This project aims to answer a fundamental question in wireless networking: what is the energy needed to transmit one bit of information over a wireless network? And the related question: how can practical networks be designed to come close to this limit? The motivation is to save energy. It is evident that there is a strong current interest in energy conservation. Currently it is estimated that consumer electronics account for 11% of total residential electricity consumption in the US. While this is not all used on communications, as most devices have wireless capability, wireless communications could account for a significant part of this energy consumption. Clearly, if this energy consumption can be cut in half, the saving is significant. In fact, preliminary results show that by optimizing the signaling, energy consumption in wireless communications can be reduced much more than 50%.
As is well known, there are few networks where the exact Shannon capacity has been found. The research therefore approaches the theoretical part of this problem in different ways. For some networks, the minimum energy per bit can be found even if the exact capacity cannot be found. When the exact minimum energy per bit cannot be found, approximations to the minimum energy per bit are sought in the form of a figure within a certain number of dB that is universal over a certain class of networks. A key part of the research will be to look at networks with correlated information and distortion. Joint source-channel coding can reduce the energy consumption beyond what a separate approach can provide. The theoretical approach will be combined with practical coding methods.
In this paper, we study the minimum energy of sending correlated information over the Gaussian MAC. We consider the following three source models of both theoretical and practical interests. For all three source models, we lower bound the minimum energy using a cut-set argument, while taking the distortion correlations into account to improve the lower bound in the high-distortion regime over that of Verdu, et al. For achievable schemes, we first study separate source and channel coding and uncoded transmission as benchmarks, we then propose a hybrid digital/analog scheme that achieves the best known energy efficiency. 1) Gaussian multiterminal sources: We study the minimum energy of sending any number of positive symmetric Gaussian sources over the Gaussian MAC such that the decoder can reconstruct individual sources and satisfy mean squared error (MSE) distortion constraints on them. Bivariate Gaussian results appeared before, but the case with more than two terminals has never been treated as a joint source-channel coding problem before. For an arbitrary number of terminals including the bivariate case, we provide the best known upper and lower bounds on the minimum energy. 2) Gaussian CEO sources: We give upper and lower bounds on the minimum energy of sending Gaussian CEO sources over the Gaussian MAC, which allows the decoder to meet the MSE distortion constraint on the remote source. We show that hybrid digital/analog transmission achieves the best known energy efficiency. 3) Correlated binary sources: We study the minimum energy of lossy transmission of correlated binary sources over the Gaussian MAC. We show that hybrid digital/analog transmission is also energy efficient for this discrete case and it approaches our lower bound as the number of sources goes to infinity.
