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Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources
KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
Aalborg Univ, Dept Elect Syst, DK-9220 Aalborg, Denmark..
Univ Cyprus, Dept Elect & Comp Engn, CY-3060 Nicosia, Cyprus..
2018 (English)In: IEEE Journal on Selected Topics in Signal Processing, ISSN 1932-4553, E-ISSN 1941-0484, Vol. 12, no 5, p. 841-856Article in journal (Refereed) Published
Abstract [en]

We deal with zero-delay source coding of a vector-valued Gauss-Markov source subject to a mean-squared error (MSE) fidelity criterion characterized by the operational zero-delay vector-valued Gaussian rate distortion function (RDF). We address this problem by considering the nonanticipative RDF (NRDF), which is a lower bound to the causal optimal performance theoretically attainable function (or simply causal RDF) and operational zero-delay RDF. We recall the realization that corresponds to the optimal "test-channel" of the Gaussian NRDF, when considering a vector Gauss-Markov source subject to a MSE distortion in the finite time horizon. Then, we introduce sufficient conditions to show existence of solution for this problem in the infinite time horizon (or asymptotic regime). For the asymptotic regime, we use the asymptotic characterization of the Gaussian NRDF to provide a new equivalent realization scheme with feedback, which is characterized by a resource allocation (reverse-waterfilling) problem across the dimension of the vector source. We leverage the new realization to derive a predictive coding scheme via lattice quantization with subtractive dither and joint memoryless entropy coding. This coding scheme offers an upper bound to the operational zero-delay vector-valued Gaussian RDF. When we use scalar quantization, then for r active dimensions of the vector Gauss-Markov source the gap between the obtained lower and theoretical upper bounds is less than or equal to 0.254r + 1 bits/vector. However, we further show that it is possible when we use vector quantization, and assume infinite dimensional Gauss-Markov sources to make the previous gap to be negligible, i.e., Gaussian NRDF approximates the operational zero-delay Gaussian RDF. We also extend our results to vector-valued Gaussian sources of any finite memory under mild conditions. Our theoretical framework is demonstrated with illustrative numerical experiments.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2018. Vol. 12, no 5, p. 841-856
Keywords [en]
Coding, Gaussian sources, Kalman filters, memory, nonanticipative rate distortion function, source coding, zero delay
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:kth:diva-237119DOI: 10.1109/JSTSP.2018.2855046ISI: 000446341300003Scopus ID: 2-s2.0-85049809534OAI: oai:DiVA.org:kth-237119DiVA, id: diva2:1259564
Note

QC 20181030

Available from: 2018-10-30 Created: 2018-10-30 Last updated: 2018-10-30Bibliographically approved

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