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Open AccessArticle

Zero-Delay Multiple Descriptions of Stationary Scalar Gauss-Markov Sources

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Department of Electronic Systems, Aalborg University, 9000 Aalborg, Denmark
2
RTX A/S, 9400 Nørresundby, Denmark
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Section on Signal and Information Processing, Deparment of Electronic Systems, Aalborg University, 9000 Aalborg, Denmark
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(12), 1185; https://doi.org/10.3390/e21121185
Received: 13 October 2019 / Revised: 21 November 2019 / Accepted: 28 November 2019 / Published: 1 December 2019
(This article belongs to the Special Issue Information Theory for Control, Games, and Decision Problems)
In this paper, we introduce the zero-delay multiple-description problem, where an encoder constructs two descriptions and the decoders receive a subset of these descriptions. The encoder and decoders are causal and operate under the restriction of zero delay, which implies that at each time instance, the encoder must generate codewords that can be decoded by the decoders using only the current and past codewords. For the case of discrete-time stationary scalar Gauss—Markov sources and quadratic distortion constraints, we present information-theoretic lower bounds on the average sum-rate in terms of the directed and mutual information rate between the source and the decoder reproductions. Furthermore, we show that the optimum test channel is in this case Gaussian, and it can be realized by a feedback coding scheme that utilizes prediction and correlated Gaussian noises. Operational achievable results are considered in the high-rate scenario using a simple differential pulse code modulation scheme with staggered quantizers. Using this scheme, we achieve operational rates within 0.415 bits / sample / description of the theoretical lower bounds for varying description rates. View Full-Text
Keywords: zero delay; multiple descriptions; Gauss-Markov; source coding; rate distortion; feedback zero delay; multiple descriptions; Gauss-Markov; source coding; rate distortion; feedback
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MDPI and ACS Style

Fuglsig, A.J.; Østergaard, J. Zero-Delay Multiple Descriptions of Stationary Scalar Gauss-Markov Sources. Entropy 2019, 21, 1185.

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