Precoding and decoding paradigms for distributed vector data compression

In this paper, we consider the problem of lossy coding of correlated vector sources with uncoded side information available at the decoder. In particular, we consider lossy coding of vector source x ∈ ℝ^N which is correlated with vector source y ∈ ℝ^N, known at the decoder. We propose two compression schemes, namely, distributed adaptive compression (DAC) and distributed universal compression (DUC) schemes. The DAC algorithm is inspired by the optimal solution for Gaussian sources and requires computation of the conditional Karhunen-Loève transform (CKLT) of the data at the encoder. The DUC algorithm, however, does not require knowledge of the CKLT at the encoder. The DUC algorithms are based on the approximation of the correlation model between the sources y and x through a linear model y = Hx + n in which H is a matrix and n is a random vector and independent of x. This model can be viewed as a fictitious communication channel with input x and output y. Utilizing channel equalization at the receiver, we convert the original vector source coding problem into a set of manageable scalar source coding problems. Furthermore, inspired by bit loading strategies employed in wireless communication systems, we propose for both compression schemes a rate allocation policy which minimizes the decoding error rate under a total rate constraint. Equalization and bit loading are paired with a quantization scheme for each vector source entry (a slightly simplified version of the so called DISCUS scheme). The merits of our work are as follows: 1) it provides a simple, yet optimized, implementation of Wyner-Ziv quantizers for correlated vector sources, by using the insight gained in the design of communication systems; 2) it provides encoding schemes that, with or without the knowledge of the correlation model at the encoder, enjoy distributed compression gains.