{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GEQUVSXZSYKOT67IL7TB7H5PHO","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":"3af86d48282476f25e71fb4c65c72befaed3f0f7e90098e0853cb699a4f63bae","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.IT","submitted_at":"2013-12-05T09:46:26Z","title_canon_sha256":"2f9710cf1db3893c6c3d5eacb83fd752dd1c7bf537667f7a80399332046c391c"},"schema_version":"1.0","source":{"id":"1312.1482","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1482","created_at":"2026-05-18T03:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1482v1","created_at":"2026-05-18T03:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1482","created_at":"2026-05-18T03:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"GEQUVSXZSYKO","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GEQUVSXZSYKOT67I","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GEQUVSXZ","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:df71efa7feb0f2da593628149c02f083d49f8f528fb9aa88fe67c6b1e72d97e7","target":"graph","created_at":"2026-05-18T03:05:27Z","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":"Classical trellis-coded modulation (TCM) as introduced by Ungerboeck in 1976/1983 uses a signal constellation of twice the cardinality compared to an uncoded transmission with one bit of redundancy per PAM symbol, i.e., application of codes with rates $\\frac{n-1}{n}$ when $2^{n}$ denotes the cardinality of the signal constellation. The original approach therefore only comprises integer transmission rates, i.e., $R=\\left\\{ 2,\\,3,\\,4\\,\\ldots \\right\\}$, additionally, when transmitting over an intersymbol interference (ISI) channel an optimum decoding scheme would perform equalization and decoding","authors_text":"Fabian Schuh, Johannes B. Huber","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.IT","submitted_at":"2013-12-05T09:46:26Z","title":"Low Complexity Decoding for Punctured Trellis-Coded Modulation Over Intersymbol Interference Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1482","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:a1bbf7c7a8c8b7d79c43d4a5834379421029dbc1e3a6b7e8dce30b59842999c3","target":"record","created_at":"2026-05-18T03:05:27Z","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":"3af86d48282476f25e71fb4c65c72befaed3f0f7e90098e0853cb699a4f63bae","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.IT","submitted_at":"2013-12-05T09:46:26Z","title_canon_sha256":"2f9710cf1db3893c6c3d5eacb83fd752dd1c7bf537667f7a80399332046c391c"},"schema_version":"1.0","source":{"id":"1312.1482","kind":"arxiv","version":1}},"canonical_sha256":"31214acaf99614e9fbe85fe61f9faf3bafd0a0e1b50c7fe56276fb8a95c68951","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31214acaf99614e9fbe85fe61f9faf3bafd0a0e1b50c7fe56276fb8a95c68951","first_computed_at":"2026-05-18T03:05:27.168857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:27.168857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YcPFDCZEamfhA8y0vTuHyU6LCzBt9UUZXxy5+tHl43TzsbbvnGst49H6614zNZ5tQ5gSXtHQpa/iACh0ABJVDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:27.169416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1482","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1bbf7c7a8c8b7d79c43d4a5834379421029dbc1e3a6b7e8dce30b59842999c3","sha256:df71efa7feb0f2da593628149c02f083d49f8f528fb9aa88fe67c6b1e72d97e7"],"state_sha256":"390f24911039bea1b5173ce42e5fa9c021136b97b1e99be72dea3a4af42321e9"}