The Time-Invariant Multidimensional Gaussian Sequential Rate-Distortion Problem Revisited

TL;DR

This paper revisits the sequential rate-distortion problem for vector-valued Gauss-Markov sources, correcting previous assumptions, and demonstrates that the SRD function is semidefinite representable and computable.

Contribution

It provides a counterexample to previous algorithms, corrects the closed-form expression, and shows the SRD function's semidefinite representability.

Findings

Counterexample invalidates previous dynamic reverse water-filling algorithm

Corrected the closed-form expression for the asymptotic SRD function

Established that the multidimensional Gaussian SRD function is semidefinite representable

Abstract

We revisit the sequential rate-distortion (SRD) trade-off problem for vector-valued Gauss-Markov sources with mean-squared error distortion constraints. We show via a counterexample that the dynamic reverse water-filling algorithm suggested by [1, eq. (15)] is not applicable to this problem, and consequently the closed form expression of the asymptotic SRD function derived in [1, eq. (17)] is not correct in general. Nevertheless, we show that the multidimensional Gaussian SRD function is semidefinite representable and thus it is readily computable.