Analog Matching of Colored Sources to Colored Channels

Uncoded transmission provides a simple, delay-less and robust scheme for communicating a Gaussian source over a filter channel under the mean squared error (MSE) distortion measure. Unfortunately, its performance is usually inferior to the all-digital solution, consisting of a rate-distortion code for the source followed by a capacity achieving code for the channel. The performance loss of uncoded transmission comes from the fact that except for very special cases, it is impossible to achieve simultaneous matching of source to channel and channel to source by linear means. We show that by combining prediction and modulo-lattice arithmetic, we can match any stationary Gaussian source to any inter-symbol interference, colored-noise Gaussian channel, hence we achieve Shannon's optimum attainable performance R(D) = C. This scheme is based upon a novel analog modulo-lattice solution to the joint source-channel coding problem for a Gaussian Wyner-Ziv source and a dirty-paper channel