{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:ABXUJ47RTKLPADXN5NLKZRVTI6","short_pith_number":"pith:ABXUJ47R","schema_version":"1.0","canonical_sha256":"006f44f3f19a96f00eedeb56acc6b347b5169a6ea55ef435916a067f844a59a8","source":{"kind":"arxiv","id":"0710.1916","version":4},"attestation_state":"computed","paper":{"title":"Evaluate the Word Error Rate of Binary Block Codes with Square Radius Probability Density Function","license":"","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hongkui Yang, Hongwen Yang, Jian Gu, Xiaogang Chen","submitted_at":"2007-10-10T03:24:28Z","abstract_excerpt":"The word error rate (WER) of soft-decision-decoded binary block codes rarely has closed-form. Bounding techniques are widely used to evaluate the performance of maximum-likelihood decoding algorithm. But the existing bounds are not tight enough especially for low signal-to-noise ratios and become looser when a suboptimum decoding algorithm is used. This paper proposes a new concept named square radius probability density function (SR-PDF) of decision region to evaluate the WER. Based on the SR-PDF, The WER of binary block codes can be calculated precisely for ML and suboptimum decoders. Furthe"},"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":"0710.1916","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2007-10-10T03:24:28Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"10d539e1b7a3f958ab3e911249666d7c79940dde98b0a6a1033af0896ce4697e","abstract_canon_sha256":"4c8dbf75baab1eab3410c75179892f775b4323bb99e5f106923fe196a258d0c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:57.844215Z","signature_b64":"KCQM99pgZqiy/g2FuZAj7JiLiUssg30rkJXesT1PAFwLPeMA0azQgAUoe1Rzw6W4R3LbjsZxIigb+FXgdKEECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"006f44f3f19a96f00eedeb56acc6b347b5169a6ea55ef435916a067f844a59a8","last_reissued_at":"2026-05-18T02:24:57.843509Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:57.843509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Evaluate the Word Error Rate of Binary Block Codes with Square Radius Probability Density Function","license":"","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hongkui Yang, Hongwen Yang, Jian Gu, Xiaogang Chen","submitted_at":"2007-10-10T03:24:28Z","abstract_excerpt":"The word error rate (WER) of soft-decision-decoded binary block codes rarely has closed-form. Bounding techniques are widely used to evaluate the performance of maximum-likelihood decoding algorithm. But the existing bounds are not tight enough especially for low signal-to-noise ratios and become looser when a suboptimum decoding algorithm is used. This paper proposes a new concept named square radius probability density function (SR-PDF) of decision region to evaluate the WER. Based on the SR-PDF, The WER of binary block codes can be calculated precisely for ML and suboptimum decoders. Furthe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.1916","kind":"arxiv","version":4},"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":"0710.1916","created_at":"2026-05-18T02:24:57.843620+00:00"},{"alias_kind":"arxiv_version","alias_value":"0710.1916v4","created_at":"2026-05-18T02:24:57.843620+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.1916","created_at":"2026-05-18T02:24:57.843620+00:00"},{"alias_kind":"pith_short_12","alias_value":"ABXUJ47RTKLP","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"ABXUJ47RTKLPADXN","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"ABXUJ47R","created_at":"2026-05-18T12:25:55.427421+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/ABXUJ47RTKLPADXN5NLKZRVTI6","json":"https://pith.science/pith/ABXUJ47RTKLPADXN5NLKZRVTI6.json","graph_json":"https://pith.science/api/pith-number/ABXUJ47RTKLPADXN5NLKZRVTI6/graph.json","events_json":"https://pith.science/api/pith-number/ABXUJ47RTKLPADXN5NLKZRVTI6/events.json","paper":"https://pith.science/paper/ABXUJ47R"},"agent_actions":{"view_html":"https://pith.science/pith/ABXUJ47RTKLPADXN5NLKZRVTI6","download_json":"https://pith.science/pith/ABXUJ47RTKLPADXN5NLKZRVTI6.json","view_paper":"https://pith.science/paper/ABXUJ47R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0710.1916&json=true","fetch_graph":"https://pith.science/api/pith-number/ABXUJ47RTKLPADXN5NLKZRVTI6/graph.json","fetch_events":"https://pith.science/api/pith-number/ABXUJ47RTKLPADXN5NLKZRVTI6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ABXUJ47RTKLPADXN5NLKZRVTI6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ABXUJ47RTKLPADXN5NLKZRVTI6/action/storage_attestation","attest_author":"https://pith.science/pith/ABXUJ47RTKLPADXN5NLKZRVTI6/action/author_attestation","sign_citation":"https://pith.science/pith/ABXUJ47RTKLPADXN5NLKZRVTI6/action/citation_signature","submit_replication":"https://pith.science/pith/ABXUJ47RTKLPADXN5NLKZRVTI6/action/replication_record"}},"created_at":"2026-05-18T02:24:57.843620+00:00","updated_at":"2026-05-18T02:24:57.843620+00:00"}