2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | A.4.1 | ||
| Paper Title | Improved efficiency for covering codes matching the sphere-covering bound | ||
| Authors | Aditya Potukuchi, Rutgers, The State University of New Jersey, United States; Yihan Zhang, The Chinese University of Hong Kong, China | ||
| Session | A.4: Combinatorial Coding Theory I | ||
| Presentation | Lecture | ||
| Track | Algebraic and Combinatorial Coding Theory | ||
| Manuscript | Click here to download the manuscript | ||
| Virtual Presentation | Click here to watch in the Virtual Symposium | ||
| Abstract | A covering code is a subset $\mathcal{C} \subseteq \{0,1\}^n$ with the property that any $z \in \{0,1\}^n$ is close to some $c \in \mathcal{C}$ in Hamming distance. For every $\epsilon,\delta>0$, we show a construction of a family of codes with relative covering radius $\delta + \epsilon$ and rate $1 - \ent(\delta) $ with block length at most $\exp(O((1/\epsilon) \log (1/\epsilon)))$ for every $\epsilon > 0$. This improves upon a folklore construction which only guaranteed codes of block length $\exp(1/\epsilon^2)$. The main idea behind this proof is to find a distribution on codes with relatively small support such that most of these codes have good covering properties. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
