Effects of transmission errors on the mean-squared error performance of transform coding systems

This study presents an analysis of the effects of statistically independent channel transmission errors on the mean-squared error performance of transform coding (TC) systems. A comparison with performance of corresponding PCM systems is given also taking into consideration the bounds on performance improvement if additional error-protection schemes are implemented. The probability density functions of the quantizer input signals are described by different model density functions which are of importance for speech and picture encoding systems. The natural binary code, the Gray code, the folded binary code, and the minimum distance code are investigated as binary representations of the quantizer reconstruction values. In addition to the analysis, simulation results for transform coding of speech signals are presented. The results show a close agreement with the theoretical performance predicted from the analysis. The main results of this study, which are valid for most cases of practical interest, can be stated as follows: TC systems are no more sensitive to channel errors than PCM systems when operating without error protection, i.e., both systems yield nearly the same value of channel error variance. The performance of a TC system is, however, significantly superior to that of a PCM system, if the code words of both systems are error-protected similarly. The channel error variance of the TC system is by a gain factor G TC smaller than that of a corresponding PCM system in the most favorable case. The gain G TC is the factor by which the quantization distortion in a TC system is reduced relative to PCM.