{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ZMZN7IZ5S2AQQQVO3AA5EFNJID","short_pith_number":"pith:ZMZN7IZ5","schema_version":"1.0","canonical_sha256":"cb32dfa33d96810842aed801d215a940ee024b1d78dc66c7b2e2edecd75fcd0c","source":{"kind":"arxiv","id":"1207.5010","version":3},"attestation_state":"computed","paper":{"title":"The GDOF of 3-user MIMO Gaussian interference channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Inyup Kang, Jung Hyun Bae, Jungwon Lee","submitted_at":"2012-07-20T18:08:48Z","abstract_excerpt":"The paper establishes the optimal generalized degrees of freedom (GDOF) of 3-user $M \\times N$ multiple-input multiple-output (MIMO) Gaussian interference channel (GIC) in which each transmitter has $M$ antennas and each receiver has $N$ antennas. A constraint of $2M \\leq N$ is imposed so that random coding with message-splitting achieves the optimal GDOF. Unlike symmetric case, two cross channels to unintended receivers from each transmitter can have different strengths, and hence, well known Han-Kobayashi common-private message splitting would not achieve the optimal GDOF. Instead, splitting"},"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":"1207.5010","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-20T18:08:48Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"917080781b058c6fc7df0dcad2a58690ab773160ef9a39bc2ecfdd22fa611b6a","abstract_canon_sha256":"e0cf4f23885e2c81d26629366a03284a21a4f6d5111e0262bffd25c8b54dd45a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:58.671611Z","signature_b64":"TFWC3upqyUeU8j4hjeRF+WQNOFbuBlDWugV3yFLFDHqvkDzgqJ2hG609S9phcG6i1ghwEW7xS3feRMRg/KFRBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb32dfa33d96810842aed801d215a940ee024b1d78dc66c7b2e2edecd75fcd0c","last_reissued_at":"2026-05-18T03:46:58.671022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:58.671022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The GDOF of 3-user MIMO Gaussian interference channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Inyup Kang, Jung Hyun Bae, Jungwon Lee","submitted_at":"2012-07-20T18:08:48Z","abstract_excerpt":"The paper establishes the optimal generalized degrees of freedom (GDOF) of 3-user $M \\times N$ multiple-input multiple-output (MIMO) Gaussian interference channel (GIC) in which each transmitter has $M$ antennas and each receiver has $N$ antennas. A constraint of $2M \\leq N$ is imposed so that random coding with message-splitting achieves the optimal GDOF. Unlike symmetric case, two cross channels to unintended receivers from each transmitter can have different strengths, and hence, well known Han-Kobayashi common-private message splitting would not achieve the optimal GDOF. Instead, splitting"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5010","kind":"arxiv","version":3},"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":"1207.5010","created_at":"2026-05-18T03:46:58.671091+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.5010v3","created_at":"2026-05-18T03:46:58.671091+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5010","created_at":"2026-05-18T03:46:58.671091+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZMZN7IZ5S2AQ","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZMZN7IZ5S2AQQQVO","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZMZN7IZ5","created_at":"2026-05-18T12:27:30.460161+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/ZMZN7IZ5S2AQQQVO3AA5EFNJID","json":"https://pith.science/pith/ZMZN7IZ5S2AQQQVO3AA5EFNJID.json","graph_json":"https://pith.science/api/pith-number/ZMZN7IZ5S2AQQQVO3AA5EFNJID/graph.json","events_json":"https://pith.science/api/pith-number/ZMZN7IZ5S2AQQQVO3AA5EFNJID/events.json","paper":"https://pith.science/paper/ZMZN7IZ5"},"agent_actions":{"view_html":"https://pith.science/pith/ZMZN7IZ5S2AQQQVO3AA5EFNJID","download_json":"https://pith.science/pith/ZMZN7IZ5S2AQQQVO3AA5EFNJID.json","view_paper":"https://pith.science/paper/ZMZN7IZ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.5010&json=true","fetch_graph":"https://pith.science/api/pith-number/ZMZN7IZ5S2AQQQVO3AA5EFNJID/graph.json","fetch_events":"https://pith.science/api/pith-number/ZMZN7IZ5S2AQQQVO3AA5EFNJID/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZMZN7IZ5S2AQQQVO3AA5EFNJID/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZMZN7IZ5S2AQQQVO3AA5EFNJID/action/storage_attestation","attest_author":"https://pith.science/pith/ZMZN7IZ5S2AQQQVO3AA5EFNJID/action/author_attestation","sign_citation":"https://pith.science/pith/ZMZN7IZ5S2AQQQVO3AA5EFNJID/action/citation_signature","submit_replication":"https://pith.science/pith/ZMZN7IZ5S2AQQQVO3AA5EFNJID/action/replication_record"}},"created_at":"2026-05-18T03:46:58.671091+00:00","updated_at":"2026-05-18T03:46:58.671091+00:00"}