Coding for the permutation channel with insertions, deletions, substitutions, and erasures

Mladen Kovacevic, Vincent Y. F. Tan

Abstract: This paper is motivated by the error-control problem in communication channels in which the transmitted sequences are subjected to random permutations, in addition to being impaired with insertions, deletions, substitutions, and erasures of symbols. Bounds on the size of optimal codes in this setting are derived, and their asymptotic behavior examined in the fixed-minimum-distance regime. A family of codes correcting these types of errors is described and is shown to be asymptotically optimal for some sets of parameters. The corresponding error-detection problem is also analyzed.