Lattice codes for deletion and repetition channels

Lin Sok, Jean Claude Belfiore, Patrick Sole, Aslan Tchamkerten

Research output: Contribution to journalArticlepeer-review

Abstract

The construction of deletion codes for the editing metric is reduced to the construction of codes over the integers for the Manhattan metric by run length coding. The latter codes are constructed by expurgation of lattices' translates. These lattices, in turn, are obtained from Construction A applied to binary codes and Z4 -codes. A lower bound on the size of our codes for the Manhattan distance are obtained through generalized theta series of the corresponding lattices. For any fixed number of deletions, provided the number of runs is large enough our method supplies a correction technique. For fixed number of runs and binary sequence length large our lattice construction is shown to be tight up to constants.

Original languageEnglish
Pages (from-to)1595-1603
Number of pages9
JournalIEEE Transactions on Information Theory
Volume64
Issue number3
DOIs
Publication statusPublished - 1 Mar 2018
Externally publishedYes

Keywords

  • Deletion and repetition codes
  • Lee metric
  • construction A
  • lattice
  • v-series
  • weight enumerator

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