Algebraic Structures for Multi-Terminal Communication Systems - Thesis Proposal

In this work, we study a distributed source coding problem with multiple encoders, a central decoder and a joint distortion criterion. The encoders observe correlated sources which they quantize and communicate to a central decoder through a rate constrained, noiseless channel. The objective is to minimize the distortion as measured by a joint distortion criterion that depends on the sources and the reconstruction. We are interested in characterizing a computable inner bound to the optimal rate-distortion region. We first consider a special case of the general problem where the sources are jointly Gaussian and the decoder is interested in reconstructing a linear function of the sources under mean square error distortion criterion and present an achievable rate-distortion region. We demonstrate a coding scheme involving structured nested lattice codes that achieves this bound by encoding in such a fashion that the decoder is able to reconstruct the function directly. For certain source distributions, this approach yields a larger ratedistortion region compared to when the decoder reconstructs lossy versions of the sources first and then estimates the function from them. We then extend this approach to the case of reconstructing a linear function of an arbitrary number of jointly Gaussian sources. Next, we consider the general distributed source coding problem involving multiple discrete sources and a central decoder with a joint distortion criterion. This formulation includes as a special case the problem of computing a function of the sources to within some distortion and also the classic SlepianWolf problem, Berger-Tung problem, Wyner-Ziv problem, Yeung-Berger problem and the Ahlswede-KornerWyner problem. We present a new achievable rate-distortion region for this problem based on “good” structured nested random codes built over abelian groups. We demonstrate rate gains for this problem