Systematic Lossy Source/Channel Coding

The fundamental limits of “systematic” communication are analyzed. In systematic transmission, the decoder has access to a noisy version of the uncoded raw data (analog or digital). The coded version of the data is used to reduce the average reproduced distortion D below that provided by the uncoded systematic link and/or increase the rate of information transmission. Unlike the case of arbitrarily reliable error correction (D ! 0) for symmetric sources/channels, where systematic codes are known to do as well as nonsystematic codes, we demonstrate that the systematic structure may degrade the performance for nonvanishing D: We characterize the achievable average distortion and we find necessary and sufficient conditions under which systematic communication does not incur loss of optimality. The Wyner–Ziv rate distortion theorem plays a fundamental role in our setting. The general result is applied to several scenarios. For a Gaussian bandlimited source and a Gaussian channel, the invariance of the bandwidth–signal-to-nosie ratio (SNR, in decibels) product is established, and the optimality of systematic 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 tolerated, systematic encoding is strictly suboptimal.