On universal quantization

  • Authors:
  • J. Ziv

  • Affiliations:
  • -

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

The quantization ofn-dimensional vectors inR^{n}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 anyn, no more than0.754bit-per-sample higher than the rate associated with the optimaln-dimensionai quantizer, regardless of the probabilistic characterization of the inputn-vector for the allowable mean-square error.