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 infinit...
Aman Jain, Deniz Gündüz, Sanjeev R. Kulk