{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YIORKUHBCGEPW5FZEWLKXKAERB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"87ffc1c57dc52c667381c5f870a8b45e2dc8caed9cb141f895db69b452a114a9","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-05-22T17:40:16Z","title_canon_sha256":"7c2b8bc854194fcc355306ae1afb630f33b331301d43fd2aa9965fd79a8dc98d"},"schema_version":"1.0","source":{"id":"0905.3733","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3733","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3733v1","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3733","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"pith_short_12","alias_value":"YIORKUHBCGEP","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YIORKUHBCGEPW5FZ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YIORKUHB","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:7589514202e26ca0e91a5808401a73ae32f04b0a1034bf671b4b16723291f99f","target":"graph","created_at":"2026-05-18T00:59:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The serial concatenation of a repetition code with two or more accumulators has the advantage of a simple encoder structure. Furthermore, the resulting ensemble is asymptotically good and exhibits minimum distance growing linearly with block length. However, in practice these codes cannot be decoded by a maximum likelihood decoder, and iterative decoding schemes must be employed. For low-density parity-check codes, the notion of trapping sets has been introduced to estimate the performance of these codes under iterative message passing decoding. In this paper, we present a closed form finite l","authors_text":"Alexandre Graell i Amat, Christian Koller, Daniel J. Costello Jr, Joerg Kliewer","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-05-22T17:40:16Z","title":"Trapping Set Enumerators for Repeat Multiple Accumulate Code Ensembles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3733","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c00b950823aac0d7123f31e3a28e954e5aacbd8c2220b7e3eec0bd1498fa2368","target":"record","created_at":"2026-05-18T00:59:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"87ffc1c57dc52c667381c5f870a8b45e2dc8caed9cb141f895db69b452a114a9","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-05-22T17:40:16Z","title_canon_sha256":"7c2b8bc854194fcc355306ae1afb630f33b331301d43fd2aa9965fd79a8dc98d"},"schema_version":"1.0","source":{"id":"0905.3733","kind":"arxiv","version":1}},"canonical_sha256":"c21d1550e11188fb74b92596aba804887bbcbbf102d17656231b4924922fb0cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c21d1550e11188fb74b92596aba804887bbcbbf102d17656231b4924922fb0cd","first_computed_at":"2026-05-18T00:59:11.340833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:11.340833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IpwROlRVk/gfiu7LJMWFW7qP6gB9fRmuAtejkukBUmyDyk69ioPv20ebCd0249fYcsK8KHAXS1Y0Qs6w44grAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:11.341584Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.3733","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c00b950823aac0d7123f31e3a28e954e5aacbd8c2220b7e3eec0bd1498fa2368","sha256:7589514202e26ca0e91a5808401a73ae32f04b0a1034bf671b4b16723291f99f"],"state_sha256":"a95688e123b6b7ced20af545d049408f55973584281719a5451c5ded9c95682c"}