TY - GEN
T1 - Feedback Capacity of MIMO Gaussian Channels
AU - Sabag, Oron
AU - Kostina, Victoria
AU - Hassibi, Babak
N1 - Funding Information:
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. The authors are with California Institute of Technology (e-mails: {oron,vkostina,hassibi}@caltech.edu).
Publisher Copyright:
© 2021 IEEE.
PY - 2021/7/12
Y1 - 2021/7/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85110366531&partnerID=8YFLogxK
U2 - 10.1109/ISIT45174.2021.9518088
DO - 10.1109/ISIT45174.2021.9518088
M3 - Conference contribution
AN - SCOPUS:85110366531
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 7
EP - 12
BT - 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PB - Institute of Electrical and Electronics Engineers
T2 - 2021 IEEE International Symposium on Information Theory, ISIT 2021
Y2 - 12 July 2021 through 20 July 2021
ER -