{"paper":{"title":"Vectorized Generalized Nearest Neighbor Decoding for In-block Memory Channel","license":"http://creativecommons.org/licenses/by/4.0/","headline":"For in-block memory channels the optimal vectorized generalized nearest neighbor decoder admits an analytical characterization when Gaussian codebooks are employed.","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hao Wu, Shuqin Pang, Wenyi Zhang, Xinwei Li, Yuhao Liu","submitted_at":"2026-05-15T13:41:19Z","abstract_excerpt":"This work extends the generalized nearest neighbor decoding (GNND), originally developed as a receiver architecture for memoryless channels, to a vectorized GNND (Vec-GNND) suitable for in-block memory (IBM) channels. Leveraging the generalized mutual information (GMI) as an operational lower bound on the mismatch capacity, an analytical characterization of the optimal Vec-GNND is obtained for general IBM channels with Gaussian codebooks. The formalism further provides closed-form optimality conditions and achievable GMIs for restricted variants of the receiver architecture. Furthermore, we fo"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Leveraging the generalized mutual information (GMI) as an operational lower bound on the mismatch capacity, an analytical characterization of the optimal Vec-GNND is obtained for general IBM channels with Gaussian codebooks. The formalism further provides closed-form optimality conditions and achievable GMIs for restricted variants of the receiver architecture.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That Gaussian codebooks are employed and that the GMI lower bound remains sufficiently tight to characterize optimality for the vectorized receiver on general IBM channels (abstract, paragraph 2).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Vec-GNND yields closed-form optimality conditions and achievable GMIs for IBM channels with Gaussian codebooks, plus a GMI-based joint covariance-metric design that reduces to covariance optimization.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"For in-block memory channels the optimal vectorized generalized nearest neighbor decoder admits an analytical characterization when Gaussian codebooks are employed.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3c892b6767c2f73bbd466379fdc205857a207f0d1f081b3daf7e5836bdca0f73"},"source":{"id":"2605.15950","kind":"arxiv","version":1},"verdict":{"id":"83a0c232-bb9a-4b66-bdd3-3bd810cd1d6c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:28:17.182306Z","strongest_claim":"Leveraging the generalized mutual information (GMI) as an operational lower bound on the mismatch capacity, an analytical characterization of the optimal Vec-GNND is obtained for general IBM channels with Gaussian codebooks. The formalism further provides closed-form optimality conditions and achievable GMIs for restricted variants of the receiver architecture.","one_line_summary":"Vec-GNND yields closed-form optimality conditions and achievable GMIs for IBM channels with Gaussian codebooks, plus a GMI-based joint covariance-metric design that reduces to covariance optimization.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That Gaussian codebooks are employed and that the GMI lower bound remains sufficiently tight to characterize optimality for the vectorized receiver on general IBM channels (abstract, paragraph 2).","pith_extraction_headline":"For in-block memory channels the optimal vectorized generalized nearest neighbor decoder admits an analytical characterization when Gaussian codebooks are employed."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15950/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T20:01:19.110769Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:40:54.467657Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:44.881486Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:01:55.714709Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"a4b8d24bb96f97b859a2ac002385e90284eaee3680c0d08855403edc2dc87859"},"references":{"count":49,"sample":[{"doi":"","year":1948,"title":"A mathematical theory of communication,","work_id":"59e0a64d-9f40-470e-81bc-784fdf0fe462","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1965,"title":"I. 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