Linear precoding and decoding for distributed data compression

Considering two correlated vector sources x, y ∈ ℝ^N, we address the problem of lossy coding of x with uncoded side information y available at the decoder. The general non-linear mapping between y and x capturing their correlation can be approximated through a linear model y = Hx + n in which n is independent of x. Viewing this model as a virtual communication channel with input x and output y we utilize linear precoding and decoding technique to convert the original vector source coding problem into a set of manageable scalar source coding problems. The scalar source coding problems can be solved using the existing distributed source coding algorithms that are primarily designed for the simple correlation model y = x + n where x and y are scalar jointly Gaussian sources.