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 -type approximation of a distribution in terms of the variational distance and the informational divergence . 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.
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