{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:73ISSHUXQGWQKQTSSBOW5YJYSA","short_pith_number":"pith:73ISSHUX","schema_version":"1.0","canonical_sha256":"fed1291e9781ad054272905d6ee1389019cfb0dde52299690b37e56b821e0e13","source":{"kind":"arxiv","id":"1211.4213","version":1},"attestation_state":"computed","paper":{"title":"On the Pareto-Optimal Beam Structure and Design for Multi-User MIMO Interference Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Juho Park, Youngchul Sung","submitted_at":"2012-11-18T12:14:22Z","abstract_excerpt":"In this paper, the Pareto-optimal beam structure for multi-user multiple-input multiple-output (MIMO) interference channels is investigated and a necessary condition for any Pareto-optimal transmit signal covariance matrix is presented for the K-pair Gaussian (N,M_1,...,M_K) interference channel. It is shown that any Pareto-optimal transmit signal covariance matrix at a transmitter should have its column space contained in the union of the eigen-spaces of the channel matrices from the transmitter to all receivers. Based on this necessary condition, an efficient parameterization for the beam se"},"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":"1211.4213","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-11-18T12:14:22Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7fbf401bd135feb3d4cc331caeb74d3e8cca933e7cfef68b650b4354d5aeea15","abstract_canon_sha256":"f05bb784952669c7d7de79335301863c9a7789a8221b98ee4eaab4c8df24c8c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:09.941728Z","signature_b64":"v8NVMXkkJAy1DUZ4YBxr+Aj5UiLuJIT4CzF3jZM/LGEVyGObrAb1LRRsvSHeGgdcJqjkJXDu0jutGIJisucUAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fed1291e9781ad054272905d6ee1389019cfb0dde52299690b37e56b821e0e13","last_reissued_at":"2026-05-18T01:53:09.941258Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:09.941258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Pareto-Optimal Beam Structure and Design for Multi-User MIMO Interference Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Juho Park, Youngchul Sung","submitted_at":"2012-11-18T12:14:22Z","abstract_excerpt":"In this paper, the Pareto-optimal beam structure for multi-user multiple-input multiple-output (MIMO) interference channels is investigated and a necessary condition for any Pareto-optimal transmit signal covariance matrix is presented for the K-pair Gaussian (N,M_1,...,M_K) interference channel. It is shown that any Pareto-optimal transmit signal covariance matrix at a transmitter should have its column space contained in the union of the eigen-spaces of the channel matrices from the transmitter to all receivers. Based on this necessary condition, an efficient parameterization for the beam se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4213","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":"1211.4213","created_at":"2026-05-18T01:53:09.941343+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.4213v1","created_at":"2026-05-18T01:53:09.941343+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4213","created_at":"2026-05-18T01:53:09.941343+00:00"},{"alias_kind":"pith_short_12","alias_value":"73ISSHUXQGWQ","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"73ISSHUXQGWQKQTS","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"73ISSHUX","created_at":"2026-05-18T12:26:56.085431+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/73ISSHUXQGWQKQTSSBOW5YJYSA","json":"https://pith.science/pith/73ISSHUXQGWQKQTSSBOW5YJYSA.json","graph_json":"https://pith.science/api/pith-number/73ISSHUXQGWQKQTSSBOW5YJYSA/graph.json","events_json":"https://pith.science/api/pith-number/73ISSHUXQGWQKQTSSBOW5YJYSA/events.json","paper":"https://pith.science/paper/73ISSHUX"},"agent_actions":{"view_html":"https://pith.science/pith/73ISSHUXQGWQKQTSSBOW5YJYSA","download_json":"https://pith.science/pith/73ISSHUXQGWQKQTSSBOW5YJYSA.json","view_paper":"https://pith.science/paper/73ISSHUX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.4213&json=true","fetch_graph":"https://pith.science/api/pith-number/73ISSHUXQGWQKQTSSBOW5YJYSA/graph.json","fetch_events":"https://pith.science/api/pith-number/73ISSHUXQGWQKQTSSBOW5YJYSA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/73ISSHUXQGWQKQTSSBOW5YJYSA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/73ISSHUXQGWQKQTSSBOW5YJYSA/action/storage_attestation","attest_author":"https://pith.science/pith/73ISSHUXQGWQKQTSSBOW5YJYSA/action/author_attestation","sign_citation":"https://pith.science/pith/73ISSHUXQGWQKQTSSBOW5YJYSA/action/citation_signature","submit_replication":"https://pith.science/pith/73ISSHUXQGWQKQTSSBOW5YJYSA/action/replication_record"}},"created_at":"2026-05-18T01:53:09.941343+00:00","updated_at":"2026-05-18T01:53:09.941343+00:00"}