emph{structured decoding diversity} by constructing multiple redundant parity-check representations via cycle-free subtree decompositions of the Tanner graph, and running BP decoding in parallel across these representations. This extends the classical Multiple-Bases Belief-Propagation (MBBP) framework to the quantum setting while preserving the linear-time complexity and efficienc"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For bivariate bicycle codes [[144,12,12]] and [[288,12,18]], MBBP-LD achieves up to 20% reduction in error rate compared to BPGD and up to 30% compared to BP-OSD in the low- and moderate-error regimes while requiring substantially fewer total BP iterations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The cycle-free subtree decompositions of the Tanner graph produce sufficiently diverse and consistent parity-check representations that improve BP convergence without introducing new inconsistencies or requiring super-linear overhead.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"MBBP-LD creates multiple cycle-free subtree decompositions of the Tanner graph to run parallel BP decodings on quantum LDPC codes, cutting error rates by up to 30% versus BP-OSD and 20% versus BPGD on tested bivariate bicycle codes with fewer total iterations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"MBBP-LD improves quantum LDPC decoding by running parallel belief propagation across multiple parity-check bases derived from cycle-free Tanner subtrees.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f61845408fbe5f7ec45fc4021c9834031a7021acd895e23a395f29ba969b914b"},"source":{"id":"2605.14170","kind":"arxiv","version":1},"verdict":{"id":"92af6d86-1966-4956-bfa6-5c79a0d177ec","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:43:21.738775Z","strongest_claim":"For bivariate bicycle codes [[144,12,12]] and [[288,12,18]], MBBP-LD achieves up to 20% reduction in error rate compared to BPGD and up to 30% compared to BP-OSD in the low- and moderate-error regimes while requiring substantially fewer total BP iterations.","one_line_summary":"MBBP-LD creates multiple cycle-free subtree decompositions of the Tanner graph to run parallel BP decodings on quantum LDPC codes, cutting error rates by up to 30% versus BP-OSD and 20% versus BPGD on tested bivariate bicycle codes with fewer total iterations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The cycle-free subtree decompositions of the Tanner graph produce sufficiently diverse and consistent parity-check representations that improve BP convergence without introducing new inconsistencies or requiring super-linear overhead.","pith_extraction_headline":"MBBP-LD improves quantum LDPC decoding by running parallel belief propagation across multiple parity-check bases derived from cycle-free Tanner subtrees."},"references":{"count":23,"sample":[{"doi":"","year":1962,"title":"R. Gallager, “Low-density parity-check codes,”IRE Transactions on information theory, vol. 8, no. 1, pp. 21–28, 1962","work_id":"e4fcd8e9-c455-415e-b63f-fd5aa6f9b259","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2015,"title":"Fifteen years of quantum LDPC coding and improved decoding strategies,","work_id":"6d1032ff-1fa0-4f30-a96d-e26cb7c65ad3","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"Quantum low-density parity- check codes,","work_id":"fcccd828-c25e-4fb1-8187-d0d9eab61fdd","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Quantum low-density parity-check codes","work_id":"309b64a3-ed84-4a6b-ab00-a1b9d6ac53d0","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"Degenerate quantum LDPC codes with good finite length performance","work_id":"45bee9f2-7c04-4106-9652-e6cd494b04c0","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":23,"snapshot_sha256":"3d2319fa80357c040efa06bf9318a75b20e5080ff07e812e937b19df3c923fda","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}