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.
In information theory, the interest is usually on characterizing inner outer bounds for the rate region. introduced the generic CEO problem, wherein the CEO wants to reproduce the source from the received signals @cite_15 . The rate region for the problem of source reproduction with constrained distortion remains unknown, except for the cases of: Vempaty and Varshney considered the CEO problem for non-regular source distributions (e.g., truncated Gaussian) with quadratic distortion and studied the asymptotic behavior of the distortion function @cite_31 .
@cite_15 @cite_31
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We consider a new problem in multiterminal source coding motivated by the following decentralized communication estimation task. A firm's Chief Executive Officer (CEO) is interested in the data sequence X(t) sub t=1 sup spl infin which cannot be observed directly, perhaps because it represents tactical decisions by a competing firm. The CEO deploys a team of L agents who observe independently corrupted versions of X(t) sub t=1 sup spl infin . Because X(t) is only one among many pressing matters to which the CEO must attend, the combined data rate at which the agents may communicate information about their observations to the CEO is limited to, say, R bits per second. If the agents were permitted to confer and pool their data, then in the limit as L spl rarr spl infin they usually would be able to smooth out their independent observation noises entirely. Then they could use their R bits per second to provide the CEO with a representation of X(t) with fidelity D(R), where D( spl middot ) is the distortion-rate function of X(t) . In particular, with such data pooling D can be made arbitrarily small if R exceeds the entropy rate H of X(t) . Suppose, however, that the agents are not permitted to convene, Agent i having to send data based solely on his own noisy observations Y sub i (t) . We show that then there does not exist a finite value of R for which even infinitely many agents can make D arbitrarily small. Furthermore, in this isolated-agents case we determine the asymptotic behavior of the minimal error frequency in the limit as L and then R tend to infinity. 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.