Feedback Capacity of Gaussian Channels with Memory

Oron Sabag, Victoria Kostina, Babak Hassibi

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

2 Scopus citations


We consider the feedback capacity of a MIMO channel whose channel output is given by a linear state-space model driven by the channel inputs and a Gaussian process. The generality of our state-space model subsumes all previous studied models such as additive channels with colored Gaussian noise, and channels with an arbitrary dependence on previous channel inputs or outputs. The main result is a computable feedback capacity expression that is given as a convex optimization problem subject to a detectability condition. We demonstrate the capacity result on the auto-regressive Gaussian noise channel, where we show that even a single time-instance delay in the feedback reduces the feedback capacity significantly in the stationary regime. On the other hand, for large regression parameters, the feedback capacity can be achieved with delayed feedback. Finally, we show that the detectability condition is satisfied for scalar models and conjecture that it is true for MIMO models.

Original languageAmerican English
Title of host publication2022 IEEE International Symposium on Information Theory, ISIT 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781665421591
StatePublished - 2022
Externally publishedYes
Event2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland
Duration: 26 Jun 20221 Jul 2022

Publication series

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


Conference2022 IEEE International Symposium on Information Theory, ISIT 2022

Bibliographical note

Publisher Copyright:
© 2022 IEEE.


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