Gaussian Multiterminal Source Coding Research Articles

Generalized Gaussian Multiterminal Source Coding in the High-Resolution Regime

A conjectural expression of the asymptotic gap between the rate-distortion function of an arbitrary generalized Gaussian multiterminal source coding system and that of its centralized counterpart in the high-resolution regime is proposed. The validity of this expression is verified when the number of sources is no more than 3.

A New Sufficient Condition for Sum-Rate Tightness in Quadratic Gaussian Multiterminal Source Coding

This paper considers the quadratic Gaussian multiterminal (MT) source coding problem and provides a new sufficient condition for the Berger-Tung (BT) sum-rate bound to be tight. The converse proof utilizes a set of virtual remote sources given which the observed sources are block independent with a maximum block size of 2. The given MT source coding problem is then related to a set of two-terminal problems with matrix-distortion constraints, for which a new lower bound on the sum-rate is given. By formulating a convex optimization problem over all distortion matrices, a sufficient condition is derived for the optimal BT scheme to satisfy the subgradient-based Karush-Kuhn-Tucker condition. The subset of the quadratic Gaussian MT problem satisfying our new sufficient condition subsumes all previously known tight cases, and our proof technique opens a new direction for more general partial solutions.

The Sum-Rate Bound for a New Class of Quadratic Gaussian Multiterminal Source Coding Problems

In this paper, we show tightness of the Berger-Tung (BT) sum-rate bound for a new class of quadratic Gaussian multiterminal (MT) source coding problems dubbed bi-eigen equal-variance with equal distortion (BEEV-ED), where the L × L source covariance matrix has equal diagonal elements with two distinct eigenvalues, and the L target distortions are equal. Let K (K <; L) be the number of repetitions of the larger eigenvalue, the BEEV covariance structure allows us to connect K i.i.d. virtual Gaussian sources with the L given MT sources via an L × K semiorthogonal transform whose rows have equal Euclidean norm plus additive i.i.d. Gaussian noises, resulting in the two sets of sources being mutually conditional i.i.d. By relating the given MT source coding problem to a generalized Gaussian CEO problem with the K virtual sources as remote sources and the L MT sources as observations, we obtain a lower bound on the MT sum-rate, and show its achievability by BT schemes under the equal distortion constraints. Our BEEV-ED class of quadratic Gaussian MT source coding problems subsumes both the positive-symmetric case considered by Wagner et al. and the negative-symmetric case. Other examples, including a subclass of sources with BE circulant symmetric covariance matrices and equal distortion constraints, are also provided to highlight tightness of the sum-rate bound.

On the Sum-Rate Loss of Quadratic Gaussian Multiterminal Source Coding

This work studies the sum-rate loss of quadratic Gaussian multiterminal source coding, i.e., the difference between the minimum sum-rates of distributed encoding and joint encoding (both with joint decoding) of correlated Gaussian sources subject to MSE distortion constraints on individual sources. It is shown that under the nondegraded assumption, i.e., all target distortions are simultaneously achievable by a Gaussian Berger-Tung scheme, the supremum of the sum-rate loss of distributed encoding over joint encoding of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> jointly Gaussian sources increases almost linearly in the number of sources <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> , with an asymptotic slope of 0.1083 bit per sample per source as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> goes to infinity. This result is obtained even though we currently do not have the full knowledge of the minimum sum-rate for the distributed encoding case. The main idea is to upper-bound the minimum sum-rate of multiterminal source coding by that achieved by parallel Gaussian test channels while lower-bounding the minimum sum-rate of joint encoding by a reverse water-filling solution to a relaxed joint encoding problem of the same set of Gaussian sources with a sum-distortion constraint (that equals the sum of the individual target distortions). We show that under the nondegraded assumption, the supremum difference between the upper bound for distributed encoding and the lower bound for joint encoding is achieved in the bi-eigen equal-variance with equal distortion case, in which both bounds are known to be tight.

On the Sum Rate of Gaussian Multiterminal Source Coding: New Proofs and Results

We show that the lower bound on the sum rate of the direct and indirect Gaussian multiterminal source coding problems can be derived in a unified manner by exploiting the semidefinite partial order of the distortion covariance matrices associated with the minimum mean squared error (MMSE) estimation and the so-called reduced optimal linear estimation, through which an intimate connection between the lower bound and the Berger-Tung upper bound is revealed. We give a new proof of the minimum sum rate of the indirect Gaussian multiterminal source coding problem (i.e., the Gaussian CEO problem). For the direct Gaussian multiterminal source coding problem, we derive a general lower bound on the sum rate and establish a set of sufficient conditions under which the lower bound coincides with the Berger-Tung upper bound. We show that the sufficient conditions are satisfied for a class of sources and distortion constraints; in particular, they hold for arbitrary positive definite source covariance matrices in the high-resolution regime. In contrast with the existing proofs, the new method does not rely on Shannon's entropy power inequality.

Rate-Distortion Theory for Gaussian Multiterminal Source Coding Systems With Several Side Informations at the Decoder

In this paper, we consider the separate coding problem for L+1 correlated Gaussian memoryless sources. We deal with the case where L sources work as partial side information at the decoder for the reconstruction of the remaining source. The determination problem of the rate-distortion region for this system is the so-called many-help-one problem and it has been known as a highly challenging problem for almost 20 years. In this paper, we give a partial solution to this problem. We determine the rate-distortion region in the case where the L sources working as partial side information are conditionally independent if the remaining source we wish to reconstruct is given. The additive white Gaussian noise CEO problem is a special case of this. We also discuss the relation of the result previous results of ours