1. The Time-Invariant Multidimensional Gaussian Sequential Rate-Distortion Problem Revisited.
- Author
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Stavrou, Photios A., Tanaka, Takashi, and Tatikonda, Sekhar
- Subjects
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GAUSSIAN function , *SEMIDEFINITE programming , *MARKOV processes , *STOCHASTIC processes , *HEURISTIC algorithms - Abstract
We revisit the sequential rate-distortion (SRD) tradeoff problem for vector-valued Gauss–Markov sources with mean-squared error distortion constraints. Our study is partly motivated by the question recently raised in the paper “Rate-cost tradeoffs in control” (in Proc. 54th Annu. Allerton Conf. Commun., Control, Comput., 2016, pp. 1157–1164) regarding the correctness of its solution algorithm known in the literature. We show via a counterexample that the dynamic reverse water-filling algorithm suggested by (15) of the paper “Stochastic linear control over a communication channel” (IEEE Trans. Autom. Control, vol. 49, pp. 1549–1561, 2004) is not applicable to this problem, and consequently, the closed-form expression of the asymptotic SRD function derived in (17) of the paper “Stochastic linear control over a communication channel” (IEEE Trans. Autom. Control, vol. 49, pp. 1549–1561, 2004) is not correct in general. Nevertheless, we show that the multidimensional Gaussian SRD function is semidefinite representable, and thus, it is readily computable. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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