Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources

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Stavrou, Photios A.KTH,Teknisk informationsvetenskap (författare)

Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources

Artikel/kapitelEngelska2018

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Institute of Electrical and Electronics Engineers (IEEE),2018
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LIBRIS-ID:oai:DiVA.org:kth-237119
https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-237119URI
https://doi.org/10.1109/JSTSP.2018.2855046DOI

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Språk:engelska
Sammanfattning på:engelska

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QC 20181030
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.

Ämnesord och genrebeteckningar

TEKNIK OCH TEKNOLOGIER Elektroteknik och elektronik Signalbehandling hsv//swe
ENGINEERING AND TECHNOLOGY Electrical Engineering, Electronic Engineering, Information Engineering Signal Processing hsv//eng
Coding
Gaussian sources
Kalman filters
memory
nonanticipative rate distortion function
source coding
zero delay

Biuppslag (personer, institutioner, konferenser, titlar ...)

Ostergaard, JanAalborg Univ, Dept Elect Syst, DK-9220 Aalborg, Denmark. (författare)
Charalambous, Charalambos D.Univ Cyprus, Dept Elect & Comp Engn, CY-3060 Nicosia, Cyprus. (författare)
KTHTeknisk informationsvetenskap (creator_code:org_t)

Sammanhörande titlar

Ingår i:IEEE Journal on Selected Topics in Signal Processing: Institute of Electrical and Electronics Engineers (IEEE)12:5, s. 841-8561932-45531941-0484

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