Bounds on the channel distortion of vector quantizers

Vector quantization (VQ) is a widely implemented method for low-bit-rate signal coding. A common assumption in the design of VQ systems is that the digital information is transmitted through a perfect channel. Under this assumption, the assignment of channel symbols to the VQ reconstruction vectors (RV) is of no importance. However, under physical channels, the effect of channel errors on the VQ system performance depends on the index assignment of the RV. For a VQ of size N, there are N! possible assignments, meaning that an exhaustive search over all possible assignments is practically impossible. Lower and upper bounds on the performance of VQ systems under channel errors, over all possible assignments, are presented. A related expression for the average performance is also discussed. Numerical examples are given in which the bounds and average performance are compared with index assignments obtained by the index-switching algorithm