Distributed sensing and transmission of sporadic random samples

This work considers distributed sensing and transmission of sporadic random samples. Lower bounds are derived for the reconstruction error of a single normally or uniformlydistributed vector imperfectly measured by a network of sensors and transmitted with finite energy to a common receiver via an additive white Gaussian noise asynchronous multiple-access channel. Transmission makes use of a perfect causal feedback link to the encoder connected to each sensor. A retransmission protocol inspired by the classical scheme in [1] applied to the transmission of single and bi-variate analog samples analyzed in
[2] and [3] is extended to the more general network scenario, for which asymptotic upper-bounds on the reconstruction error are provided. Both the upper and lower-bounds show that collaboration can be achieved through energy accumulation under certain circumstances.