Efficient Systematic Deletions/Insertions of 0’s Error Control Codes

This paper gives some theory and efficient design of binary block codes capable of controlling 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 controlling 0-deletions and/or 0-insertions (referred to as 0-errors) is shown to be equivalent to the efficient design of L-1 metric asymmetric error control codes over the natural alphabet, IN. Optimal systematic code designs are given. In particular, for all t, k is an element of IN, a recursive method is presented to encode k information bits into efficient systematic t Symmetric 0-Error Correcting, (t + 1) Symmetric 0-Error Detecting and All Unidirectional 0-Error Detecting (t-Sy0EC/(t + 1)-Sy0ED/AU0ED) codes of length n <= k + t log(2) k + o(t log n) as n is an element of IN increases. Decoding can be efficiently performed by algebraic means using the Extended Euclidean Algorithm (EEA).