Distributed Sensing and Transmission of Sporadic Random Samples Over a Multiple-Access Channel

This work considers distributed sensing and transmission of sporadic random samples. A new lower-bound is presented on the reconstruction error of a common vector imperfectly measured by a network of sensors. The noisy correlated observations of the source vector are transmitted with finite energy to a single receiver via an additive white Gaussian noise asynchronous multiple-access channel (MAC). Transmission makes use of a perfect causal feedback link to the encoder connected to each sensor. Asymptotic upper-bounds on the distortion are provided for a retransmission protocol which is inspired by the classical scheme of Yamamoto and Itoh and extended to a more general network scenario. Additionally, we introduce lower-bounds on the reconstruction error for individual estimators of the noisy observations themselves. Both the upper and lower-bounds show that collaboration can be achieved through energy accumulation under certain circumstances. To investigate the practical performance of the proposed protocol we provide a numerical evaluation of the upper-bounds in the non-asymptotic energy regime using low-order quantization in the sensors. It is shown that an increase in the size of the network brings benefit in terms of performance, but that the gain in terms of energy efficiency diminishes quickly at finite energies due to a non-coherent combining loss.