{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:GCZKEU7DIESOUBJVPLO77UTOI2","short_pith_number":"pith:GCZKEU7D","schema_version":"1.0","canonical_sha256":"30b2a253e34124ea05357addffd26e46a1bb64944b2f6f9f34fff39770ff2fcf","source":{"kind":"arxiv","id":"1109.2944","version":1},"attestation_state":"computed","paper":{"title":"Real Interference Alignment and Degrees of Freedom Region of Wireless X Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Zhengdao Wang","submitted_at":"2011-09-13T22:01:36Z","abstract_excerpt":"We consider a single hop wireless X network with $K$ transmitters and $J$ receivers, all with single antenna. Each transmitter conveys for each receiver an independent message. The channel is assumed to have constant coefficients. We develop interference alignment scheme for this setup and derived several achievable degrees of freedom regions. We show that in some cases, the derived region meets a previous outer bound and are hence the DoF region. For our achievability schemes, we divide each message into streams and use real interference alignment on the streams. Several previous results on t"},"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":"1109.2944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-13T22:01:36Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7fda7bb1b453e4eb869e9c68c9a593b514096e3ae996ec3f02313accddfed7ee","abstract_canon_sha256":"3a3d27d4969814c9503a6c7cef37e9492a0986ac596c1c29905b55fc567f931f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:06.664891Z","signature_b64":"mvwMA+9u+L28xEKeQJT2WN6jCc7XvnQpVTmTEXwSCWXYrrNsuMnd69XaDCa0UIfQUNxPziLWHvSHF4XdcpfjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30b2a253e34124ea05357addffd26e46a1bb64944b2f6f9f34fff39770ff2fcf","last_reissued_at":"2026-05-18T04:13:06.664246Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:06.664246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Real Interference Alignment and Degrees of Freedom Region of Wireless X Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Zhengdao Wang","submitted_at":"2011-09-13T22:01:36Z","abstract_excerpt":"We consider a single hop wireless X network with $K$ transmitters and $J$ receivers, all with single antenna. Each transmitter conveys for each receiver an independent message. The channel is assumed to have constant coefficients. We develop interference alignment scheme for this setup and derived several achievable degrees of freedom regions. We show that in some cases, the derived region meets a previous outer bound and are hence the DoF region. For our achievability schemes, we divide each message into streams and use real interference alignment on the streams. Several previous results on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2944","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":"1109.2944","created_at":"2026-05-18T04:13:06.664334+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.2944v1","created_at":"2026-05-18T04:13:06.664334+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2944","created_at":"2026-05-18T04:13:06.664334+00:00"},{"alias_kind":"pith_short_12","alias_value":"GCZKEU7DIESO","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"GCZKEU7DIESOUBJV","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"GCZKEU7D","created_at":"2026-05-18T12:26:28.662955+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/GCZKEU7DIESOUBJVPLO77UTOI2","json":"https://pith.science/pith/GCZKEU7DIESOUBJVPLO77UTOI2.json","graph_json":"https://pith.science/api/pith-number/GCZKEU7DIESOUBJVPLO77UTOI2/graph.json","events_json":"https://pith.science/api/pith-number/GCZKEU7DIESOUBJVPLO77UTOI2/events.json","paper":"https://pith.science/paper/GCZKEU7D"},"agent_actions":{"view_html":"https://pith.science/pith/GCZKEU7DIESOUBJVPLO77UTOI2","download_json":"https://pith.science/pith/GCZKEU7DIESOUBJVPLO77UTOI2.json","view_paper":"https://pith.science/paper/GCZKEU7D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.2944&json=true","fetch_graph":"https://pith.science/api/pith-number/GCZKEU7DIESOUBJVPLO77UTOI2/graph.json","fetch_events":"https://pith.science/api/pith-number/GCZKEU7DIESOUBJVPLO77UTOI2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GCZKEU7DIESOUBJVPLO77UTOI2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GCZKEU7DIESOUBJVPLO77UTOI2/action/storage_attestation","attest_author":"https://pith.science/pith/GCZKEU7DIESOUBJVPLO77UTOI2/action/author_attestation","sign_citation":"https://pith.science/pith/GCZKEU7DIESOUBJVPLO77UTOI2/action/citation_signature","submit_replication":"https://pith.science/pith/GCZKEU7DIESOUBJVPLO77UTOI2/action/replication_record"}},"created_at":"2026-05-18T04:13:06.664334+00:00","updated_at":"2026-05-18T04:13:06.664334+00:00"}