{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:HBKYJTUFU7MAOF2OPTOOCFYKZ7","short_pith_number":"pith:HBKYJTUF","schema_version":"1.0","canonical_sha256":"385584ce85a7d807174e7cdce1170acffce83161fb540b5c72bb93d776688e07","source":{"kind":"arxiv","id":"1002.2164","version":1},"attestation_state":"computed","paper":{"title":"Efficient LLR Calculation for Non-Binary Modulations over Fading Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Masoud Ardakani, Raman Yazdani","submitted_at":"2010-02-10T18:42:04Z","abstract_excerpt":"Log-likelihood ratio (LLR) computation for non-binary modulations over fading channels is complicated. A measure of LLR accuracy on asymmetric binary channels is introduced to facilitate good LLR approximations for non-binary modulations. Considering piecewise linear LLR approximations, we prove convexity of optimizing the coefficients according to this measure. For the optimized approximate LLRs, we report negligible performance losses compared to true LLRs."},"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":"1002.2164","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-10T18:42:04Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"dd7f45f560be6e026f0bba491705337b3336ea12b7be67331e776a17e677b74e","abstract_canon_sha256":"c4114ac5d4ec5f686badab4b7406534ba14ce0b6c38d3aa5476dfcda5eb891b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:53.760819Z","signature_b64":"ccdiHuKczvFKA1Ymm+Tnu4EyLA+iL7IgkQ5Zv3jwaEvB/FHS6c7UgpWIk5u8gWjAR0cOD6WUM3Lv/DM0+ygwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"385584ce85a7d807174e7cdce1170acffce83161fb540b5c72bb93d776688e07","last_reissued_at":"2026-05-18T03:57:53.760003Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:53.760003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient LLR Calculation for Non-Binary Modulations over Fading Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Masoud Ardakani, Raman Yazdani","submitted_at":"2010-02-10T18:42:04Z","abstract_excerpt":"Log-likelihood ratio (LLR) computation for non-binary modulations over fading channels is complicated. A measure of LLR accuracy on asymmetric binary channels is introduced to facilitate good LLR approximations for non-binary modulations. Considering piecewise linear LLR approximations, we prove convexity of optimizing the coefficients according to this measure. For the optimized approximate LLRs, we report negligible performance losses compared to true LLRs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2164","kind":"arxiv","version":1},"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":"1002.2164","created_at":"2026-05-18T03:57:53.760133+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.2164v1","created_at":"2026-05-18T03:57:53.760133+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2164","created_at":"2026-05-18T03:57:53.760133+00:00"},{"alias_kind":"pith_short_12","alias_value":"HBKYJTUFU7MA","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"HBKYJTUFU7MAOF2O","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"HBKYJTUF","created_at":"2026-05-18T12:26:07.630475+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/HBKYJTUFU7MAOF2OPTOOCFYKZ7","json":"https://pith.science/pith/HBKYJTUFU7MAOF2OPTOOCFYKZ7.json","graph_json":"https://pith.science/api/pith-number/HBKYJTUFU7MAOF2OPTOOCFYKZ7/graph.json","events_json":"https://pith.science/api/pith-number/HBKYJTUFU7MAOF2OPTOOCFYKZ7/events.json","paper":"https://pith.science/paper/HBKYJTUF"},"agent_actions":{"view_html":"https://pith.science/pith/HBKYJTUFU7MAOF2OPTOOCFYKZ7","download_json":"https://pith.science/pith/HBKYJTUFU7MAOF2OPTOOCFYKZ7.json","view_paper":"https://pith.science/paper/HBKYJTUF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.2164&json=true","fetch_graph":"https://pith.science/api/pith-number/HBKYJTUFU7MAOF2OPTOOCFYKZ7/graph.json","fetch_events":"https://pith.science/api/pith-number/HBKYJTUFU7MAOF2OPTOOCFYKZ7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HBKYJTUFU7MAOF2OPTOOCFYKZ7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HBKYJTUFU7MAOF2OPTOOCFYKZ7/action/storage_attestation","attest_author":"https://pith.science/pith/HBKYJTUFU7MAOF2OPTOOCFYKZ7/action/author_attestation","sign_citation":"https://pith.science/pith/HBKYJTUFU7MAOF2OPTOOCFYKZ7/action/citation_signature","submit_replication":"https://pith.science/pith/HBKYJTUFU7MAOF2OPTOOCFYKZ7/action/replication_record"}},"created_at":"2026-05-18T03:57:53.760133+00:00","updated_at":"2026-05-18T03:57:53.760133+00:00"}