Quadratic Gaussian CEO Problem Research Articles

The CEO Problem With rth Power of Difference and Logarithmic Distortions

The CEO problem has received much attention since first introduced by Berger et al., but there are limited results on non-Gaussian models with non-quadratic distortion measures. In this work, we extend the quadratic Gaussian CEO problem to two non-Gaussian settings with general rth power of difference distortion. Assuming an identical observation channel across agents, we study the asymptotics of distortion decay as the number of agents and sum-rate, R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sum</sub> , grow without bound, while individual rates vanish. The first setting is a regular source-observation model with rth power of difference distortion, which subsumes the quadratic Gaussian CEO problem, and we establish that the distortion decays at <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sum</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-r/2</sup> ) when r ≥ 2. We use sample median estimation after the Berger-Tung scheme for achievability. The other setting is a non-regular source-observation model, including uniform additive noise models, with rth power of difference distortion for which estimation-theoretic regularity conditions do not hold. The distortion decay <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sum</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-r</sup> ) when r ≥ 1 is obtained for the non-regular model by midrange estimator following the Berger-Tung scheme. We also provide converses based on the Shannon lower bound for the regular model and the Chazan-Zakai-Ziv bound for the non-regular model, respectively. Lastly, we provide a sufficient condition for the regular model, under which quadratic and logarithmic distortions are asymptotically equivalent by an entropy power relationship as the number of agents grows. This proof relies on the Bernstein-von Mises theorem.

On the Generalized Gaussian CEO Problem

This paper considers a distributed source coding (DSC) problem where L encoders observe noisy linear combinations of K correlated remote Gaussian sources, and separately transmit the compressed observations to the decoder to reconstruct the remote sources subject to a sum-distortion constraint. This DSC problem is referred to as the generalized Gaussian CEO problem since it can be viewed as a generalization of the quadratic Gaussian CEO problem where the number of remote source K=1. First, we provide a new outer region obtained using the entropy power inequality and an equivalent argument (in the sense of having the same rate-distortion region and Berger-Tung inner region) among a certain class of generalized Gaussian CEO problems. We then give two sufficient conditions for our new outer region to match the inner region achieved by Berger-Tung schemes, where the second matching condition implies that in the low-distortion regime, the Berger-Tung inner rate region is always tight, while in the high-distortion regime, the same region is tight if a certain condition holds. The sum-rate part of the outer region is also studied and shown to meet the Berger-Tung sum-rate upper bound under a certain condition, which is obtained using the Karush-Kuhn-Tucker conditions of the underlying convex semidefinite optimization problem, and is in general weaker than the aforesaid two for rate region tightness.

Successive Wyner&amp;#x2013;Ziv Coding Scheme and Its Application to the Quadratic Gaussian CEO Problem

We introduce a distributed source coding scheme called successive Wyner-Ziv coding. We show that any point in the rate region of the quadratic Gaussian CEO problem can be achieved via the successive Wyner-Ziv coding. The concept of successive refinement in the single source coding is generalized to the distributed source coding scenario, which we refer to as distributed successive refinement. For the quadratic Gaussian CEO problem, we establish a necessary and sufficient condition for distributed successive refinement, where the successive Wyner-Ziv coding scheme plays an important role.

Distortion sum-rate performance of successive coding strategy in quadratic gaussian CEO problem

We consider a distributed sensor network, modeled by the CEO problem, in which each sensor communicates its observation to the fusion center (FC) using limited transmission rate. Based on the successive coding strategy, we obtain the optimal rate allocation strategy for the Gaussian CEO problem which minimizes the average distortion in the source estimate produced by the FC. This strategy can be simplified in a general parallel sensor network with L sensors by assigning equal rates to sensors if the sum-rate R macr is very large given a fixed L or if L is very large given a fixed R macr.

An Upper Bound on the Sum-Rate Distortion Function and Its Corresponding Rate Allocation Schemes for the CEO Problem

We consider a distributed sensor network in which several observations are communicated to the fusion center using limited transmission rate. The observation must be separately encoded so that the target can be estimated with minimum average distortion. We address the problem from an information theoretic perspective and establish the inner and outer bound of the admissible rate-distortion region. We derive an upper bound on the sum-rate distortion function and its corresponding rate allocation schemes by exploiting the contra-polymatroid structure of the achievable rate region. The quadratic Gaussian case is analyzed in detail and the optimal rate allocation schemes in the achievable rate region are characterized. We show that our upper bound on the sum-rate distortion function is tight for the quadratic Gaussian CEO problem in the case of same signal-to-noise ratios at the sensors.

The rate-distortion function for the quadratic Gaussian CEO problem

A new multiterminal source coding problem called the CEO problem was presented and investigated by Berger, Zhang, and Viswanathan. Recently, Viswanathan and Berger have investigated an extension of the CEO problem to Gaussian sources and call it the quadratic Gaussian CEO problem. They considered this problem from a statistical viewpoint, deriving some interesting results. In this paper, we consider the quadratic Gaussian CEO problem from a standpoint of multiterminal rate-distortion theory. We regard the CEO problem as a certain multiterminal remote source coding problem with infinitely many separate encoders whose observations are conditionally independent if the remote source is given. This viewpoint leads us to a complete solution to the problem. We determine the tradeoff between the total amount of rate and squared distortion, deriving an explicit formula of the rate-distortion function. The derived function has the form of a sum of two nonnegative functions. One is a classical rate-distortion function for single Gaussian source and the other is a new rate-distortion function which dominates the performance of the system for a relatively small distortion. It follows immediately from our result that the conjecture of Viswanathan and Berger on the asymptotic behavior of minimum squared distortion for large rates is true.

The quadratic Gaussian CEO problem

A firm's CEO employs a team of L agents who observe independently corrupted versions of a data sequence {X(t)}/sub t=1//sup /spl infin//. Let R be the total data rate at which the agents may communicate information about their observations to the CEO. The agents are not allowed to convene. Berger, Zhang and Viswanathan (see ibid., vol.42, no.5, p.887-902, 1996) determined the asymptotic behavior of the minimal error frequency in the limit as L and R tend to infinity for the case in which the source and observations are discrete and memoryless. We consider the same multiterminal source coding problem when {X(t)}/sub t=1//sup /spl infin// is independent and identically distributed (i.i.d.) Gaussian random variable corrupted by independent Gaussian noise. We study, under quadratic distortion, the rate-distortion tradeoff in the limit as L and R tend to infinity. As in the discrete case, there is a significant loss between the cases when the agents are allowed to convene and when they are not. As L/spl rarr//spl infin/, if the agents may pool their data before communicating with the CEO, the distortion decays exponentially with the total rate R; this corresponds to the distortion-rate function for an i.i.d. Gaussian source. However, for the case in which they are not permitted to convene, we establish that the distortion decays asymptotically only as R-l.