Energy and sampling constrained asynchronous communication

The minimum energy, and, more generally, the minimum cost, to transmit 1 bit of information was recently derived for bursty communication when the information is available infrequently at random times at the transmitter. This result assumes that the receiver is always in the listening mode and samples all channel outputs until it makes a decision. Since sampling is in practice one of the receiver's most energy consuming functions, a natural question is to evaluate capacity per unit cost when the receiver is sampling constrained. This paper investigates such a setting where the receiver can sample only a given fraction ρ ε (0, 1] of the channel outputs. It is shown that regardless of ρ > 0 , the asynchronous capacity per unit cost is the same as under full sampling, i.e., when ρ = 1. Moreover, a sparse output sampling does not even impact decoding delay - the elapsed time between when information is available and when it is decoded. Hence, surprisingly, it suffices to sample an arbitrarily small fraction of the channel outputs and yet achieve the same (asymptotic) performance as under full output sampling.