{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZGG524XPPOBAYPRV4JZYEOSX23","short_pith_number":"pith:ZGG524XP","schema_version":"1.0","canonical_sha256":"c98ddd72ef7b820c3e35e273823a57d6c565899a6ba3263ab9a0d7c9b4e6c121","source":{"kind":"arxiv","id":"1504.04934","version":1},"attestation_state":"computed","paper":{"title":"On the Symmetry of Polar Codes for Symmetric Binary-Input Discrete Memoryless Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Liping Li, Qiming Wang","submitted_at":"2015-04-20T04:19:03Z","abstract_excerpt":"In this paper, we study the symmetry of polar codes on symmetric binary-input discrete memoryless channels (B-DMC). The symmetry property of polar codes is originally pointed out in Arikan's work for general B-DMC channels. With the symmetry, the output vector $y_1^N$ ($N$ be the block length) can be divided into equivalence classes in terms of their transition probabilities. In this paper, we present a new frame of analysis on the symmetry of polar codes for B-DMC channels. Theorems are provided to characterize the symmetries among the received vectors."},"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":"1504.04934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-20T04:19:03Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"24ce1aa8fe1a8e3fdc08147f98cab4841854dbdd1e8ca457b7834891e50faae8","abstract_canon_sha256":"634d971f917ba865a64fcb27fb232fa26e0721ae2d6601a1806a23c697b5f815"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:24.305074Z","signature_b64":"5ciBB6kEVS4DqLhy0lIRFitLqE31hCvabARoqMB0hZhf9MB2icgR83Pm73qa3RBW9CuXvOJ93JcPX5oZ3zHaDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c98ddd72ef7b820c3e35e273823a57d6c565899a6ba3263ab9a0d7c9b4e6c121","last_reissued_at":"2026-05-18T02:18:24.304377Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:24.304377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Symmetry of Polar Codes for Symmetric Binary-Input Discrete Memoryless Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Liping Li, Qiming Wang","submitted_at":"2015-04-20T04:19:03Z","abstract_excerpt":"In this paper, we study the symmetry of polar codes on symmetric binary-input discrete memoryless channels (B-DMC). The symmetry property of polar codes is originally pointed out in Arikan's work for general B-DMC channels. With the symmetry, the output vector $y_1^N$ ($N$ be the block length) can be divided into equivalence classes in terms of their transition probabilities. In this paper, we present a new frame of analysis on the symmetry of polar codes for B-DMC channels. Theorems are provided to characterize the symmetries among the received vectors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04934","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":"1504.04934","created_at":"2026-05-18T02:18:24.304491+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.04934v1","created_at":"2026-05-18T02:18:24.304491+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04934","created_at":"2026-05-18T02:18:24.304491+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZGG524XPPOBA","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZGG524XPPOBAYPRV","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZGG524XP","created_at":"2026-05-18T12:29:52.810259+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/ZGG524XPPOBAYPRV4JZYEOSX23","json":"https://pith.science/pith/ZGG524XPPOBAYPRV4JZYEOSX23.json","graph_json":"https://pith.science/api/pith-number/ZGG524XPPOBAYPRV4JZYEOSX23/graph.json","events_json":"https://pith.science/api/pith-number/ZGG524XPPOBAYPRV4JZYEOSX23/events.json","paper":"https://pith.science/paper/ZGG524XP"},"agent_actions":{"view_html":"https://pith.science/pith/ZGG524XPPOBAYPRV4JZYEOSX23","download_json":"https://pith.science/pith/ZGG524XPPOBAYPRV4JZYEOSX23.json","view_paper":"https://pith.science/paper/ZGG524XP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.04934&json=true","fetch_graph":"https://pith.science/api/pith-number/ZGG524XPPOBAYPRV4JZYEOSX23/graph.json","fetch_events":"https://pith.science/api/pith-number/ZGG524XPPOBAYPRV4JZYEOSX23/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZGG524XPPOBAYPRV4JZYEOSX23/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZGG524XPPOBAYPRV4JZYEOSX23/action/storage_attestation","attest_author":"https://pith.science/pith/ZGG524XPPOBAYPRV4JZYEOSX23/action/author_attestation","sign_citation":"https://pith.science/pith/ZGG524XPPOBAYPRV4JZYEOSX23/action/citation_signature","submit_replication":"https://pith.science/pith/ZGG524XPPOBAYPRV4JZYEOSX23/action/replication_record"}},"created_at":"2026-05-18T02:18:24.304491+00:00","updated_at":"2026-05-18T02:18:24.304491+00:00"}