Feedback Capacity of MIMO Gaussian Channels

Oron Sabag, Victoria Kostina, Babak Hassibi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations


Finding a computable expression for the feedback capacity of channels with non-white Gaussian, additive 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.

Original languageEnglish
Title of host publication2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers
Number of pages6
ISBN (Electronic)9781538682098
StatePublished - 12 Jul 2021
Externally publishedYes
Event2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia
Duration: 12 Jul 202120 Jul 2021

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


Conference2021 IEEE International Symposium on Information Theory, ISIT 2021
CityVirtual, Melbourne

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics


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