Energy-distortion tradeoffs in multiple-access channels with feedback

The energy-distortion function E(D) for the joint source-channel coding problem in networks is defined and studied. The energy-distortion function E(D) is defined as the minimum energy required to transmit a source to a receiver within the target distortion D, when there is no restriction on the number of channel uses per source sample. For point-to-point channels, E(D) is shown to be equal to the product of the minimum energy per bit E_bmin and the rate-distortion function R(D), establishing the optimality of source-channel separation in this setting. Then, it is shown that the optimality of separation does not extend to multi-user networks. A scenario with two encoders observing correlated Gaussian sources in which the encoders communicate to the receiver over a Gaussian multiple-access channel (MAC) with perfect channel output feedback is studied. First a lower bound on E(D) is provided and compared against an upper bound achievable by separation. Even though the separation based scheme does not achieve the lower bound in general, its energy requirement is shown to be within a constant gap of E(D) in the low distortion regime, for which the energy requirement grows unbounded. Another upper bound using uncoded transmission based on the well-known Schalkwijk-Kailath (SK) scheme is also considered. Through simulation, it is shown that this scheme outperforms the separation based scheme in various scenarios, thus establishing the sub-optimality of separation in this model of multiple users with correlated sources.