{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FBIZJEUSP6ZXIP4LURZUHURWEB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0eb4c1940c0c0dc91a004a11645d100a47f8d9f04f62c07d204d6342fb81ea00","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-06T15:03:10Z","title_canon_sha256":"a2658f17396054d3f42e5a2d28c6bdc70a760b042f8b09941429e26c280dddac"},"schema_version":"1.0","source":{"id":"1604.01653","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01653","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01653v2","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01653","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"FBIZJEUSP6ZX","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FBIZJEUSP6ZXIP4L","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FBIZJEUS","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:fe2d7c86fbadb599075a3d39cf70ddc11c25d7e4737f5ad45eda59467f9c5b34","target":"graph","created_at":"2026-05-18T00:57:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This work studies the optimal Degrees-of-Freedom (DoF) of the $K$-User MISO Broadcast Channel (BC) with delayed Channel-State Information at the Transmitter (CSIT) and with additional current noisy CSIT where the current channel estimation error scales in~$P^{-\\alpha}$ for $\\alpha\\in[0,1]$. This papers establishes for the first time the optimal DoF in this setting thanks to a new transmission scheme which achieves the elusive DoF-optimal combining of the Maddah-Ali and Tse scheme (MAT) introduced in their seminal work in $2010$ with Zero-Forcing (ZF) for an arbitrary number of users. The deriv","authors_text":"David Gesbert, Jingjing Zhang, Paul de Kerret, Petros Elia","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-06T15:03:10Z","title":"Optimal DoF of the K-User Broadcast Channel with Delayed and Imperfect Current CSIT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01653","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:780779cbac28718583244fad10434b6f8cc58b46e6059337733f2423bbd6a1ae","target":"record","created_at":"2026-05-18T00:57:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0eb4c1940c0c0dc91a004a11645d100a47f8d9f04f62c07d204d6342fb81ea00","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-06T15:03:10Z","title_canon_sha256":"a2658f17396054d3f42e5a2d28c6bdc70a760b042f8b09941429e26c280dddac"},"schema_version":"1.0","source":{"id":"1604.01653","kind":"arxiv","version":2}},"canonical_sha256":"28519492927fb3743f8ba47343d236207694d526f0c0e701ec7e84d700fe9983","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28519492927fb3743f8ba47343d236207694d526f0c0e701ec7e84d700fe9983","first_computed_at":"2026-05-18T00:57:44.059568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:44.059568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6w8Lrian6x9/mDrNLfPzjc/J7RKQ6Q1IXGzRhcS4Me+BKEFTxuYnIf3Bl9hJwH+rIMCgrRaDjCe8aaCoP2GaBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:44.060156Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.01653","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:780779cbac28718583244fad10434b6f8cc58b46e6059337733f2423bbd6a1ae","sha256:fe2d7c86fbadb599075a3d39cf70ddc11c25d7e4737f5ad45eda59467f9c5b34"],"state_sha256":"f6c541587f79021fed5ee763083fedc6e8f827c619b94c0cf3ebf8c252682898"}