{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NYQM5HNCVYXS5PZCI4CA3YCTCF","short_pith_number":"pith:NYQM5HNC","schema_version":"1.0","canonical_sha256":"6e20ce9da2ae2f2ebf2247040de053115774afb1eb19c47bc6098576c826bd5d","source":{"kind":"arxiv","id":"1106.2464","version":1},"attestation_state":"computed","paper":{"title":"On the Sum Capacity of K-user Cascade Gaussian Z-Interference Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Elza Erkip, Yuanpeng Liu","submitted_at":"2011-06-13T15:07:13Z","abstract_excerpt":"A $K$-user cascade Gaussian Z-interference channel is a subclass of the general $K$-user Gaussian interference channel, where each user, except the first one, experiences interference only from the previous user. Under simple Han-Kobayashi schemes assuming Gaussian inputs and no time sharing, it is shown that the maximum sum rate is achieved by each user transmitting either common or private signals. For K=3, channel conditions under which the achieved sum rate is either equal to or within 0.5 bits to the sum capacity are identified."},"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":"1106.2464","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-13T15:07:13Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d94ad09e22cfd06651f0717e4c06e354c6477d11ae5a4629c05868eab36e1e5d","abstract_canon_sha256":"fbc8ca62143ca945705aeae878db854b258f8ea59339ba71b023ca267bce1b76"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:05.773687Z","signature_b64":"D8f4E7x4HOs6tMOG3F9YI7GnIyMhRLzIb1+aHOQHf2qVK4EmFtIIgkOR/MeQAcGRf/ouqgTJou3rVNyInG8bDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e20ce9da2ae2f2ebf2247040de053115774afb1eb19c47bc6098576c826bd5d","last_reissued_at":"2026-05-18T04:20:05.773299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:05.773299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Sum Capacity of K-user Cascade Gaussian Z-Interference Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Elza Erkip, Yuanpeng Liu","submitted_at":"2011-06-13T15:07:13Z","abstract_excerpt":"A $K$-user cascade Gaussian Z-interference channel is a subclass of the general $K$-user Gaussian interference channel, where each user, except the first one, experiences interference only from the previous user. Under simple Han-Kobayashi schemes assuming Gaussian inputs and no time sharing, it is shown that the maximum sum rate is achieved by each user transmitting either common or private signals. For K=3, channel conditions under which the achieved sum rate is either equal to or within 0.5 bits to the sum capacity are identified."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2464","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":"1106.2464","created_at":"2026-05-18T04:20:05.773367+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.2464v1","created_at":"2026-05-18T04:20:05.773367+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2464","created_at":"2026-05-18T04:20:05.773367+00:00"},{"alias_kind":"pith_short_12","alias_value":"NYQM5HNCVYXS","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NYQM5HNCVYXS5PZC","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NYQM5HNC","created_at":"2026-05-18T12:26:37.096874+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/NYQM5HNCVYXS5PZCI4CA3YCTCF","json":"https://pith.science/pith/NYQM5HNCVYXS5PZCI4CA3YCTCF.json","graph_json":"https://pith.science/api/pith-number/NYQM5HNCVYXS5PZCI4CA3YCTCF/graph.json","events_json":"https://pith.science/api/pith-number/NYQM5HNCVYXS5PZCI4CA3YCTCF/events.json","paper":"https://pith.science/paper/NYQM5HNC"},"agent_actions":{"view_html":"https://pith.science/pith/NYQM5HNCVYXS5PZCI4CA3YCTCF","download_json":"https://pith.science/pith/NYQM5HNCVYXS5PZCI4CA3YCTCF.json","view_paper":"https://pith.science/paper/NYQM5HNC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.2464&json=true","fetch_graph":"https://pith.science/api/pith-number/NYQM5HNCVYXS5PZCI4CA3YCTCF/graph.json","fetch_events":"https://pith.science/api/pith-number/NYQM5HNCVYXS5PZCI4CA3YCTCF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NYQM5HNCVYXS5PZCI4CA3YCTCF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NYQM5HNCVYXS5PZCI4CA3YCTCF/action/storage_attestation","attest_author":"https://pith.science/pith/NYQM5HNCVYXS5PZCI4CA3YCTCF/action/author_attestation","sign_citation":"https://pith.science/pith/NYQM5HNCVYXS5PZCI4CA3YCTCF/action/citation_signature","submit_replication":"https://pith.science/pith/NYQM5HNCVYXS5PZCI4CA3YCTCF/action/replication_record"}},"created_at":"2026-05-18T04:20:05.773367+00:00","updated_at":"2026-05-18T04:20:05.773367+00:00"}