English

Optimal Quantization for Distribution Synthesis

Information Theory 2017-05-08 v4 math.IT

Abstract

Finite precision approximations of discrete probability distributions are considered, applicable for distribution synthesis, e.g., probabilistic shaping. Two algorithms are presented that find the optimal MM-type approximation QQ of a distribution PP in terms of the variational distance QP1| Q-P|_1 and the informational divergence D(QP)\mathbb{D}(Q| P). Bounds on the approximation errors are derived and shown to be asymptotically tight. Several examples illustrate that the variational distance optimal approximation can be quite different from the informational divergence optimal approximation.

Keywords

Cite

@article{arxiv.1307.6843,
  title  = {Optimal Quantization for Distribution Synthesis},
  author = {Georg Böcherer and Bernhard C. Geiger},
  journal= {arXiv preprint arXiv:1307.6843},
  year   = {2017}
}

Comments

Submitted to the IEEE Transactions on Information Theory

R2 v1 2026-06-22T00:58:00.564Z