Bounds on the Performance of Vector-Quantizers operating under Channel Errors over all Index Assignments

Abstract

Vector-Quantization (VQ) is an effective and widely implemented method for low-bit-rate communication of speech and image signals. A common assumption in the design of VQ-based communication systems is that the compressed digital information is transmitted through a perfect channel. Under this assumption, quantization distortion is the only factor in output signal fidelity. Moreover, the assignment of channel symbols to the VQ Reconstruction Vectors is of no importance. However, under physical channels, errors may be present, degrading overall system performance. In this case, the effect of channel errors on the VQ system performance depends on the index assignment of the Reconstruction Vectors. For a VQ with N Reconstruction Vectors there are N! possible assignments. Hence, even for relatively small values of N, an exhaustive search over all possible assignments is practically impossible. In this paper, upper and lower bounds on the performance of VQ systems under channel errors over all possible assignments are presented using Linear Programming arguments. These bounds may give the system designer more insight about the gain that could be achieved by improving the index assignment. In numerical examples, the bounds are compared with the performance obtained by using a set of random assignments, as well as with an index assignment obtained by the well-known index switching algorithm.