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Open AccessArticle

Bounds on the Sum-Rate of MIMO Causal Source Coding Systems with Memory under Spatio-Temporal Distortion Constraints

1
Department of Intelligent Systems, Division of Information Science and Engineering, KTH Royal Institute of Technology, 11428 Stockholm, Sweden
2
Section on Signal and Information Processing, Department of Electronic Systems, Aalborg University, 9000 Aalborg, Denmark
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(8), 842; https://doi.org/10.3390/e22080842
Received: 18 June 2020 / Revised: 22 July 2020 / Accepted: 27 July 2020 / Published: 30 July 2020
(This article belongs to the Special Issue Multiuser Information Theory III)
In this paper, we derive lower and upper bounds on the OPTA of a two-user multi-input multi-output (MIMO) causal encoding and causal decoding problem. Each user’s source model is described by a multidimensional Markov source driven by additive i.i.d. noise process subject to three classes of spatio-temporal distortion constraints. To characterize the lower bounds, we use state augmentation techniques and a data processing theorem, which recovers a variant of rate distortion function as an information measure known in the literature as nonanticipatory ϵ-entropy, sequential or nonanticipative RDF. We derive lower bound characterizations for a system driven by an i.i.d. Gaussian noise process, which we solve using the SDP algorithm for all three classes of distortion constraints. We obtain closed form solutions when the system’s noise is possibly non-Gaussian for both users and when only one of the users is described by a source model driven by a Gaussian noise process. To obtain the upper bounds, we use the best linear forward test channel realization that corresponds to the optimal test channel realization when the system is driven by a Gaussian noise process and apply a sequential causal DPCM-based scheme with a feedback loop followed by a scaled ECDQ scheme that leads to upper bounds with certain performance guarantees. Then, we use the linear forward test channel as a benchmark to obtain upper bounds on the OPTA, when the system is driven by an additive i.i.d. non-Gaussian noise process. We support our framework with various simulation studies. View Full-Text
Keywords: bounds; causal coding; one-shot information theory; convex programming; estimation; spatial distortion constraints; temporal distortion constraints; multi-user rate distortion theory bounds; causal coding; one-shot information theory; convex programming; estimation; spatial distortion constraints; temporal distortion constraints; multi-user rate distortion theory
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MDPI and ACS Style

Stavrou, P.A.; Østergaard, J.; Skoglund, M. Bounds on the Sum-Rate of MIMO Causal Source Coding Systems with Memory under Spatio-Temporal Distortion Constraints. Entropy 2020, 22, 842. https://doi.org/10.3390/e22080842

AMA Style

Stavrou PA, Østergaard J, Skoglund M. Bounds on the Sum-Rate of MIMO Causal Source Coding Systems with Memory under Spatio-Temporal Distortion Constraints. Entropy. 2020; 22(8):842. https://doi.org/10.3390/e22080842

Chicago/Turabian Style

Stavrou, Photios A.; Østergaard, Jan; Skoglund, Mikael. 2020. "Bounds on the Sum-Rate of MIMO Causal Source Coding Systems with Memory under Spatio-Temporal Distortion Constraints" Entropy 22, no. 8: 842. https://doi.org/10.3390/e22080842

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