{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ISM5U2WFM6RMBQPS7LWVCSRIL7","short_pith_number":"pith:ISM5U2WF","schema_version":"1.0","canonical_sha256":"4499da6ac567a2c0c1f2faed514a285fc3db14747ad3e6211ec834a2f62ec630","source":{"kind":"arxiv","id":"1603.04591","version":1},"attestation_state":"computed","paper":{"title":"Threshold Saturation of Spatially Coupled Sparse Superposition Codes for All Memoryless Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.IT"],"primary_cat":"cs.IT","authors_text":"Jean Barbier, Mohamad Dia, Nicolas Macris","submitted_at":"2016-03-15T08:43:25Z","abstract_excerpt":"We recently proved threshold saturation for spatially coupled sparse superposition codes on the additive white Gaussian noise channel. Here we generalize our analysis to a much broader setting. We show for any memoryless channel that spatial coupling allows generalized approximate message-passing (GAMP) decoding to reach the potential (or Bayes optimal) threshold of the code ensemble. Moreover in the large input alphabet size limit: i) the GAMP algorithmic threshold of the underlying (or uncoupled) code ensemble is simply expressed as a Fisher information; ii) the potential threshold tends to "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1603.04591","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-03-15T08:43:25Z","cross_cats_sorted":["cond-mat.dis-nn","math.IT"],"title_canon_sha256":"caa16e6627a826bdf31c3b7776df84234c4c9898b88d737542560df5a8b3395e","abstract_canon_sha256":"7580587bb771d8dcb522fa036b89ed47af598d9ed7c7bbc1137be36ecd7d2c29"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:04.420897Z","signature_b64":"CUn876uf4kCZyH/OuLtPk6FBfbPnopDa7UdcZzbI5jqayU0BjAeBng1Trc2IvZbkeU+HETvCY8mbfdSZ9kUHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4499da6ac567a2c0c1f2faed514a285fc3db14747ad3e6211ec834a2f62ec630","last_reissued_at":"2026-05-18T01:19:04.420434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:04.420434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Threshold Saturation of Spatially Coupled Sparse Superposition Codes for All Memoryless Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.IT"],"primary_cat":"cs.IT","authors_text":"Jean Barbier, Mohamad Dia, Nicolas Macris","submitted_at":"2016-03-15T08:43:25Z","abstract_excerpt":"We recently proved threshold saturation for spatially coupled sparse superposition codes on the additive white Gaussian noise channel. Here we generalize our analysis to a much broader setting. We show for any memoryless channel that spatial coupling allows generalized approximate message-passing (GAMP) decoding to reach the potential (or Bayes optimal) threshold of the code ensemble. Moreover in the large input alphabet size limit: i) the GAMP algorithmic threshold of the underlying (or uncoupled) code ensemble is simply expressed as a Fisher information; ii) the potential threshold tends to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04591","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.04591","created_at":"2026-05-18T01:19:04.420503+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.04591v1","created_at":"2026-05-18T01:19:04.420503+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04591","created_at":"2026-05-18T01:19:04.420503+00:00"},{"alias_kind":"pith_short_12","alias_value":"ISM5U2WFM6RM","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"ISM5U2WFM6RMBQPS","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"ISM5U2WF","created_at":"2026-05-18T12:30:22.444734+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ISM5U2WFM6RMBQPS7LWVCSRIL7","json":"https://pith.science/pith/ISM5U2WFM6RMBQPS7LWVCSRIL7.json","graph_json":"https://pith.science/api/pith-number/ISM5U2WFM6RMBQPS7LWVCSRIL7/graph.json","events_json":"https://pith.science/api/pith-number/ISM5U2WFM6RMBQPS7LWVCSRIL7/events.json","paper":"https://pith.science/paper/ISM5U2WF"},"agent_actions":{"view_html":"https://pith.science/pith/ISM5U2WFM6RMBQPS7LWVCSRIL7","download_json":"https://pith.science/pith/ISM5U2WFM6RMBQPS7LWVCSRIL7.json","view_paper":"https://pith.science/paper/ISM5U2WF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.04591&json=true","fetch_graph":"https://pith.science/api/pith-number/ISM5U2WFM6RMBQPS7LWVCSRIL7/graph.json","fetch_events":"https://pith.science/api/pith-number/ISM5U2WFM6RMBQPS7LWVCSRIL7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ISM5U2WFM6RMBQPS7LWVCSRIL7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ISM5U2WFM6RMBQPS7LWVCSRIL7/action/storage_attestation","attest_author":"https://pith.science/pith/ISM5U2WFM6RMBQPS7LWVCSRIL7/action/author_attestation","sign_citation":"https://pith.science/pith/ISM5U2WFM6RMBQPS7LWVCSRIL7/action/citation_signature","submit_replication":"https://pith.science/pith/ISM5U2WFM6RMBQPS7LWVCSRIL7/action/replication_record"}},"created_at":"2026-05-18T01:19:04.420503+00:00","updated_at":"2026-05-18T01:19:04.420503+00:00"}