On universal quantization

The quantization of -dimensional vectors in with an arbitrary probability measure, under a mean-square error constraint, is discussed. It is demonstrated that a uniform, one-dimensional quantizer followed by a noiseless digital variable-rate encoder ("entropy encoding") can yield a rate that is, for any , no more than bit-per-sample higher than the rate associated with the optimal -dimensionai quantizer, regardless of the probabilistic characterization of the input -vector for the allowable mean-square error.