Tracking Markov targets in binary sensor networks: Source coding and large deviation limits on the required number of queries

Using concepts from coding theory, we define e-achievability for target tracking in binary sensor networks and compare this to the more usual notion of trackability: a target can be tracked in a binary sensor network through a query mechanism if the tracker obtains the correct target track history at infinitely many times almost surely. Trackability is a relatively weak conclusion, allowing the possibility that at most times the track history estimate will be incorrect with high probability. The stronger condition of e-achievability requires the existence of a query strategy that ensures that the probability of error in estimating the track history converges exponentially to zero over time with a given exponent e. We provide necessary and sufficient conditions on the query rate of the network for e-achievability by extending the concept of e-achievability from that for fixed length codes to weak variable length codes. These conditions are related to the Renyi entropy rate of the target, and has similarities with results on fixed length source coding, though the derivation of our sufficient condition is based entirely on large deviation theory.