{"paper":{"title":"The Capacity of Online (Causal) $q$-ary Error-Erasure Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Michael Langberg, Sidharth Jaggi, Zitan Chen","submitted_at":"2016-01-31T16:27:05Z","abstract_excerpt":"In the $q$-ary online (or \"causal\") channel coding model, a sender wishes to communicate a message to a receiver by transmitting a codeword $\\mathbf{x} =(x_1,\\ldots,x_n) \\in \\{0,1,\\ldots,q-1\\}^n$ symbol by symbol via a channel limited to at most $pn$ errors and/or $p^{*} n$ erasures. The channel is \"online\" in the sense that at the $i$th step of communication the channel decides whether to corrupt the $i$th symbol or not based on its view so far, i.e., its decision depends only on the transmitted symbols $(x_1,\\ldots,x_i)$. This is in contrast to the classical adversarial channel in which the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00276","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"}