Asynchronous Capacity per Unit Cost under a Receiver Sampling Constraint

In a recently proposed asynchronous communication setup, the receiver observes mostly pure background noise except for a brief and a priori unknown period of time when data is transmitted. Capacity per unit cost and minimum communication delay were characterized and shown to be unaffected by a sparse sampling at the receiver as long as the number of samples represents a constant fraction of the total channel outputs. This paper strengthens this result and shows that it continues to hold even if the sampling rate tends to zero. More specifically, if the sampling rate is omega (1/B), where B denotes the number of transmitted message bits, capacity per unit cost and minimum decoding delay are the same as under full output sampling. Conversely, if the sampling rate decreases as o(1/B), reliable communication is impossible. The main ingredient in the achievability argument is a time series sampling/detection procedure that detects transient changes in distribution. This procedure has the property of simultaneously minimizing detection delay and sampling rate, in the regime of vanishing false-alarm probability.