Covering Codes Using Insertions or Deletions

Andreas Lenz, Cyrus Rashtchian, Paul H. Siegel, Eitan Yaakobi

Research output: Contribution to journalArticlepeer-review


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 either insertions or 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 ≥q 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.

Original languageEnglish
Article number9057555
Pages (from-to)3376-3388
Number of pages13
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - Jun 2021


  • Covering codes
  • deletions
  • insertions

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


Dive into the research topics of 'Covering Codes Using Insertions or Deletions'. Together they form a unique fingerprint.

Cite this