Zero-error feedback capacity of channels with state information via dynamic programming

Lei Zhao; Haim H. Permuter

doi:10.1109/TIT.2010.2046211

Zero-error feedback capacity of channels with state information via dynamic programming

Lei Zhao, Haim H. Permuter

Department of Electrical & Computer Engineering

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

In this paper, we study the zero-error capacity for finite state channels with feedback when channel state information is known to both the transmitter and the receiver. We prove that the zero-error capacity in this case can be obtained through the solution of a dynamic programming problem. Each iteration of the dynamic programming provides lower and upper bounds on the zero-error capacity, and in the limit, the lower bound coincides with the zero-error feedback capacity. Furthermore, a sufficient condition for solving the dynamic programming problem is provided through a fixed-point equation. Analytical solutions for several examples are provided.

Original language	English
Article number	2046211
Pages (from-to)	2640-2650
Number of pages	11
Journal	IEEE Transactions on Information Theory
Volume	56
Issue number	6
DOIs	https://doi.org/10.1109/TIT.2010.2046211
State	Published - 1 Jun 2010

Keywords

Bellman equations
Competitive Markov decision processes (MDPs)
Dynamic programming (DP)
Feedback capacity
Fixed-point equation
Infinite-horizon average reward
Stochastic games
Zero-error capacity

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2010.2046211

Cite this

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title = "Zero-error feedback capacity of channels with state information via dynamic programming",

abstract = "In this paper, we study the zero-error capacity for finite state channels with feedback when channel state information is known to both the transmitter and the receiver. We prove that the zero-error capacity in this case can be obtained through the solution of a dynamic programming problem. Each iteration of the dynamic programming provides lower and upper bounds on the zero-error capacity, and in the limit, the lower bound coincides with the zero-error feedback capacity. Furthermore, a sufficient condition for solving the dynamic programming problem is provided through a fixed-point equation. Analytical solutions for several examples are provided.",

keywords = "Bellman equations, Competitive Markov decision processes (MDPs), Dynamic programming (DP), Feedback capacity, Fixed-point equation, Infinite-horizon average reward, Stochastic games, Zero-error capacity",

author = "Lei Zhao and Permuter, {Haim H.}",

note = "Funding Information: Manuscript received July 11, 2009; revised February 21, 2010. Current version published May 19, 2010. The work of L. Zhao was supported in part by the National Science Foundation through the grants CCF-0515303 and CCF-0635318. The work of H. Permuter was supported in part by the BSF grant 2008402 and in part by the Marie Curie International Reintegration Grants (IRG).",

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AU - Permuter, Haim H.

N1 - Funding Information: Manuscript received July 11, 2009; revised February 21, 2010. Current version published May 19, 2010. The work of L. Zhao was supported in part by the National Science Foundation through the grants CCF-0515303 and CCF-0635318. The work of H. Permuter was supported in part by the BSF grant 2008402 and in part by the Marie Curie International Reintegration Grants (IRG).

PY - 2010/6/1

Y1 - 2010/6/1

N2 - In this paper, we study the zero-error capacity for finite state channels with feedback when channel state information is known to both the transmitter and the receiver. We prove that the zero-error capacity in this case can be obtained through the solution of a dynamic programming problem. Each iteration of the dynamic programming provides lower and upper bounds on the zero-error capacity, and in the limit, the lower bound coincides with the zero-error feedback capacity. Furthermore, a sufficient condition for solving the dynamic programming problem is provided through a fixed-point equation. Analytical solutions for several examples are provided.

AB - In this paper, we study the zero-error capacity for finite state channels with feedback when channel state information is known to both the transmitter and the receiver. We prove that the zero-error capacity in this case can be obtained through the solution of a dynamic programming problem. Each iteration of the dynamic programming provides lower and upper bounds on the zero-error capacity, and in the limit, the lower bound coincides with the zero-error feedback capacity. Furthermore, a sufficient condition for solving the dynamic programming problem is provided through a fixed-point equation. Analytical solutions for several examples are provided.

KW - Bellman equations

KW - Competitive Markov decision processes (MDPs)

KW - Dynamic programming (DP)

KW - Feedback capacity

KW - Fixed-point equation

KW - Infinite-horizon average reward

KW - Stochastic games

KW - Zero-error capacity

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JF - IEEE Transactions on Information Theory

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Zero-error feedback capacity of channels with state information via dynamic programming

Abstract

Keywords

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