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The Feedback Capacity of Noisy Output Is the STate (NOST) Channels

Shemuel, Eli and Sabag, Oron and Permuter, Haim H. (2022) The Feedback Capacity of Noisy Output Is the STate (NOST) Channels. IEEE Transactions on Information Theory, 68 (8). pp. 5044-5059. ISSN 0018-9448. doi:10.1109/tit.2022.3165538.

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We consider finite-state channels (FSCs) where the channel state is stochastically dependent on the previous channel output. We refer to these as Noisy Output is the STate (NOST) channels. We derive the feedback capacity of NOST channels in two scenarios: with and without causal state information (CSI) available at the encoder. If CSI is unavailable, the feedback capacity is C_(FB) = max_(P(x|y′))I(X;Y|Y′) , while if it is available at the encoder, the feedback capacity is C_(FB-CSI) = max_(P(u|y′),x(u,s′))I(U;Y|Y′) , where U is an auxiliary RV with finite cardinality. In both formulas, the output process is a Markov process with stationary distribution. The derived formulas generalize special known instances from the literature, such as where the state is i.i.d. and where it is a deterministic function of the output. C_(FB) and C_(FB-CSI) are also shown to be computable via convex optimization problem formulations. Finally, we present an example of an interesting NOST channel for which CSI available at the encoder does not increase the feedback capacity.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Shemuel, Eli0000-0002-6181-1566
Sabag, Oron0000-0002-7907-1463
Permuter, Haim H.0000-0003-3170-3190
Additional Information:© 2022 IEEE. Manuscript received 13 July 2021; revised 20 January 2022; accepted 7 March 2022. Date of publication 7 April 2022; date of current version 13 July 2022. This work was supported in part by the German Research Foundation (DFG) via the German–Israeli Project Cooperation [DIP], in part by the Israel Science Foundation (ISF) Research Grant 899/21, and in part by the Israeli Innovation Authority as part of the Wireless Intelligent Networks (WIN) Consortium. The work of Eli Shemuel was supported by the Ministry of Science, Technology and Space of Israel. The work of Oron Sabag was supported in part by the Israel Scholarship Education Foundation (ISEF) Postdoctoral Fellowship. The authors would like to thank the associate editor and the anonymous reviewers for their valuable and constructive comments, which helped to improve this paper.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)UNSPECIFIED
Israel Science Foundation899/21
Israeli Innovation AuthorityUNSPECIFIED
Ministry of Science, Technology and Space (Israel)UNSPECIFIED
Israel Scholarship Education FoundationUNSPECIFIED
Subject Keywords:Channel capacity, channels with memory, convex optimization, feedback capacity, finite state channels
Issue or Number:8
Record Number:CaltechAUTHORS:20220414-461308000
Persistent URL:
Official Citation:E. Shemuel, O. Sabag and H. H. Permuter, "The Feedback Capacity of Noisy Output Is the STate (NOST) Channels," in IEEE Transactions on Information Theory, vol. 68, no. 8, pp. 5044-5059, Aug. 2022, doi: 10.1109/TIT.2022.3165538
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:114334
Deposited By: George Porter
Deposited On:15 Apr 2022 15:00
Last Modified:26 Jul 2022 21:20

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