Technical Program

Paper Detail

Paper IDM.7.1
Paper Title Covering Codes for Insertions and Deletions
Authors Andreas Lenz, Technical University of Munich, Germany; Cyrus Rashtchian, Paul Siegel, University of California, San Diego, United States; Eitan Yaakobi, Technion - Israel Institute of Technology, Israel
Session M.7: Insertion Deletion Substitution Codes 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 A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most prior work on covering codes has focused on the Hamming metric, we consider the problem of designing covering codes defined in terms of insertions and deletions. First, we provide new sphere-covering lower bounds on the minimum possible size of such codes. Then, we provide new existential upper bounds on the size of optimal covering codes for a single insertion or a single deletion that are tight up to a constant factor. Finally, we derive improved upper bounds for covering codes using R >= 2 insertions or deletions. We prove that codes exist with density that is only a factor O(R \log R) larger than the lower bounds for all fixed R. In particular, our upper bounds have an optimal dependence on the word length, and we achieve asymptotic density matching the best known bounds for Hamming distance covering codes.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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