{"paper":{"title":"Sequential Automorphism Ensemble Decoding with Early Stopping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A sequential activation scheme with early stopping thresholds cuts the complexity of automorphism ensemble decoding by 6 to 22 times while keeping block error rates almost unchanged.","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Bassant Selim, Charles Pillet, Fran\\c{c}ois Leduc-Primeau, Pascal Giard","submitted_at":"2026-04-30T21:37:54Z","abstract_excerpt":"In this paper, a low-complexity approach for the automorphism ensemble decoder (AED) using successive cancellation (SC) as constituent decoders is proposed. The approach sequentially activates sub-decoders and terminates the decoding process based on pre-optimized parameters, derived from the strong correlation observed between the decoding outcome and the SC path metric. An algorithm is proposed to find a list of early termination thresholds that minimize average decoding complexity subject to a block-error rate (BLER) constraint. For various code parameters and a BLER below $10^{-3}$, simula"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For various code parameters and a BLER below 10^{-3}, simulation results show that average decoding complexity is reduced by a factor of at least 6×, and up to 22×, compared to the original AED complexity, with a negligible degradation in BLER.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the observed correlation between the SC path metric and the final decoding outcome is strong enough and stable enough across code parameters that pre-optimized thresholds chosen on one set of simulations will continue to satisfy the BLER constraint on unseen data without requiring per-instance re-tuning.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Sequential activation with early termination thresholds for automorphism ensemble SC decoders reduces average complexity by 6x to 22x at BLER below 10^{-3} with negligible error-rate loss.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A sequential activation scheme with early stopping thresholds cuts the complexity of automorphism ensemble decoding by 6 to 22 times while keeping block error rates almost unchanged.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1922da497a3479828830ad4db0897d87523ccd51d8e4d3d996153c9d0edd5ad6"},"source":{"id":"2605.00255","kind":"arxiv","version":1},"verdict":{"id":"21acee6d-c948-4746-87e5-15ef45be052e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T19:25:43.563344Z","strongest_claim":"For various code parameters and a BLER below 10^{-3}, simulation results show that average decoding complexity is reduced by a factor of at least 6×, and up to 22×, compared to the original AED complexity, with a negligible degradation in BLER.","one_line_summary":"Sequential activation with early termination thresholds for automorphism ensemble SC decoders reduces average complexity by 6x to 22x at BLER below 10^{-3} with negligible error-rate loss.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the observed correlation between the SC path metric and the final decoding outcome is strong enough and stable enough across code parameters that pre-optimized thresholds chosen on one set of simulations will continue to satisfy the BLER constraint on unseen data without requiring per-instance re-tuning.","pith_extraction_headline":"A sequential activation scheme with early stopping thresholds cuts the complexity of automorphism ensemble decoding by 6 to 22 times while keeping block error rates almost unchanged."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.00255/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T20:35:40.875643Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:22:43.934244Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"9510f6aad214c87405d67c331388be8474addf15ddcbb33d785a3cae2d3b7b96"},"references":{"count":21,"sample":[{"doi":"","year":1954,"title":"A class of multiple-error-correcting codes and the decoding scheme,","work_id":"","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1954,"title":"Application of boolean algebra to switching circuit design and to error detection,","work_id":"","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"Channel polarization: a method for constructing capacity- achieving codes for symmetric binary-input memoryless channels,","work_id":"","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"On the efficiency of polar-like decoding for symmetric codes,","work_id":"","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"Automorphism ensemble decoding of Reed-Muller codes,","work_id":"","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":2,"snapshot_sha256":"c31790c96f3c0184d3c023fd71428b149f5b29d04aaea762b8b7e2dacb7b0efc","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"}