{"paper":{"title":"Polar codes with a stepped boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ilya Dumer","submitted_at":"2017-02-16T08:28:05Z","abstract_excerpt":"We consider explicit polar constructions of blocklength $n\\rightarrow\\infty$ for the two extreme cases of code rates $R\\rightarrow1$ and $R\\rightarrow0.$ For code rates $R\\rightarrow1,$ we design codes with complexity order of $n\\log n$ in code construction, encoding, and decoding. These codes achieve the vanishing output bit error rates on the binary symmetric channels with any transition error probability $p\\rightarrow 0$ and perform this task with a substantially smaller redundancy $(1-R)n$ than do other known high-rate codes, such as BCH codes or Reed-Muller (RM). We then extend our design"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04886","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"}