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 (SNR) 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.
Bibliographical noteFunding Information:
Manuscript received July 04, 2008; revised May 24, 2010; accepted October 11, 2010. Date of current version May 25, 2011. Y. Kochman was supported by a fellowship from the Yitzhak and Chaya Weinstein Research Institute for Signal Processing, Tel Aviv University. This work was supported in part by the Israeli Science Foundation (ISF) by Grant 1259/07, and in part by the Advanced Communication Center (ACC). The material in this paper was presented at the IEEE International Symposium on Information Theory (ISIT), Seattle, WA, July 2006, and the IEEE International Symposium on Information Theory (ISIT), Nice, France, July 2007.
- Analog transmission
- MMSE estimation
- Wyner-Ziv problem
- bandwidth expansion/reduction
- broadcast channel
- intersymbol interference (ISI) channel
- joint source/channel coding
- modulo lattice modulation
- unknown signal-to-noise ratio (SNR)
- writing on dirty paper