{"paper":{"title":"Sequential Necessary and Sufficient Conditions for Capacity Achieving Distributions of Channels with Memory and Feedback","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Charalambos D. Charalambous, Christos K. Kourtellaris, Photios A. Stavrou","submitted_at":"2016-04-10T21:42:42Z","abstract_excerpt":"We derive sequential necessary and sufficient conditions for any channel input conditional distribution ${\\cal P}_{0,n}\\triangleq\\{P_{X_t|X^{t-1},Y^{t-1}}:~t=0,\\ldots,n\\}$ to maximize the finite-time horizon directed information defined by $$C^{FB}_{X^n \\rightarrow Y^n} \\triangleq \\sup_{{\\cal P}_{0,n}} I(X^n\\rightarrow{Y^n}),~~~ I(X^n \\rightarrow Y^n) =\\sum_{t=0}^n{I}(X^t;Y_t|Y^{t-1})$$ for channel distributions $\\{P_{Y_t|Y^{t-1},X_t}:~t=0,\\ldots,n\\}$ and $\\{P_{Y_t|Y_{t-M}^{t-1},X_t}:~t=0,\\ldots,n\\}$, where $Y^t\\triangleq\\{Y_0,\\ldots,Y_t\\}$ and $X^t\\triangleq\\{X_0,\\ldots,X_t\\}$ are the channel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02742","kind":"arxiv","version":2},"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"}