Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userJoint Rate Distortion Function of a Tuple of Correlated Multivariate Gaussian Sources with Individual Fidelity Criteria
169
0
0.0
(
0
)
Added by
Evagoras Stylianou
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In this paper we analyze the joint rate distortion function (RDF), for a tuple of correlated sources taking values in abstract alphabet spaces (i.e., continuous) subject to two individual distortion criteria. First, we derive structural properties of the realizations of the reproduction Random Variables (RVs), which induce the corresponding optimal test channel distributions of the joint RDF. Second, we consider a tuple of correlated multivariate jointly Gaussian RVs, $X_1 : Omega rightarrow {mathbb R}^{p_1}, X_2 : Omega rightarrow {mathbb R}^{p_2}$ with two square-error fidelity criteria, and we derive additional structural properties of the optimal realizations, and use these to characterize the RDF as a convex optimization problem with respect to the parameters of the realizations. We show that the computation of the joint RDF can be performed by semidefinite programming. Further, we derive closed-form expressions of the joint RDF, such that Grays [1] lower bounds hold with equality, and verify their consistency with the semidefinite programming computations.
rate research
Read More
The joint nonanticipative rate distortion function (NRDF) for a tuple of random processes with individual fidelity criteria is considered. Structural properties of optimal test channel distributions are derived. Further, for the application example of the joint NRDF of a tuple of jointly multivariate Gaussian Markov processes with individual square-error fidelity criteria, a realization of the reproduction processes which induces the optimal test channel distribution is derived, and the corresponding joint NRDF is characterized. The analysis of the simplest example, of a tuple of scalar correlated Markov processes, illustrates many of the challenging aspects of such problems.
The water-filling solution for the quadratic rate-distortion function of a stationary Gaussian source is given in terms of its power spectrum. This formula naturally lends itself to a frequency domain test-channel realization. We provide an alternative time-domain realization for the rate-distortion function, based on linear prediction. This solution has some interesting implications, including the optimality at all distortion levels of pre/post filtered vector-quantized differential pulse code modulation (DPCM), and a duality relationship with decision-feedback equalization (DFE) for inter-symbol interference (ISI) channels.
The objective of this paper is to further investigate various applications of information Nonanticipative Rate Distortion Function (NRDF) by discussing two working examples, the Binary Symmetric Markov Source with parameter $p$ (BSMS($p$)) with Hamming distance distortion, and the multidimensional partially observed Gaussian-Markov source. For the BSMS($p$), we give the solution to the NRDF, and we use it to compute the Rate Loss (RL) of causal codes with respect to noncausal codes. For the multidimensional Gaussian-Markov source, we give the solution to the NRDF, we show its operational meaning via joint source-channel matching over a vector of parallel Gaussian channels, and we compute the RL of causal and zero-delay codes with respect to noncausal codes.
This paper focuses on the structural properties of test channels, of Wyners operational information rate distortion function (RDF), $overline{R}(Delta_X)$, of a tuple of multivariate correlated, jointly independent and identically distributed Gaussian random variables (RVs), ${X_t, Y_t}_{t=1}^infty$, $X_t: Omega rightarrow {mathbb R}^{n_x}$, $Y_t: Omega rightarrow {mathbb R}^{n_y}$, with average mean-square error at the decoder, $frac{1}{n} {bf E}sum_{t=1}^n||X_t - widehat{X}_t||^2leq Delta_X$, when ${Y_t}_{t=1}^infty$ is the side information available to the decoder only. We construct optimal test channel realizations, which achieve the informational RDF, $overline{R}(Delta_X) triangleqinf_{{cal M}(Delta_X)} I(X;Z|Y)$, where ${cal M}(Delta_X)$ is the set of auxiliary RVs $Z$ such that, ${bf P}_{Z|X,Y}={bf P}_{Z|X}$, $widehat{X}=f(Y,Z)$, and ${bf E}{||X-widehat{X}||^2}leq Delta_X$. We show the fundamental structural properties: (1) Optimal test channel realizations that achieve the RDF, $overline{R}(Delta_X)$, satisfy conditional independence, $ {bf P}_{X|widehat{X}, Y, Z}={bf P}_{X|widehat{X},Y}={bf P}_{X|widehat{X}}, hspace{.2in} {bf E}Big{XBig|widehat{X}, Y, ZBig}={bf E}Big{XBig|widehat{X}Big}=widehat{X} $ and (2) similarly for the conditional RDF, ${R}_{X|Y}(Delta_X) triangleq inf_{{bf P}_{widehat{X}|X,Y}:{bf E}{||X-widehat{X}||^2} leq Delta_X} I(X; widehat{X}|Y)$, when ${Y_t}_{t=1}^infty$ is available to both the encoder and decoder, and the equality $overline{R}(Delta_X)={R}_{X|Y}(Delta_X)$.
The rate-distortion-perception function (RDPF; Blau and Michaeli, 2019) has emerged as a useful tool for thinking about realism and distortion of reconstructions in lossy compression. Unlike the rate-distortion function, however, it is unknown whether encoders and decoders exist that achieve the rate suggested by the RDPF. Building on results by Li and El Gamal (2018), we show that the RDPF can indeed be achieved using stochastic, variable-length codes. For this class of codes, we also prove that the RDPF lower-bounds the achievable rate
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
