{"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"}