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Paper IDA.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.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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