I. Introduction
Joint source-channel coding [1] received a great attention in the literature in virtue of its technological impact on sensor networks, whose infrastructure is usually based on multiple sources and a single destination (called sink). The aim is to obtain the minimum distortion, according to some measure, between transmitted and reconstructed (at the sink) variables, under a power constraint at the sensors (or viceversa, a given distortion with minimum power). The real-time operation considers source and channel coding jointly and deals with continuous, rather than discrete, random variables. In many cases, simple analog amplification of the signals at the sensors (known as Amplify and Forward - AF) is adopted. The largest part of the results are based on Gaussian sources and channels, for which optimal linear coders and decoders are obtainable in closed form or by means of a gradient numerical optimization with Lagrange multipliers, see, e.g., [2], [3]. The optimal design can be also derived in the case of imperfect knowledge of channel state [4]. Nonlinear structures have been recently investigated for bandwidth compression or expansion problems, in which appropriate functions are sought for the mapping of a source vector of size onto a given number of channels . The mapping is performed in an informationally centralized way. These approaches are based on proper sinusoidal projections, which are tractable under small and (practical examples are given for 2:1, 3:1, 4:1 and 3:2 systems) [5]–, [7]. They provide performance improvements over linear coding-decoding for Gaussian or Laplacian sources. Other kinds of nonlinear structures are obtained numerically through functional optimization [8], [9], again under small dimensionalities.