Many modern day systems comprise of small energy-limited devices which are capable of communicating over the wireless medium. In the future, they are expected to substantially increase the amount of data they handle, and also take on diverse communication and sensing roles while facing severe energy constraints due to limited battery sizes. Furthermore, in these systems, wireless transmission accounts for a major portion of the total energy consumption. Therefore, in this thesis we study fundamental limits on the minimum transmission energy requirements. In particular, we consider the information-theoretic notion of energy efficiency in wireless networks, for both channel coding as well as joint source-channel coding problems.

For the channel coding problems, the notion of energy efficiency is expressed by the quantity—minimum energy per bit. We provide a lower bound on the minimum energy per bit for wireless networks which suffer from additive white Gaussian noise and circularly symmetric fading (no channel state information at the transmitters). This lower bound is applicable even when there are multiple destinations for a common message (multicasting ), and when there is no restriction on the transmission bandwidth. We also provide upper bounds by proposing two different kinds of communication schemes—decode-and-forward, and aggregate-and-forward. In many scenarios, like random networks, directed acyclic graphs or networks with a remote source, the proposed schemes are either optimal or close to optimal.

For the joint source-channel coding problems, we study the problem of minimizing the energy consumption of transmission from one or many sensor nodes to a central receiver (fusion center), such that the receiver is able to reconstruct the observations at the sensor(s) within an average distortion criterion. To properly capture the energy consumption in such systems, we propose and define an information-theoretic notion of energy-distortion tradeoff. For the case of a single sensor and point-to-point communication link to the receiver, separate source and channel coding is optimal. However, the same is not true when there are two sensors communicating to the receiver over a wireless multiple-access channel (MAC). We provide upper and lower bounds on the energy-distortion tradeoff for MAC. Additionally, we also study the case when there is perfect channel output feedback available to the sensors. In particular, uncoded transmission is shown to outperform separate source and channel coding in various scenarios, for both feedback and no feedback cases.