{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GAOLSZDELNNNBCW5UYJOE74I6J","short_pith_number":"pith:GAOLSZDE","canonical_record":{"source":{"id":"1807.03872","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-07-10T21:34:00Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3331e027400595e25dd30fe5d95de26a5df8c151970a3898d787ab67813cb2b0","abstract_canon_sha256":"fb4e04f2a4fa693d7b56e7d414f7ab100fdb056e106037e87a63461262fc644d"},"schema_version":"1.0"},"canonical_sha256":"301cb964645b5ad08adda612e27f88f24a3fe5b6b180f7bed4da109074f7ad6c","source":{"kind":"arxiv","id":"1807.03872","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.03872","created_at":"2026-05-18T00:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1807.03872v2","created_at":"2026-05-18T00:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03872","created_at":"2026-05-18T00:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"GAOLSZDELNNN","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GAOLSZDELNNNBCW5","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GAOLSZDE","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GAOLSZDELNNNBCW5UYJOE74I6J","target":"record","payload":{"canonical_record":{"source":{"id":"1807.03872","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-07-10T21:34:00Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3331e027400595e25dd30fe5d95de26a5df8c151970a3898d787ab67813cb2b0","abstract_canon_sha256":"fb4e04f2a4fa693d7b56e7d414f7ab100fdb056e106037e87a63461262fc644d"},"schema_version":"1.0"},"canonical_sha256":"301cb964645b5ad08adda612e27f88f24a3fe5b6b180f7bed4da109074f7ad6c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:09.823710Z","signature_b64":"C+rr09vvrzgDe6BlZIPn1rKdPNc+3F4tTX26fAC5lcLfxw4+5CfY+xvg7UPXwQF1cOPX5fgTFXtw5fWC+oFsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"301cb964645b5ad08adda612e27f88f24a3fe5b6b180f7bed4da109074f7ad6c","last_reissued_at":"2026-05-18T00:10:09.822882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:09.822882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.03872","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eMInMQUHkwWaCYMPWGxOyWkKr7PLPOz+SZ8ViJnYTBJY++Q7TeD88bKSgzrAXOUZVO2d7bP5cNjJPLhz1IIcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:19:07.841526Z"},"content_sha256":"c450ed891594aeae6cd2d71c9e963e16ae772e669c57adc22d05afbb4f22ebfd","schema_version":"1.0","event_id":"sha256:c450ed891594aeae6cd2d71c9e963e16ae772e669c57adc22d05afbb4f22ebfd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GAOLSZDELNNNBCW5UYJOE74I6J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effects of Some Lattice Reductions on the Success Probability of the Zero-Forcing Decoder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chao Tong, Jinming Wen, Shi Bai","submitted_at":"2018-07-10T21:34:00Z","abstract_excerpt":"Zero-forcing (ZF) decoder is a commonly used approximation solution of the integer least squares problem which arises in communications and many other applications. Numerically simulations have shown that the LLL reduction can usually improve the success probability $P_{ZF}$ of the ZF decoder. In this paper, we first rigorously show that both SQRD and V-BLAST, two commonly used lattice reductions, have no effect on $P_{ZF}$. Then, we show that LLL reduction can improve $P_{ZF}$ when $n=2$, we also analyze how the parameter $\\delta$ in the LLL reduction affects the enhancement of $P_{ZF}$. Fina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03872","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"93Wp7d+YWhMFJ059JFHNWTACGjsJyNXnBGW0v2zxB6Aw4Fx0oX/2Cv+T4PHNm7383gUsibcogL+/pKeUrchgCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:19:07.842714Z"},"content_sha256":"b4590aa165928d16fcf8aeb4084e0323512503c5d8406f733d917f1710f6c398","schema_version":"1.0","event_id":"sha256:b4590aa165928d16fcf8aeb4084e0323512503c5d8406f733d917f1710f6c398"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GAOLSZDELNNNBCW5UYJOE74I6J/bundle.json","state_url":"https://pith.science/pith/GAOLSZDELNNNBCW5UYJOE74I6J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