Asymptotic Reverse Waterfilling Algorithm of NRDF for Certain Classes of
Vector Gauss-Markov Processes
Abstract
In this paper, we revisit the asymptotic reverse-waterfilling
characterization of the nonanticipative rate distortion
function (NRDF) derived for a time-invariant multidimensional
Gauss-Markov processes with mean-squared error (MSE) distortion in
[1]. We show that for certain classes of time-invariant
multidimensional Gauss-Markov processes, the specific characterization
behaves as a reverse-waterfilling algorithm obtained in matrix form
ensuring that the numerical approach of [1, Algorithm 1] is optimal.
In addition, we give an equivalent characterization that utilizes the
eigenvalues of the involved matrices reminiscent of the well-known
reverse-waterfilling algorithm in information theory. For the latter, we
also propose a novel numerical approach to solve the algorithm
optimally. The efficacy of our proposed iterative scheme compared to
similar existing schemes is demonstrated via experiments. Finally, we
use our new results to derive an analytical solution of the asymptotic
NRDF for a correlated time-invariant two-dimensional Gauss-Markov
process.