2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | S.1.4 | ||
| Paper Title | Computability of the Zero-Error capacity with Kolmogorov Oracle | ||
| Authors | Holger Boche, Christian Deppe, Technische Universität München, Germany | ||
| Session | S.1: Capacity Computation | ||
| Presentation | Lecture | ||
| Track | Shannon Theory | ||
| Manuscript | Click here to download the manuscript | ||
| Virtual Presentation | Click here to watch in the Virtual Symposium | ||
| Abstract | The zero-error capacity of a discrete classical channel was first defined by Shannon as the least upper bound of rates for which one transmits information with zero probability of error. The problem of finding the zero-error capacity $C_0$, which assigns a capacity to each channel as a function, was reformulated in terms of graph theory as a function $\Theta$, which assigns a value to each simple graph. This paper studies the computability of the zero-error capacity. For the computability, the concept of a Turing machine and a Kolmogorov oracle is used. It is unknown if the zero-error capacity is computable in general. We show that in general the zero-error capacity is semi-computable with the help of a Kolmogorov Oracle. Furthermore, we show that $C_0$ and $\Theta$ are computable functions if and only if there is a computable sequence of computable functions of upper bounds, i.e. the converse exist in the sense of information theory, which point-wise converges to $C_0$ or $\Theta$. Finally, we examine Zuiddam's characterization of $C_0$ and $\Theta$ in terms of algorithmic computability. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
