Analog Codes on Graphs

Abstract

We consider the problem of transmission of a sequence of real data produced by a Nyquist sampled band-limited analog source over a band-limited analog channel, which introduces an additive white Gaussian noise. An analog coding scheme is described, which can achieve a mean-squared error distortion proportional to $(1+SNR)^{-B}$ for a bandwidth expansion factor of $B/R$, where $0 < R < 1$ is the rate of individual component binary codes used in the construction and $B \geq 1$ is an integer. Thus, over a wide range of SNR values, the proposed code performs much better than any single previously known analog coding system.

18 pages, 15 figures, Portions appeared in Proceedings of the International Symposium on Information Theory (ISIT), Yokohama, Japan, July 2003