On Deletion/Insertion of Zeros and Asymmetric Error Control Codes

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 L 1 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 L 1 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.