Energy and sampling constrained asynchronous communication

The minimum energy, and, more generally, the minimum input cost, to transmit one bit of information has been recently derived for bursty communication when information is available infrequently at random times at the transmitter. This result assumes that the receiver can sample at no cost all channel outputs. Suppose now there is a cost associated to output sampling and that the receiver is constrained to observe only a fraction ρ (0, 1] of all channel outputs. What is the input cost penalty due to sparse output sampling? Remarkably, there is no penalty: regardless of ρ > 0 the asynchronous capacity per unit cost is the same as under full sampling, i.e., when ρ = 1. Moreover, there is no penalty in terms of decoding delay with respect to full sampling. This latter result relies on the possibility to sample adaptively; the next sample is a function of past samples. When sampling is non-adaptive it is possible to achieve the full sampling asynchronous capacity per unit cost, but the decoding delay gets multiplied by 1/ρ. Therefore adaptive sampling strategies are of particular interest in the very sparse sampling regime.