{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:HHLUICK3D4M5JVKMB2DIK5VHB4","short_pith_number":"pith:HHLUICK3","schema_version":"1.0","canonical_sha256":"39d744095b1f19d4d54c0e868576a70f1b6df8627c0386e1e4e4d1f0a2f31453","source":{"kind":"arxiv","id":"1107.4965","version":3},"attestation_state":"computed","paper":{"title":"Polar codes for q-ary channels, q=2^r","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alexander Barg, Woomyoung Park","submitted_at":"2011-07-25T14:54:30Z","abstract_excerpt":"We study polarization for nonbinary channels with input alphabet of size q=2^r,r=2,3,... Using Arikan's polarizing kernel H_2, we prove that the virtual channels that arise in the process of polarization converge to q-ary channels with capacity 1,2,...,r bits, and that the total transmission rate approaches the symmetric capacity of the channel. This leads to an explicit transmission scheme for q-ary channels. The error probability of decoding using successive cancellation behaves as exp(-N^\\alpha), where N is the code length and {\\alpha} is any constant less than 0.5."},"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":"1107.4965","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-07-25T14:54:30Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"43e6815c519496e487c213f6740fe6613c75fc2a3b355a421a9b470f9be1fb6d","abstract_canon_sha256":"2d76e1b17c99cd536a1c90471db28d4bb4e26dfc5fabf7ceec67128f5d0c393a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:56.896526Z","signature_b64":"swosfgB5b3jFOp2tdpqMgJsAGF6D7ai7EIZLoqz4r2TKtf7o7TAcTWWLKeoMDutYj8dKcWbhTuOiYjgKS4PTCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39d744095b1f19d4d54c0e868576a70f1b6df8627c0386e1e4e4d1f0a2f31453","last_reissued_at":"2026-05-18T04:03:56.896038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:56.896038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polar codes for q-ary channels, q=2^r","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alexander Barg, Woomyoung Park","submitted_at":"2011-07-25T14:54:30Z","abstract_excerpt":"We study polarization for nonbinary channels with input alphabet of size q=2^r,r=2,3,... Using Arikan's polarizing kernel H_2, we prove that the virtual channels that arise in the process of polarization converge to q-ary channels with capacity 1,2,...,r bits, and that the total transmission rate approaches the symmetric capacity of the channel. This leads to an explicit transmission scheme for q-ary channels. The error probability of decoding using successive cancellation behaves as exp(-N^\\alpha), where N is the code length and {\\alpha} is any constant less than 0.5."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4965","kind":"arxiv","version":3},"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":"1107.4965","created_at":"2026-05-18T04:03:56.896109+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.4965v3","created_at":"2026-05-18T04:03:56.896109+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4965","created_at":"2026-05-18T04:03:56.896109+00:00"},{"alias_kind":"pith_short_12","alias_value":"HHLUICK3D4M5","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"HHLUICK3D4M5JVKM","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"HHLUICK3","created_at":"2026-05-18T12:26:30.835961+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/HHLUICK3D4M5JVKMB2DIK5VHB4","json":"https://pith.science/pith/HHLUICK3D4M5JVKMB2DIK5VHB4.json","graph_json":"https://pith.science/api/pith-number/HHLUICK3D4M5JVKMB2DIK5VHB4/graph.json","events_json":"https://pith.science/api/pith-number/HHLUICK3D4M5JVKMB2DIK5VHB4/events.json","paper":"https://pith.science/paper/HHLUICK3"},"agent_actions":{"view_html":"https://pith.science/pith/HHLUICK3D4M5JVKMB2DIK5VHB4","download_json":"https://pith.science/pith/HHLUICK3D4M5JVKMB2DIK5VHB4.json","view_paper":"https://pith.science/paper/HHLUICK3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.4965&json=true","fetch_graph":"https://pith.science/api/pith-number/HHLUICK3D4M5JVKMB2DIK5VHB4/graph.json","fetch_events":"https://pith.science/api/pith-number/HHLUICK3D4M5JVKMB2DIK5VHB4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HHLUICK3D4M5JVKMB2DIK5VHB4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HHLUICK3D4M5JVKMB2DIK5VHB4/action/storage_attestation","attest_author":"https://pith.science/pith/HHLUICK3D4M5JVKMB2DIK5VHB4/action/author_attestation","sign_citation":"https://pith.science/pith/HHLUICK3D4M5JVKMB2DIK5VHB4/action/citation_signature","submit_replication":"https://pith.science/pith/HHLUICK3D4M5JVKMB2DIK5VHB4/action/replication_record"}},"created_at":"2026-05-18T04:03:56.896109+00:00","updated_at":"2026-05-18T04:03:56.896109+00:00"}