High-resolution source coding for non-difference distortion measures: Multidimensional companding

Entropy-coded vector quantization is studied using high-resolution multidim ensional companding over a class of non-difference distortion measures. For distortion measures which are "locally quadratic" a rigorous derivation of the asymptotic distortion and entropy-coded rate of multidimensional compa nders is given along with conditions for the optimal choice of the compress or function. This optimum compressor, when it exists, depends on the distor tion measure but not on the source distribution. The rate-distortion perfor mance of the companding scheme is studied using a recently obtained asympto tic expression for the rate-distortion function which parallels the Shannon lower bound for difference distortion measures. It is proved that the high -resolution performance of the scheme is arbitrarily close to the rate-dist ortion limit for large quantizer dimensions if the compressor function and the lattice quantizer used in the companding scheme are optimal, extending an analogous statement for entropy-coded lattice quantization and MSE disto rtion. The companding approach is applied to obtain a high-resolution quant izing scheme for noisy sources.