Akshay Kashyap

Quantized consensus

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 the finite capacity channel (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

Correlated jamming on MIMO Gaussian fading channels

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.

Distributed source coding in dense sensor networks

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 sensors 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 sensors 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.

Consensus with Quantized Information Updates

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 the computation of sufficient statistics in various sensing problems) 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. We obtain bounds on the convergence time of these algorithms for fully connected networks and linear networks

Comments on "On the optimality of the likelihood-ratio test for local sensor decision rules in the presence of nonideal channels"

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

Minimum distortion transmission of Gaussian sources over fading channels

We consider the problem of reliably communicating the output of a Gaussian source across average power constrained multi-antenna channels. We consider both fading and constant gain channels, and assume that in the former case the receiver has perfect channel state information. We are interested in designing simple memoryless encoding and decoding strategies to minimize the mean-square error between the transmitted and reconstructed vectors. We find the optimal encoder and decoder pair when the encoder is restricted to the class of linear transformations on the input and evaluate its performance. We also derive the theoretically achievable optimal performance. For the constant gain channel, we find that linear coding can be optimal under certain conditions. For the Rayleigh fading channel, we prove that the performance of the linear encoder/decoder pair in the low SNR regime is the same as the optimal to the first order. We prove the same approximate optimality result for the Rician channel in some special cases.

Asymptotically optimal quantization for detection in power constrained decentralized sensor networks

We study a Bayesian decentralized binary hypothesis testing problem, in which N sensors make observations related to a two-valued hypothesis, and send messages based on the observations to a fusion center, with the objective of enabling the fusion center to accurately reconstruct the realized hypothesis. We assume that the observations at the sensors are independent and identically distributed conditioned on the hypothesis, and that the sensors transmit their messages over independent, parallel channels to the fusion center. We also make the natural assumption that the sensors have identical, finite message sets at their disposal, that each message has some cost associated with it, and that there is a constraint on the average cost incurred by a sensor. We study the large N asymptote, and therefore are interested in schemes that optimize the error exponent at the fusion center. Our main contributions are 1) proving that the problem of finding the optimal schemes is a finite dimensional optimization problem, 2) a description of the structure of optimal rules: we prove that optimal sensor rules are randomized likelihood ratio quantizers (LRQs), with randomization being over at most two deterministic LRQs. We further show that under some conditions, randomization is not required

Real-time transmission of Gaussian sources over fading channels

We find the linear encoder and decoder pair that minimizes the mean square error in the transmission of a white Gaussian source over a Rayleigh fading channel and show that at low SNR the performance of linear coding is, to the first order, the same as the optimal performance theoretically achievable.