Mukul Agarwal

Structural Properties of Optimal Transmission Policies Over a Randomly Varying Channel

We consider the problem of transmitting packets over a randomly varying point to point channel with the objective of minimizing the expected power consumption subject to a constraint on the average packet delay. By casting it as a constrained Markov decision process in discrete time with time-averaged costs, we prove structural results about the dependence of the optimal policy on buffer occupancy, number of packet arrivals in the previous slot and the channel fading state for both i.i.d. and Markov arrivals and channel fading. The techniques we use to establish such results: convexity, stochastic dominance, decreasing-differences, are among the standard ones for the purpose. Our main contribution, however, is the passage to the average cost case, a notoriously difficult problem for which rather limited results are available. The novel proof techniques used here are likely to have utility in other stochastic control problems well beyond their immediate application considered here.

Architecture for communication with a fidelity criterion in unknown networks

We prove that in order to communicate independent sources (this is the unicast problem) between various users over an unknown medium to within various distortion levels, it is sufficient to consider source-channel separation based architectures: architectures which first compress the sources to within the corresponding distortion levels followed by reliable communication over the unknown medium. We are reducing the problem of universal rate-distortion communication of independent sources over a network to the universal reliable communication problem over networks. This is a reductionist view. We are not solving the reliable communication problem in networks.

Universal capacity of channels with given rate-distortion in absence of common randomness, and failure of universal source-channel separation

Recently, [3] studied the universal capacity of a set of channels where each channel in the set communicates a random source to within a distortion level D, when the transmitter and receiver have access to common randomness. In this paper, we study the universal capacity for this channel set in the case when there is no access to common randomness. We show that when the distortion level D is positive, the universal capacity is 0. This also leads to the conclusion that universal source-channel separation for rate-distortion as stated in [4], is false.