Separation Theorems And Partial Orderings For Sensor Network Problems
In this chapter, we discuss information-theoretic techniques to understand sensor network performance. From an information-theoretic perspective, sensor network problems are typically joint source-channel coding problems: The goal is to recover an approximate version of the underlying source information (by contrast to, for example, the standard channel coding problems where the goal is to communicate bits at the smallest possible error probability). Hence, the overall encoding process maps a sequence of source observations into a suitable sequence of channel inputs in such a way that the decoder, upon observing a noisy version of that sequence, can get an estimate of the source observations at the highest possible fidelity. Successful code constructions must exploit the structure of the underlying source (and the mechanism by which the source is observed) and the communication channel. Designing codes that simultaneously achieve both should be expected to be a rather difficult task, and it is therefore somewhat surprising that Shannon  found a very elegant solution for the case of point-to-point communication (as long as both the source and the channel are stationary and ergodic, and cost and fidelity are assessed by per-letter criteria). The solution consists in a separation of the overall task into two separate tasks. Specifically, an optimal communication strategy can be designed in two parts, a source code, exploiting the structure of the source and the observation process, followed by a channel code, exploiting the structure of the communication channel. The two stages are connected by a universal interface - bits- that does not depend on the precise structure. For the purpose of this chapter, we will refer to such an architecture as separation-based.
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