Coding Under Observation Constraints

We consider coding schemes when performance is measured by the average signal observation time to reliably decode an information bit, as opposed to conventional metrics of transmit energy per bit or spectral efficiency. This formulation is motivated by energy constrained communications devices where sampling the signal, rather than transmitting or processing it, dominates energy consumption. We show that sequentially observing samples with the maximum a posteriori entropy can significantly reduce observation costs. Equivalently, observation costs identical to traditional coding are achieved at blocklengths that are an order of magnitude smaller. To put this in perspective, our sampling strategy can be applied to realizing feedback systems that surpass the cutoff rate limit using the (24,12) Golay code, the highest such performance reported over the AWGN channel at these blocklengths.