In many resource allocation problems, a centralized controller needs to award some resource to a user selected from a collection of distributed users with the goal of maximizing the utility the user would receive from the resource. This can be modeled as the controller computing an extremum of the distributed users’ utilities. The overhead rate necessary to enable the controller to reproduce the users’ local state can be prohibitively high. An approach to reduce this overhead is interactive communication wherein rate savings are achieved by tolerating an increase in delay. In this paper, we consider the design of a simple achievable scheme based on successive refinements of scalar quantization at each user. The optimal quantization policy is computed via a dynamic program and we demonstrate that tolerating a small increase in delay can yield significant rate savings. We then consider two simpler quantization policies to investigate the scaling properties of the rate-delay tradeoffs. Using a combination of these simpler policies, the performance of the optimal policy can be closely approximated with lower computational costs.
For the general rate-distortion problem, an algorithm for building optimized distributed quantizers was given wherein the CEO uses the quantized observations to perform hypothesis testing @cite_17 . A two-stage distributed scheme was proposed for the case when the users each have a noisy observation on the same source, and the CEO needs to reproduce the source with a bounded expected distortion @cite_9 @cite_13 . A first stage of local quantization is followed by a second stage of encoding the quantized signals based on Slepian-Wolf coding using syndrome codes @cite_13 or index reuse techniques @cite_9 . In their treatment of the CEO problem with non-regular source distributions, Vempaty and Varshney provided an acheivability proof that utilized a layered approach of quantization followed by entropy coding @cite_31 .
@cite_31 @cite_9 @cite_13 @cite_17
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We consider the CEO problem for non-regular source distributions (such as uniform or truncated Gaussian). A group of agents observe independently corrupted versions of data and transmit coded versions over rate-limited links to a CEO. The CEO then estimates the underlying data based on the received coded observations. Agents are not allowed to convene before transmitting their observations. This formulation is motivated by the practical problem of a firm’s CEO estimating (non-regular) beliefs about a sequence of events, before acting on them. Agents’ observations are modeled as jointly distributed with the underlying data through a given conditional probability density function. We study the asymptotic behavior of the minimum achievable mean squared error distortion at the CEO in the limit when the number of agents @math and the sum rate @math tend to infinity. We establish a @math convergence of the distortion, an intermediate regime of performance between the exponential behavior in discrete CEO problems [Berger, Zhang, and Viswanathan (1996)], and the @math behavior in Gaussian CEO problems [Viswanathan and Berger (1997)]. Achievability is proved by a layered architecture with scalar quantization, distributed entropy coding, and midrange estimation. The converse is proved using the Bayesian Chazan–Zakai–Ziv bound. An important class of engineering problems involves sensing an environment and making estimates based on the phenomena sensed. In the traditional model of this problem, the sensors' observations are available to the estimator without alteration. There is .growing interest in distributed sensing systems in which several observations are communicated to the estimator over channels of limited capacity. The observations must be separately encoded so that the target can be estimated with minimum distortion. Two questions are addressed for a special case of this problem wherein there are two sensors which observe noisy data and communicate with a single estimator: 1) if the encoder is unlimited in complexity, what communication rates and distortions can be achieved, 2) if the encoder must be a quantizer (a mapping of a single observation sample into a digital output), how can it be designed for good performance? The first question is treated by the techniques of information theory. It is proved that a given combination of rates and distortion is achievable if there exist degraded versions of the observations that satisfy certain formulas. The second question is treated by two approaches. In the first, the outputs of the quantizers undergo a second stage of encoding which exploits their correlation to reduce the output rate. Algorithms which design the second stage are presented and tested. The second approach is based on the distributional distance , a measure of dissimilarity between two probability distributions. An algorithm to modify a quantizer for increased distributional distance is derived and tested. Distributed nature of the sensor network architecture introduces unique challenges and opportunities for collaborative networked signal processing techniques that can potentially lead to significant performance gains. Many evolving low-power sensor network scenarios need to have high spatial density to enable reliable operation in the face of component node failures as well as to facilitate high spatial localization of events of interest. This induces a high level of network data redundancy, where spatially proximal sensor readings are highly correlated. We propose a new way of removing this redundancy in a completely distributed manner, i.e., without the sensors needing to talk, to one another. Our constructive framework for this problem is dubbed DISCUS (distributed source coding using syndromes) and is inspired by fundamental concepts from information theory. We review the main ideas, provide illustrations, and give the intuition behind the theory that enables this framework.We present a new domain of collaborative information communication and processing through the framework on distributed source coding. This framework enables highly effective and efficient compression across a sensor network without the need to establish inter-node communication, using well-studied and fast error-correcting coding algorithms. In a decentralized hypothesis testing network, several peripheral nodes observe an environment and communicate their observations to a central node for the final decision. The presence of capacity constraints introduces theoretical and practical problems. The following problem is addressed: given that the peripheral encoders that satisfy these constraints are scalar quantizers, how should they be designed in order that the central test to be performed on their output indices is most powerful? The scheme is called cooperative design-separate encoding since the quantizers process separate observations but have a common goal; they seek to maximize a system-wide performance measure. The Bhattacharyya distance of the joint index space as such a criterion is suggested, and a design algorithm to optimize arbitrarily many quantizers cyclically is proposed. A simplified version of the algorithm, namely an independent design-separate encoding scheme, where the correlation is either absent or neglected for the sake of simplicity, is outlined. Performances are compared through worked examples. >