Energy efficient lossy transmission over sensor networks with feedback

The energy-distortion function (E(D)) for a network is defined as the minimum total energy required to achieve a target distortion D at the receiver without putting any restrictions on the number of channel uses per source sample. E(D) is studied for a sensor network in which multiple sensors transmit their noisy observations of a Gaussian source to the destination over a Gaussian multiple access channel with perfect channel output feedback. While the optimality of separate source and channel coding is proved for the case of a single sensor, this optimality is shown to fail when there are multiple sensors in the network. A network with two sensors is studied in detail. First a lower bound on E(D) is given. Then, two achievability schemes are proposed: a separation based digital scheme and a Schalkwijk-Kailath (SK) type uncoded scheme. The gap between the lower bound and the upper bound based on separation is shown to be a constant even as the total energy requirement goes to infinity in the low distortion regime. On the other hand, as the distortion requirement is relaxed, the SK based scheme is shown to outperform separation in certain cases, proving that the optimality of source-channel separation does not hold in the multi-sensor setting.