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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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 68; no. 3; pp. 1465 - 1479
Main Authors: Wu, Chengyu, Han, Guangyue, Anantharam, Venkat, Marcus, Brian
Format: Journal Article
Language:English
Published: New York IEEE 01.03.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2021.3132675