Energy-efficient communication via feedback

We propose a feedback optimization framework to minimize the total energy consumption in point-to-point links. The energy cost of both the forward link and the feedback link are taken into account. Given the energy consumption profile of both links, we minimize error probability subject to the total energy budget and a delay constraint. The proposed framework is based on a multi-phase feedback scheme in which a transmission, if decoded incorrectly, is followed by a retransmission with boosted energy. We show that the gain of using feedback is highly dependent on the energy consumption profile of the links and the total available energy. To illustrate this fact, we study the above framework under two different error probability models. In the first model, we assume that the one shot decoding error probability in each direction (forward or feedback) decreases exponentially with the amount of energy consumed for the corresponding transmission. In this model, the use of feedback significantly increases the energy efficiency if the total available energy is large enough. Surprisingly, this is not the case when the total energy budget is below a given threshold. In such cases, the use of feedback is strictly suboptimal in terms of energy efficiency. Interestingly, the opposite behavior occurs under the second error probability model in which we assume a super-exponential decay in probability of decoding error as a function of consumed energy. Under this model, we show that feedback does not increase energy efficiency for energy levels above a certain threshold.