On the Rate Region of the Vector Gaussian One-Helper Distributed Source-Coding Problem

Abstract

In this paper we consider the rate region of the vector Gaussian one-helper distributed source coding problem. In particular, we derive optimality conditions under which a weighted sum rate is minimum by using a contradiction-based argument. When the sources are specified to be scalar, the optimality conditions can always be constructed for any weighted sum rate. In the derivation of the optimality conditions, we introduce a new concept of "source enhancement", which can be viewed as a dual to the wellknown "channel enhancement" technique. In particular, source enhancement refers to the operation of increasing the covariance matrix of a Gaussian source in a partial ordering sense. This new technique makes the derivation of the optimality conditions straightforward.

Rate Region of the Vector Gaussian One-Helper Source-Coding Problem

“…We shall show that this is indeed true. Source enhancement and Oohama's converse technique are lifted directly from [1] and [6]. The distortion projection, on the other hand, requires an extension beyond what was needed in the scalar helper case [7].…”

“…The enhanced optimization problem (P) is now defined as We next show that v(P) lower bounds v(P) using a variation on an argument of Zhang [6]. Since KX KX by (45), we may coupleX to (X,Ỹ) in such a way that…”

“…This was later improved slightly by the present authors to show that the Gaussian scheme achieves a portion of the boundary of the rate region [5]. Liu and Viswanath's approach was later subsumed by Zhang [6], who applied enhacement in a different way and called it source enhancement, but this also yielded an outer bound that is not always tight. The case in which Y is a scalar and X is a vector was recently solved by the authors [7].…”

Rate region of the vector Gaussian one-helper source-coding problem

“…We shall show that this is indeed true. Source enhancement and Oohama's converse technique are lifted directly from [1,6]. The distortion projection, on the other hand, requires an extension beyond what was needed in the scalar helper case [7].…”

Distributed Remote Vector Gaussian Source Coding for Wireless Acoustic Sensor Networks

“…We derive the rate-distortion (RD) function for an arbitrary node in the network with a distortion constraint defined in form of a covariance matrix, cf. [6], [7]. In Section II, we introduce the notation and formulate the problem, which turns out to involve joint coding of multiple sources.…”