GAOLSZDELNNNBCW5UYJOE74I6J/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T21:19:07Z","links":{"resolver":"https://pith.science/pith/GAOLSZDELNNNBCW5UYJOE74I6J","bundle":"https://pith.science/pith/GAOLSZDELNNNBCW5UYJOE74I6J/bundle.json","state":"https://pith.science/pith/GAOLSZDELNNNBCW5UYJOE74I6J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GAOLSZDELNNNBCW5UYJOE74I6J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GAOLSZDELNNNBCW5UYJOE74I6J","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":"fb4e04f2a4fa693d7b56e7d414f7ab100fdb056e106037e87a63461262fc644d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-07-10T21:34:00Z","title_canon_sha256":"3331e027400595e25dd30fe5d95de26a5df8c151970a3898d787ab67813cb2b0"},"schema_version":"1.0","source":{"id":"1807.03872","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.03872","created_at":"2026-05-18T00:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1807.03872v2","created_at":"2026-05-18T00:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03872","created_at":"2026-05-18T00:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"GAOLSZDELNNN","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GAOLSZDELNNNBCW5","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GAOLSZDE","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:b4590aa165928d16fcf8aeb4084e0323512503c5d8406f733d917f1710f6c398","target":"graph","created_at":"2026-05-18T00:10:09Z","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":"Zero-forcing (ZF) decoder is a commonly used approximation solution of the integer least squares problem which arises in communications and many other applications. Numerically simulations have shown that the LLL reduction can usually improve the success probability $P_{ZF}$ of the ZF decoder. In this paper, we first rigorously show that both SQRD and V-BLAST, two commonly used lattice reductions, have no effect on $P_{ZF}$. Then, we show that LLL reduction can improve $P_{ZF}$ when $n=2$, we also analyze how the parameter $\\delta$ in the LLL reduction affects the enhancement of $P_{ZF}$. Fina","authors_text":"Chao Tong, Jinming Wen, Shi Bai","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-07-10T21:34:00Z","title":"Effects of Some Lattice Reductions on the Success Probability of the Zero-Forcing Decoder"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03872","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:c450ed891594aeae6cd2d71c9e963e16ae772e669c57adc22d05afbb4f22ebfd","target":"record","created_at":"2026-05-18T00:10:09Z","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":"fb4e04f2a4fa693d7b56e7d414f7ab100fdb056e106037e87a63461262fc644d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-07-10T21:34:00Z","title_canon_sha256":"3331e027400595e25dd30fe5d95de26a5df8c151970a3898d787ab67813cb2b0"},"schema_version":"1.0","source":{"id":"1807.03872","kind":"arxiv","version":2}},"canonical_sha256":"301cb964645b5ad08adda612e27f88f24a3fe5b6b180f7bed4da109074f7ad6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"301cb964645b5ad08adda612e27f88f24a3fe5b6b180f7bed4da109074f7ad6c","first_computed_at":"2026-05-18T00:10:09.822882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:09.822882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C+rr09vvrzgDe6BlZIPn1rKdPNc+3F4tTX26fAC5lcLfxw4+5CfY+xvg7UPXwQF1cOPX5fgTFXtw5fWC+oFsAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:09.823710Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.03872","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c450ed891594aeae6cd2d71c9e963e16ae772e669c57adc22d05afbb4f22ebfd","sha256:b4590aa165928d16fcf8aeb4084e0323512503c5d8406f733d917f1710f6c398"],"state_sha256":"c6ba2a930ed1c2722cfddfd578d3c216e276eeae6e2d22485fe1bb6b8c7bae6f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YutjbGEaZPfO/le5xh0/pZfI02Olm0H8MG4rnEiY+P21DoJbw1dMaZim61gQSLrkvjMNFzJKt/HFfMQ8KU2xCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:19:07.845665Z","bundle_sha256":"a57a44fc1a29583a4eff32a07e521f21fab2d543fde556f645e4e71a20fc1380"}}