{"paper":{"title":"The Structure of the Realizations of the Causal Information Rate-Distortion Function for Markovian Sources: Realizations with Densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Milan S. Derpich","submitted_at":"2018-09-16T22:10:36Z","abstract_excerpt":"The main purpose of this note is to show that in a realization $(x_{1}^{n}, y_{1}^{n})$ of the causal \\textit{information rate-distortion function} (IRDF) for a $\\kappa$-th order Markovian source $x_{1}^{n}$, under a single letter sum distortion constraint, the smallest integer $\\ell$ for which $y_{k} \\leftrightarrow y_{1}^{k-1},x_{k-\\ell+1}^{k} \\leftrightarrow x_{1}^{k-\\ell}$ holds is $\\ell=\\kappa$. This result is derived under the assumption that the sequences $(x_{1}^{n},y_{1}^{n})$ have a joint probability density function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05968","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"}