SYSTEMATICS LOSSY SOURCE CHANNEL CODING

The fundamental limits of ''systematic'' communication are analyzed. I n systematic transmission, the decoder has access to a noisy version o f the uncoded raw data (analog or digital), The coded version of the d ata is used to reduce the average reproduced distortion D below that p rovided hy the uncoded systematic link and/or increase the rate of inf ormation transmission, Unlike the case of arbitrarily reliable error c orrection (D --> 0) for symmetric sources/channels, where systematic c odes are known to do as well as nonsystematic codes, we demonstrate th at the systematic structure may degrade the performance for nonvanishi ng D. We characterize the achievable average distortion and we find ne cessary and sufficient conditions under which systematic communication does not incur loss of optimality. The Wyner-Ziv rate distortion theo rem plays a fundamental role in our setting, The general result is app lied to several scenarios. For a Gaussian bandlimited source and a Gau ssian channel, the invariance of the bandwidth-signal-to-noise ratio ( SNR, in decibels) product is established, and the optimality of system atic transmission is demonstrated, Bernoulli sources transmitted over binary-symmetric channels and over certain Gaussian channels are also analyzed. It is shown that if nonnegligible bit-error rate is tolerate d, systematic encoding is strictly suboptimal.