  The Internet of Things paradigm envisages the presence of many
battery-powered sensors and this entails the design of energy-aware protocols.
Source coding techniques allow to save some energy by compressing the packets
sent over the network, but at the cost of a poorer accuracy in the
representation of the data. This paper addresses the problem of designing
efficient policies to jointly perform processing and transmission tasks. In
particular, we aim at defining an optimal scheduling strategy with the twofold
ultimate goal of extending the network lifetime and guaranteeing a low overall
distortion of the transmitted data. We propose a Time Division Multiple Access
(TDMA)-based access scheme that optimally allocates resources to heterogeneous
nodes. We use realistic rate-distortion curves to quantify the impact of
compression on the data quality and propose a complete energy model that
includes the energy spent for processing and transmitting the data, as well as
the circuitry costs. Both full knowledge and statistical knowledge of the
wireless channels are considered, and optimal policies are derived for both
cases. The overall problem is structured in a modular fashion and solved
through convex and alternate programming techniques. Finally, we thoroughly
evaluate the proposed algorithms and the influence of the design variables on
the system performance adopting parameters of real sensors.
