The Rate-and-State Capacity with Feedback

Shraga I. Bross; Amos Lapidoth

doi:10.1109/tit.2017.2777389

The Rate-and-State Capacity with Feedback

Shraga I. Bross, Amos Lapidoth

Bar-Ilan University - The Alexander Kofkin Faculty of Engineering

Swiss Federal Institute of Technology Zurich

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

7 Scopus citations

Abstract

The rate-and-state capacity of a state-dependent channel with a state-cognizant encoder is the highest possible rate of communication over the channel when the decoder-in addition to reliably decoding the data-must also reconstruct the state sequence with some required fidelity. Feedback from the channel output to the encoder is shown to increase this capacity even for channels that are memoryless with memoryless states. This capacity is calculated here for such channels with feedback when the state reconstruction fidelity is measured using a single-letter distortion function and the state sequence is revealed to the encoder in one of two different ways: strictly-causally or causally. For the noncausal case, we provide bounds on the capacity and identify a condition under which the bounds coincide. Feedback does not increase the rate-and-state capacity when the decoder must reconstruct the state sequence perfectly or, in some settings, when the channel is Gaussian and fidelity is measured in terms of mean squared-error.

Original language	English
Pages (from-to)	1893-1918
Number of pages	26
Journal	IEEE Transactions on Information Theory
Volume	64
Issue number	3
DOIs	https://doi.org/10.1109/tit.2017.2777389
State	Published - Mar 2018

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

Funding

Manuscript received March 28, 2017; revised August 15, 2017; accepted October 28, 2017. Date of publication November 23, 2017; date of current version February 15, 2018. S. Bross was supported by the Israel Science Foundation under Grant 455/14. S. Bross is with the Faculty of Engineering, Bar-Ilan University, Ramat Gan 52900, Israel (e-mail: [email protected]). A. Lapidoth is with ETH Zurich, 8092 Zurich, Switzerland (e-mail: [email protected]). This paper was presented in part at the 2016 IEEE International Symposium on Information Theory and the 2016 IEEE Convention of Electrical and Electronics Engineers, Israel. Communicated by A. Khisti Associate Editor for Shannon Theory. Digital Object Identifier 10.1109/TIT.2017.2777389

Funders	Funder number
Israel Science Foundation	455/14

Keywords

Gelfand-Pinsker
capacity
causal
distortion
feedback
fidelity
noncausal
rate
side-information
state

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10.1109/tit.2017.2777389

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The Rate-and-State Capacity with Feedback

Abstract

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Keywords

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