The Renyi Capacity and Center

Renyi's information measures-the Renyi information, mean, capacity, radius, and center-are analyzed relying on the elementary properties of the Renyi divergence and the power means. The van Erven-Harremoes 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. The finiteness of the order alpha Renyi capacity is shown to imply the continuity of the Renyi capacity on (0, alpha] and the uniform equicontinuity of the Renyi information, both as a family of functions of the order indexed by the priors and as a family of functions of the prior indexed by the orders.


The Sphere Packing Bound via Augustin's Method
Nakiboğlu, Barış (Institute of Electrical and Electronics Engineers (IEEE), 2019-02-01)
A sphere packing bound (SPB) with a prefactor that is polynomial in the block length n is established for codes on a length n product channel W-[1,W- n], assuming that the maximum order 1/2 Renyi capacity among the component channels, i.e. max(t is an element of[1, n]) C-1/2, W-t, is O(ln n). The reliability function of the discrete stationary product channels with feedback is bounded from above by the sphere packing exponent. Both results are proved by first establishing a non-asymptotic SPB. The latter re...
A Simple Converse of Burnashev's Reliability Function
Berlin, Peter; Nakiboğlu, Barış; Rimoldi, Bixio; Telatar, Emre İ (Institute of Electrical and Electronics Engineers (IEEE), 2009-07-01)
In a remarkable paper published in 1976, Burnashev determined the reliability function of variable-length block codes over discrete memoryless channels (DMCs) with feedback. Subsequently, an alternative achievability proof was obtained by Yamamoto and Itoh via a particularly simple and instructive scheme. Their idea is to alternate between a communication and a confirmation phase until the receiver detects the codeword used by the sender to acknowledge that the message is correct. We provide a converse that...
The Augustin Capacity and Center
Nakiboğlu, Barış (Pleiades Publishing Ltd, 2019-10-01)
For any channel, the existence of a unique Augustin mean is established for any positive order and probability mass function on the input set. The Augustin mean is shown to be the unique fixed point of an operator defined in terms of the order and the input distribution. The Augustin information is shown to be continuously differentiable in the order. For any channel and convex constraint set with finite Augustin capacity, the existence of a unique Augustin center and the associated van Erven-Harremoes boun...
A quantitative analysis of Turkish publication output in physics between 1938–1987
Uzun, A. (Springer Science and Business Media LLC, 1990-7)
The output of a total of 860 publications in physics for the period 1938–1987 is used to analyse the mainstream of physics research in Turkey. The productivity and growth characteristics of the research in experimental and theoretical areas as well as in different subfields and institutions in the country are briefly discussed. The total output is also assessed by its citation impact.
Constructing linear unequal error protection codes from algebraic curves
Özbudak, Ferruh (Institute of Electrical and Electronics Engineers (IEEE), 2003-06-01)
We show that the concept of "generalized algebraic geometry codes" which was recently introduced by Xing, Niederreiter, and Lam gives a natural framework for constructing linear unequal error protection codes.
Citation Formats
B. Nakiboğlu, “The Renyi Capacity and Center,” IEEE TRANSACTIONS ON INFORMATION THEORY, pp. 841–860, 2019, Accessed: 00, 2020. [Online]. Available: