{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YUOBNLF7CYOSJI4XDKNYEN433W","short_pith_number":"pith:YUOBNLF7","schema_version":"1.0","canonical_sha256":"c51c16acbf161d24a3971a9b82379bdd81f962a14645c23a34d93acd13877b29","source":{"kind":"arxiv","id":"1511.08887","version":2},"attestation_state":"computed","paper":{"title":"On the Degrees of Freedom of the Symmetric Multi-Relay MIMO Y Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Soung Chang Liew, Tian Ding, Xiaojun Yuan","submitted_at":"2015-11-28T10:14:26Z","abstract_excerpt":"In this paper, we study the degrees of freedom (DoF) of the symmetric multi-relay multiple-input multiple-output (MIMO) Y channel, where three user nodes, each with M antennas, communicate via K geographically separated relay nodes, each with N antennas. For this model, we establish a general DoF achievability framework based on linear precoding and post-processing methods. The framework poses a nonlinear problem with respect to user precoders and post-processors, as well as relay precoders. To solve this problem, we adopt an uplink-downlink asymmetric strategy, where the user precoders are de"},"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":"1511.08887","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-28T10:14:26Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"624f68aac91dc377764730a87b6c4fded873b4261eb6bc435230186b913bd4b6","abstract_canon_sha256":"3b4067099bc3571644a04e08be9a2b83131b65945c42a596cea6226364f45b6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:51.265437Z","signature_b64":"y6kkZYVpW/PDJ+IVG6sFXGedCs2h+5LLwSbk9kfXOnS2pSBlXTK2K5LebrJ/t4xN61w21TIA15o7YgLG85pyCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c51c16acbf161d24a3971a9b82379bdd81f962a14645c23a34d93acd13877b29","last_reissued_at":"2026-05-18T00:07:51.264881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:51.264881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Degrees of Freedom of the Symmetric Multi-Relay MIMO Y Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Soung Chang Liew, Tian Ding, Xiaojun Yuan","submitted_at":"2015-11-28T10:14:26Z","abstract_excerpt":"In this paper, we study the degrees of freedom (DoF) of the symmetric multi-relay multiple-input multiple-output (MIMO) Y channel, where three user nodes, each with M antennas, communicate via K geographically separated relay nodes, each with N antennas. For this model, we establish a general DoF achievability framework based on linear precoding and post-processing methods. The framework poses a nonlinear problem with respect to user precoders and post-processors, as well as relay precoders. To solve this problem, we adopt an uplink-downlink asymmetric strategy, where the user precoders are de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08887","kind":"arxiv","version":2},"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":"1511.08887","created_at":"2026-05-18T00:07:51.264972+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.08887v2","created_at":"2026-05-18T00:07:51.264972+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08887","created_at":"2026-05-18T00:07:51.264972+00:00"},{"alias_kind":"pith_short_12","alias_value":"YUOBNLF7CYOS","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"YUOBNLF7CYOSJI4X","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"YUOBNLF7","created_at":"2026-05-18T12:29:52.810259+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/YUOBNLF7CYOSJI4XDKNYEN433W","json":"https://pith.science/pith/YUOBNLF7CYOSJI4XDKNYEN433W.json","graph_json":"https://pith.science/api/pith-number/YUOBNLF7CYOSJI4XDKNYEN433W/graph.json","events_json":"https://pith.science/api/pith-number/YUOBNLF7CYOSJI4XDKNYEN433W/events.json","paper":"https://pith.science/paper/YUOBNLF7"},"agent_actions":{"view_html":"https://pith.science/pith/YUOBNLF7CYOSJI4XDKNYEN433W","download_json":"https://pith.science/pith/YUOBNLF7CYOSJI4XDKNYEN433W.json","view_paper":"https://pith.science/paper/YUOBNLF7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.08887&json=true","fetch_graph":"https://pith.science/api/pith-number/YUOBNLF7CYOSJI4XDKNYEN433W/graph.json","fetch_events":"https://pith.science/api/pith-number/YUOBNLF7CYOSJI4XDKNYEN433W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YUOBNLF7CYOSJI4XDKNYEN433W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YUOBNLF7CYOSJI4XDKNYEN433W/action/storage_attestation","attest_author":"https://pith.science/pith/YUOBNLF7CYOSJI4XDKNYEN433W/action/author_attestation","sign_citation":"https://pith.science/pith/YUOBNLF7CYOSJI4XDKNYEN433W/action/citation_signature","submit_replication":"https://pith.science/pith/YUOBNLF7CYOSJI4XDKNYEN433W/action/replication_record"}},"created_at":"2026-05-18T00:07:51.264972+00:00","updated_at":"2026-05-18T00:07:51.264972+00:00"}