A Deterministic Algorithm for the Capacity of Finite-State Channels

We propose two modified versions of the classical gradient ascent method to compute the capacity of finite-state channels with Markovian inputs. For the case that the channel mutual information rate is strongly concave in a parameter taking values in a compact convex subset of some Euclidean space,...

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Vydané v:	IEEE transactions on information theory Ročník 68; číslo 3; s. 1465 - 1479
Hlavní autori:	Wu, Chengyu, Han, Guangyue, Anantharam, Venkat, Marcus, Brian
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York IEEE 01.03.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	Algorithms Approximation algorithms Channel capacity Channels Convergence Euclidean geometry Euclidean space finite-state channels gradient ascent hidden Markov processes Markov processes Monte Carlo methods Mutual information Polynomials Power capacitors
ISSN:	0018-9448, 1557-9654
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Abstract	We propose two modified versions of the classical gradient ascent method to compute the capacity of finite-state channels with Markovian inputs. For the case that the channel mutual information rate is strongly concave in a parameter taking values in a compact convex subset of some Euclidean space, our first algorithm proves to achieve polynomial accuracy in polynomial time and, moreover, for some special families of finite-state channels our algorithm can achieve exponential accuracy in polynomial time under some technical conditions. For the case that the channel mutual information rate may not be strongly concave, our second algorithm proves to be at least locally convergent.
AbstractList	We propose two modified versions of the classical gradient ascent method to compute the capacity of finite-state channels with Markovian inputs. For the case that the channel mutual information rate is strongly concave in a parameter taking values in a compact convex subset of some Euclidean space, our first algorithm proves to achieve polynomial accuracy in polynomial time and, moreover, for some special families of finite-state channels our algorithm can achieve exponential accuracy in polynomial time under some technical conditions. For the case that the channel mutual information rate may not be strongly concave, our second algorithm proves to be at least locally convergent.
Author	Han, Guangyue Anantharam, Venkat Wu, Chengyu Marcus, Brian
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SubjectTerms	Algorithms Approximation algorithms Channel capacity Channels Convergence Euclidean geometry Euclidean space finite-state channels gradient ascent hidden Markov processes Markov processes Monte Carlo methods Mutual information Polynomials Power capacitors
Title	A Deterministic Algorithm for the Capacity of Finite-State Channels
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