{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WKORVCNKUVT4UPSCKROHTJWJC7","short_pith_number":"pith:WKORVCNK","schema_version":"1.0","canonical_sha256":"b29d1a89aaa567ca3e42545c79a6c917fc8d628ecadc2e7a92ed652007f437a8","source":{"kind":"arxiv","id":"1812.08106","version":1},"attestation_state":"computed","paper":{"title":"Log-logarithmic Time Pruned Polar Coding on Binary Erasure Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hsin-Po Wang, Iwan Duursma","submitted_at":"2018-12-19T17:36:18Z","abstract_excerpt":"A pruned variant of polar coding is reinvented for all binary erasure channels. For small $\\varepsilon>0$, we construct codes with block length $\\varepsilon^{-5}$, code rate $\\text{Capacity}-\\varepsilon$, error probability $\\varepsilon$, and encoding and decoding time complexity $O(N\\log|\\log\\varepsilon|)$ per block, equivalently $O(\\log|\\log\\varepsilon|)$ per information bit (Propositions 5 to 8).\n  This result also follows if one applies systematic polar coding [Ar{\\i}kan 10.1109/LCOMM.2011.061611.110862] with simplified successive cancelation decoding [Alamdar-Yazdi-Kschischang 10.1109/LCOM"},"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":"1812.08106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-12-19T17:36:18Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"5aa29f831ab361fbf4c06165a044229dda35c356d74f7e9054a58417bb43dada","abstract_canon_sha256":"62e4d1f94a4902b60433eef05818eedb5bc0f9e8470fda4fe9152d821d54e936"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:54.852946Z","signature_b64":"i3W19XVjHYQPX8ax2R6BtKFDmSVb1dQM5aP3XEO4K8gVpo57sQCW4kTWstHyxNEDYnm8QZHLmYgadZgLZDp6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b29d1a89aaa567ca3e42545c79a6c917fc8d628ecadc2e7a92ed652007f437a8","last_reissued_at":"2026-05-17T23:57:54.852366Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:54.852366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Log-logarithmic Time Pruned Polar Coding on Binary Erasure Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hsin-Po Wang, Iwan Duursma","submitted_at":"2018-12-19T17:36:18Z","abstract_excerpt":"A pruned variant of polar coding is reinvented for all binary erasure channels. For small $\\varepsilon>0$, we construct codes with block length $\\varepsilon^{-5}$, code rate $\\text{Capacity}-\\varepsilon$, error probability $\\varepsilon$, and encoding and decoding time complexity $O(N\\log|\\log\\varepsilon|)$ per block, equivalently $O(\\log|\\log\\varepsilon|)$ per information bit (Propositions 5 to 8).\n  This result also follows if one applies systematic polar coding [Ar{\\i}kan 10.1109/LCOMM.2011.061611.110862] with simplified successive cancelation decoding [Alamdar-Yazdi-Kschischang 10.1109/LCOM"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08106","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":"1812.08106","created_at":"2026-05-17T23:57:54.852461+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.08106v1","created_at":"2026-05-17T23:57:54.852461+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08106","created_at":"2026-05-17T23:57:54.852461+00:00"},{"alias_kind":"pith_short_12","alias_value":"WKORVCNKUVT4","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"WKORVCNKUVT4UPSC","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"WKORVCNK","created_at":"2026-05-18T12:33:01.666342+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/WKORVCNKUVT4UPSCKROHTJWJC7","json":"https://pith.science/pith/WKORVCNKUVT4UPSCKROHTJWJC7.json","graph_json":"https://pith.science/api/pith-number/WKORVCNKUVT4UPSCKROHTJWJC7/graph.json","events_json":"https://pith.science/api/pith-number/WKORVCNKUVT4UPSCKROHTJWJC7/events.json","paper":"https://pith.science/paper/WKORVCNK"},"agent_actions":{"view_html":"https://pith.science/pith/WKORVCNKUVT4UPSCKROHTJWJC7","download_json":"https://pith.science/pith/WKORVCNKUVT4UPSCKROHTJWJC7.json","view_paper":"https://pith.science/paper/WKORVCNK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.08106&json=true","fetch_graph":"https://pith.science/api/pith-number/WKORVCNKUVT4UPSCKROHTJWJC7/graph.json","fetch_events":"https://pith.science/api/pith-number/WKORVCNKUVT4UPSCKROHTJWJC7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WKORVCNKUVT4UPSCKROHTJWJC7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WKORVCNKUVT4UPSCKROHTJWJC7/action/storage_attestation","attest_author":"https://pith.science/pith/WKORVCNKUVT4UPSCKROHTJWJC7/action/author_attestation","sign_citation":"https://pith.science/pith/WKORVCNKUVT4UPSCKROHTJWJC7/action/citation_signature","submit_replication":"https://pith.science/pith/WKORVCNKUVT4UPSCKROHTJWJC7/action/replication_record"}},"created_at":"2026-05-17T23:57:54.852461+00:00","updated_at":"2026-05-17T23:57:54.852461+00:00"}