Analog Matching of Colored Sources to Colored Channels † Yuval Kochman and Ram Zamir

Analog (uncoded) transmission provides a simple and robust scheme for communicating a Gaussian source over a Gaussian channel under the mean squared error (MSE) distortion measure. Unfortunately, its performance is usually inferior to the all-digital, separation-based source-channel coding solution, which requires exact knowledge of the channel at the encoder. The loss comes from the fact that except for very special cases, e.g. white source and channel of matching bandwidth (BW), it is impossible to achieve perfect matching of source to channel and channel to source by linear means. We show that by combining prediction and modulo-lattice operations, it is possible to match any colored Gaussian source to any colored Gaussian noise channel (of possibly different BW), hence achieve Shannon’s optimum attainable performance R(D) = C. Furthermore, when the source and channel BWs are equal (but otherwise their spectra are arbitrary), this scheme is asymptotically robust in the sense that for high signal-to-noise ratio a single encoder (independent of the noise variance) achieves the optimum performance. The derivation is based upon a recent modulo-lattice modulation scheme for transmitting a Wyner-Ziv source over a dirty-paper channel. keywords: joint source/channel coding, analog transmission, Wyner-Ziv problem, writing on dirty paper, modulo lattice modulation, MMSE estimation, prediction, unknown SNR, broadcast channel, ISI channel, bandwidth expansion/reduction. Parts of this work were presented at ISIT2006, Seattle, WA, July 2006 and at ISIT2007, Nice, France, July 2007. This work was supported by the Israeli Science Foundation (ISF) under grant # 1259/07, and by the Advanced Communication Center (ACC). The first author was also supported by a fellowship of the Yitzhak and Chaya Weinstein Research Institute for Signal Processing at Tel Aviv University.