2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | M.5.3 | ||
| Paper Title | Codes over Trees | ||
| Authors | Lev Yohananov, Eitan Yaakobi, Technion, Israel | ||
| Session | M.5: Coding for Storage and Memories I | ||
| Presentation | Lecture | ||
| Track | Coding for Storage and Memories | ||
| Manuscript | Click here to download the manuscript | ||
| Virtual Presentation | Click here to watch in the Virtual Symposium | ||
| Abstract | In graph theory, a tree is one of the more popular families of graphs with a wide range of applications in computer science as well as many other related fields. While there are several distance measures over the set of all trees, we consider here the one which defines the so-called tree distance, defined by the minimum number of edit operations, of removing and adding edges, in order to change one tree into another. From a coding theoretic perspective, codes over the tree distance are used for the correction of edge erasures and errors. However, studying this distance measure is important for many other applications that use trees and properties on their locality and the number of neighbor trees. Under this paradigm, the largest size of code over trees with a prescribed minimum tree distance is investigated. Upper bounds on these codes as well as code constructions are presented. A significant part of our study is dedicated to the problem of calculating the size of the ball of trees of a given radius. These balls are not regular and thus we show that while the star tree has asymptotically the smallest size of the ball, the maximum is achieved for the line tree. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
