We study the distributed averaging problem on arbitrary connected graphs, with the additional constraint that the value at each node is an integer. This discretized distributed averaging problem models averaging in a network with finite capacity channels (and in this form has applications to distributed detection in sensor networks) and load balancing in a processor network. We describe simple randomized distributed algorithms which achieve consensus to the extent that the discrete nature of the problem permits.

In a decentralized detection problem where N sensors make observations (the laws of which depend on the realized hypothesis) and communicate one of a finite and prespecified set of messages to a fusion center, optimal sensor decision rules have polyhedral decision regions in the space of likelihood vectors for a large class of Bayesian costs. We point out in this comment that this result can be easily derived from earlier results, even in the case when the communication from the sensors to the fusion center is over (parallel, independent) noisy channels

We study the problem of the reconstruction of a Gaussian field defined in [0,1] using N sensors deployed at regular intervals. The goal is to quantify the total data rate required for the reconstruction of the field with a given mean square distortion. We consider a class of two-stage mechanisms which (a) send information to allow the reconstruction of the sensor's samples within sufficient accuracy, and then (b) use these reconstructions to estimate the entire field. To implement the first stage, the heavy correlation between the sensor samples suggests the use of distributed coding schemes to reduce the total rate. Our main contribution is to demonstrate the existence of a distributed block coding scheme that achieves, for a given fidelity criterion for the sensor's measurements, a total information rate that is within a constant, independent of N, of the minimum information rate required by an encoder that has access to all the sensor measurements simultaneously. The constant in general depends on the autocorrelation function of the field and the desired distortion criterion for the sensor samples.

A zero-sum mutual information game on MIMO Gaussian Rayleigh fading channels is considered in this paper. The players are an encoder-decoder pair as the maximizer, and a jammer as the minimizer, of the mutual information between the input and the output of the channel. There are total power constraints on both the jammer and the encoder. Also, the jammer has access to the encoder output. We find the unique saddle point of this game, and prove the somewhat surprising result that the knowledge of the channel input is useless to the jammer.

We consider a zero-sum mutual information game on multiple-input multiple-output (MIMO) Gaussian Rayleigh-fading channels. The players are an encoder-decoder pair as the maximizer, and a jammer as the minimizer, of the mutual information between the input and the output of the channel. There are total power constraints on both the jammer and the encoder. Also, the jammer has access to the encoder output. We find the unique saddle point of this game, and prove the somewhat surprising result that the knowledge of the channel input is useless to the jammer.