Wireless sensor networks are networks consisting of spatially distributed autonomous devices called sensors, deployed to cooperatively collect information and send it back to a location in which it can be extracted and analyzed. One of the most challenging topic in these networks is how to efficiently use the limited energy resource in each sensor node in order to increase the lifetime of the whole network. In this thesis, we address the source-channel coding problem applied to wireless sensor network models where sensor nodes are observing sources of information and sending back their gathered data through a Gaussian multiple-access channel to a given receiver or collector node. In a first part, independent random sources varying slowly in time are considered. A source-channel code adapted with the application characteristics is proposed and bounds on the optimal achievable performance are derived. Several model variants involving noncoherent detection and the presence of observation noise are also studied. In a second part, arbitrarily correlated discrete sources of finite alphabets are considered. After being encoded, they are sent through a Gaussian multiple-access channel with phase shifts unknown at the transmitters and completely known at the receiver. For both random ergodic and arbitrary non-random models for the phase shifts, it is proved that the separation theorem holds, and consequently, the strategy of combining Slepian-Wolf coding to capacity achieving channel encoders is optimal. For continuous sources, it is shown that the source-channel separation is asymptotically optimal. Finally, a wireless sensor network monitoring a random physical field is considered. The performance of a linear encoder scheme is investigated and bounds on the optimal achievable performance are derived.
