On the Existence of the Augustin Mean

  title={On the Existence of the Augustin Mean},
  author={Hao-Chung Cheng and Barış Nakiboğlu},
  journal={2021 IEEE Information Theory Workshop (ITW)},
The existence of a unique Augustin mean and its invariance under the Augustin operator are established for arbitrary input distributions with finite Augustin information for channels with countably generated output $\sigma$-algebras. The existence is established by representing the conditional Rényi divergence as a lower semi-continuous and convex functional in an appropriately chosen uniformly convex space and then invoking the Banach-Saks property in conjunction with the lower semi-continuity… 


The Augustin Capacity and Center
For any channel, the existence of a unique Augustin mean is established for any positive order and probability mass function on the input set and the Augustin information is shown to be continuously differentiable in the order.
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A Simple Derivation of the Refined Sphere Packing Bound Under Certain Symmetry Hypotheses.
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The Rényi Capacity and Center
  • B. Nakiboğlu
  • Computer Science
    IEEE Transactions on Information Theory
  • 2019
The van Erven– Harremoës conjecture is proved for any positive order and for any set of probability measures on a given measurable space and a generalization of it is established for the constrained variant of the problem.
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