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.
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. 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. >