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arXiv · 1411.7632

Semidefinite Programming Approach to Gaussian Sequential Rate-Distortion Trade-offs

Takashi Tanaka·Kwang-Ki K. Kim·Pablo A. Parrilo·Sanjoy K. Mitter
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Abstract

Sequential rate-distortion (SRD) theory provides a framework for studying the fundamental trade-off between data-rate and data-quality in real-time communication systems. In this paper, we consider the SRD problem for multi-dimensional time-varying Gauss-Markov processes under mean-square distortion criteria. We first revisit the sensor-estimator separation principle, which asserts that considered SRD problem is equivalent to a joint sensor and estimator design problem in which data-rate of the sensor output is minimized while the estimator's performance satisfies the distortion criteria. We then show that the optimal joint design can be performed by semidefinite programming. A semidefinite representation of the corresponding SRD function is obtained. Implications of the obtained result in the context of zero-delay source coding theory and applications to networked control theory are also discussed.

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Takashi Tanaka, Kwang-Ki K. Kim, Pablo A. Parrilo, Sanjoy K. Mitter. 2014-11-27. Semidefinite Programming Approach to Gaussian Sequential Rate-Distortion Trade-offs. https://doi.org/10.1109/tac.2016.2601148

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