Analog Matching of Colored Sources to Colored Channels

TL;DR

This paper introduces a novel analog matching scheme using prediction and modulo-lattice operations that enables optimal transmission of colored Gaussian sources over colored Gaussian channels, achieving Shannon's limit.

Contribution

It presents a new method combining prediction and modulo-lattice techniques to match any colored Gaussian source to any colored Gaussian channel, achieving optimal performance.

Findings

Achieves Shannon's capacity with colored sources and channels.

Asymptotically robust for high SNR when BWs are equal.

Extends modulo-lattice schemes to colored Gaussian scenarios.

Abstract

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.