Rate-distortion function upper bounds for Gaussian vectors and their applications in coding AR sources

source coding; rate-distortion function (RDF); Gaussian vector; autoregressive (AR) source; discrete Fourier transform (DFT

On the relation of nonanticipative rate distortion function and filtering theory

In this paper the relation between nonanticipative rate distortion function (RDF) and Bayesian filtering theory is investigated using the topology of weak convergence of probability measures on Polish spaces. The relation is established via an optimization on the space of conditional distributions of the so-called directed information subject to fidelity constraints. Existence of the optimal reproduction distribution of the nonanticipative RDF is shown, while the optimal nonanticipative reproduction conditional distribution for stationary processes is derived in closed form. The realization procedure of nonanticipative RDF which is equivalent to joint-source channel matching for symbol-by-symbol transmission is described, while an example is introduced to illustrate the concepts.Comment: 6 pages, 4 figures, final version submitted for publication at 12th Biannual European Control Conference (ECC), 201

Distributed Remote Vector Gaussian Source Coding with Covariance Distortion Constraints

In this paper, we consider a distributed remote source coding problem, where a sequence of observations of source vectors is available at the encoder. The problem is to specify the optimal rate for encoding the observations subject to a covariance matrix distortion constraint and in the presence of side information at the decoder. For this problem, we derive lower and upper bounds on the rate-distortion function (RDF) for the Gaussian case, which in general do not coincide. We then provide some cases, where the RDF can be derived exactly. We also show that previous results on specific instances of this problem can be generalized using our results. We finally show that if the distortion measure is the mean squared error, or if it is replaced by a certain mutual information constraint, the optimal rate can be derived from our main result.Comment: This is the final version accepted at ISIT'1