On Deletion/Insertion of Zeros and Asymmetric Error Control Codes*

Abstract

This paper gives some theory and efficient design of binary block codes capable of correcting the deletions of the symbol "0" (referred to as 0-deletions) and/or the insertions of the symbol "0" (referred to as 0-insertions). This problem of correcting 0-deletions and/or 0-insertions (referred to as 0-errors) is shown to be equivalent to the efficient design of some L1 metric asymmetric error control codes over the natural alphabet, ℕ. In particular, it is shown that t 0-insertion correcting codes are actually capable of correcting t 0-errors, detecting (t+1) 0-errors and, simultaneously, detecting all occurrences of only 0-deletions or only 0-insertions in every received word (briefly, they are t-Sy0EC/(t + 1)-Sy0ED/AU0ED codes). From the relations with the L1 distance error control codes, new improved bounds are given for the optimal t 0-error correcting codes. In addition, some optimal non-systematic code designs are also given. Decoding can be efficiently performed by algebraic means with the Extended Euclidean Algorithm.