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Feedback Capacity of MIMO Gaussian Channels

Sabag, Oron and Kostina, Victoria and Hassibi, Babak (2021) Feedback Capacity of MIMO Gaussian Channels. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210719-210210078

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Abstract

Finding a computable expression for the feedback capacity of additive channels with colored Gaussian noise is a long standing open problem. In this paper, we solve this problem in the scenario where the channel has multiple inputs and multiple outputs (MIMO) and the noise process is generated as the output of a state-space model (a hidden Markov model). The main result is a computable characterization of the feedback capacity as a finite-dimensional convex optimization problem. Our solution subsumes all previous solutions to the feedback capacity including the auto-regressive moving-average (ARMA) noise process of first order, even if it is a non-stationary process. The capacity problem can be viewed as the problem of maximizing the measurements' entropy rate of a controlled (policy-dependent) state-space subject to a power constraint. We formulate the finite-block version of this problem as a sequential convex optimization problem, which in turn leads to a single-letter and computable upper bound. By optimizing over a family of time-invariant policies that correspond to the channel inputs distribution, a tight lower bound is realized. We show that one of the optimization constraints in the capacity characterization boils down to a Riccati equation, revealing an interesting relation between explicit capacity formulae and Riccati equations.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2106.01994arXivDiscussion Paper
ORCID:
AuthorORCID
Sabag, Oron0000-0002-7907-1463
Kostina, Victoria0000-0002-2406-7440
Additional Information:Attribution 4.0 International (CC BY 4.0) This work was supported in part by the National Science Foundation (NSF) under grants CCF-1751356 and CCF-1956386. O. Sabag is partially supported by the ISEF international postdoctoral fellowship.
Funders:
Funding AgencyGrant Number
NSFCCF-1751356
NSFCCF-1956386
ISEF FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20210719-210210078
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210719-210210078
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109928
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:20 Jul 2021 17:54
Last Modified:20 Jul 2021 17:57

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