Youla Coding and Computation of Gaussian Feedback Capacity

Chong Li; Nicola Elia

doi:10.1109/TIT.2018.2802538

Youla Coding and Computation of Gaussian Feedback Capacity

Chong Li, Nicola Elia

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	3197-3215
Number of pages	19
Journal	IEEE Transactions on Information Theory
Volume	64
Issue number	4
DOIs	https://doi.org/10.1109/TIT.2018.2802538
State	Published - Apr 2018

Bibliographical note

Funding 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 [1]. C. Li is with Qualcomm Research, Bridgewater, NJ 08807 USA (e-mail: [email protected] ). N. Elia is with the Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011 USA (e-mail: [email protected]). 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 [3] uses λ-transform instead of the z−tranform, where λ = 1/z.

Publisher Copyright:
© 2018 IEEE.

Keywords

Gaussian noise
Youla parametrization
capacity
convex optimization
duality

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10.1109/TIT.2018.2802538

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abstract = "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.",

keywords = "Gaussian noise, Youla parametrization, capacity, convex optimization, duality",

author = "Chong Li and Nicola Elia",

note = "Funding 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 [1]. C. Li is with Qualcomm Research, Bridgewater, NJ 08807 USA (e-mail: [email protected] ). N. Elia is with the Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011 USA (e-mail: [email protected]). 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 [3] uses λ-transform instead of the z−tranform, where λ = 1/z. Publisher Copyright: {\textcopyright} 2018 IEEE.",

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N2 - 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.

AB - 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.

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Youla Coding and Computation of Gaussian Feedback Capacity

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