Hybrid digital-analog (HDA) joint source-channel codes for broadcasting and robust communications

TLDR: It is demonstrated that robust codes exist whenever the source and channel bandwidths are equal and a matched tandem code whose channel encoder's output is partially/fully matched to its input is proposed and the existence of an asymptotically optimal matched tandemcode is shown.

Abstract: We consider the problem of transmitting a band-limited Gaussian source on an additive band-limited Gaussian noise channel. The well-known "threshold effect" dictates that the more powerful a code is, the more sensitive it is to the exact knowledge of the channel noise. A code is said to be robust if it is asymptotically optimal for a wide range of channel noise. Thus, robust codes have a "graceful degradation" characteristic and are free of the threshold effect. It is demonstrated that robust codes exist whenever the source and channel bandwidths are equal. In the unequal-bandwidth case, a collection of nearly robust joint source-channel codes is constructed using a hybrid digital-analog (HDA) coding technique. For designing nearly robust codes, a matched tandem code whose channel encoder's output is partially/fully matched to its input is proposed and the existence of an asymptotically optimal matched tandem code is shown. The nearly robust codes achieve the Shannon limit (theoretically optimum distortion) and have a less severe threshold effect. Finally, for the case of two different noise conditions, the distortion regions of these codes are determined.