High-Rate Analysis of Vector Quantization for Noisy Channels

In this paper, the sensitivity of the high-rate performance of conventional source coding to symmetric channel errors (i.e., a channel where all index errors are equally likely) with arbitrary distortion measures is analyzed. It is shown that, in general, the overall distortion due to source quantization and channel errors cannot be expressed as the sum of the distortion due to the finite bit representation of the source and the distortion due to channel errors. An exception to this is when the distortion is measured as the mean-squared error. The binary symmetric channel with random index assignment is a special case of the analysis, and as the number of code-points gets large, the performance approaches a nonzero constant. Finally, the framework is applied to the wideband speech spectrum quantization problem, where it correctly predicts the channel error rate permissible for operation at a particular distortion level