{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:OYU7NQTCUZCWKDJRSJDELG6FPP","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":"ba69197aefd10bb312247c5417a102ad223e8a67515ade96249d440cf4fb5426","cross_cats_sorted":["cond-mat.stat-mech","math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2007-06-08T12:21:04Z","title_canon_sha256":"88e509d55e06433f71f0310abade5d233e49446642048edf80a9dce1f097ac4f"},"schema_version":"1.0","source":{"id":"0706.1169","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.1169","created_at":"2026-05-18T00:59:12Z"},{"alias_kind":"arxiv_version","alias_value":"0706.1169v1","created_at":"2026-05-18T00:59:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.1169","created_at":"2026-05-18T00:59:12Z"},{"alias_kind":"pith_short_12","alias_value":"OYU7NQTCUZCW","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"OYU7NQTCUZCWKDJR","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"OYU7NQTC","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:5bd8f3f2ccfde159e18b170a06af0d7b215ab016e16315ce2882a772750802bd","target":"graph","created_at":"2026-05-18T00:59:12Z","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":"We apply the replica method to analyze vector precoding, a method to reduce transmit power in antenna array communications. The analysis applies to a very general class of channel matrices. The statistics of the channel matrix enter the transmitted energy per symbol via its R-transform. We find that vector precoding performs much better for complex than for real alphabets. As a byproduct, we find a nonlinear precoding method with polynomial complexity that outperforms NP-hard Tomlinson-Harashima precoding for binary modulation on complex channels if the number of transmit antennas is slightly ","authors_text":"Aris L. Moustakas, Dongning Guo, Ralf R. Mueller","cross_cats":["cond-mat.stat-mech","math.IT"],"headline":"","license":"","primary_cat":"cs.IT","submitted_at":"2007-06-08T12:21:04Z","title":"Vector Precoding for Wireless MIMO Systems: A Replica Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.1169","kind":"arxiv","version":1},"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:e94520005920fc98131bac545c6b9f5c59257ea15a4ffd5f2efc78de64d8cfd9","target":"record","created_at":"2026-05-18T00:59:12Z","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":"ba69197aefd10bb312247c5417a102ad223e8a67515ade96249d440cf4fb5426","cross_cats_sorted":["cond-mat.stat-mech","math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2007-06-08T12:21:04Z","title_canon_sha256":"88e509d55e06433f71f0310abade5d233e49446642048edf80a9dce1f097ac4f"},"schema_version":"1.0","source":{"id":"0706.1169","kind":"arxiv","version":1}},"canonical_sha256":"7629f6c262a645650d319246459bc57be0969027cf3f4101f1e26be20e18a3c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7629f6c262a645650d319246459bc57be0969027cf3f4101f1e26be20e18a3c4","first_computed_at":"2026-05-18T00:59:12.110479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:12.110479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vV1AS2Y67SyGCWDD7kHeG6wGDrLvou1wWTyplQys/DyiErAycycXT+o5A1pUg1JnSZ7I2LobohurJ5p2N5GMCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:12.111175Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.1169","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e94520005920fc98131bac545c6b9f5c59257ea15a4ffd5f2efc78de64d8cfd9","sha256:5bd8f3f2ccfde159e18b170a06af0d7b215ab016e16315ce2882a772750802bd"],"state_sha256":"c837045b3ff51bc2d18b94bc5fd9a3af1609544b0ba018b42c0d59fa509bc664"}