In this paper, we propose an approach to numerically compute the feedback capacity of stationary finite-dimensional (FD) Gaussian channels and construct (arbitrarily close to) capacity-achieving feedback codes. In particular, we first extend the interpretation of feedback communication over stationary FD Gaussian channels as feedback control systems. We show that the problem of finding stabilizing feedback controllers with maximal reliable transmission rate over Youla parameters coincides with the problem of finding strictly causal filters to achieve feedback capacity. This extended interpretation provides an approach to construct deterministic feedback coding schemes with double exponential decaying error probability. We next propose asymptotic capacity-achieving upper bounds, which can be numerically evaluated by solving FD convex optimizations. From the filters that achieve the upper bounds, we apply the Youla-based interpretation to construct feasible filters, i.e., feedback codes, leading to a sequence of lower bounds. We prove that the sequence of lower bounds is asymptotically capacity achieving.
Bibliographical noteFunding Information:
Manuscript received June 1, 2017; revised December 26, 2017; accepted January 18, 2018. Date of publication February 5, 2018; date of current version March 15, 2018. C. Li was supported by NSF under Grant CNS-CPS-1239319. N. Elia was supported by NSF under Grant CCF-CIF-1320643. This paper was presented in . C. Li is with Qualcomm Research, Bridgewater, NJ 08807 USA (e-mail: firstname.lastname@example.org ). N. Elia is with the Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011 USA (e-mail: email@example.com). Communicated by P. Vijay Kumar, Guest Editor. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIT.2018.2802538 1In general, H∞ ⊂ H2, for discrete-time systems. When restricted to the real-rational functions, however, RH∞ = RH2. Note that Francis  uses λ-transform instead of the z−tranform, where λ = 1/z.
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- Gaussian noise
- Youla parametrization
- convex optimization