SYSTEMATIC VARIABLE LENGTH CHECK BINARY UNORDERED/AUED CODES

In an unordered code no codeword is contained into any other codeword. Unordered codes are All Unidirectional Error Detecting (AUED) codes. It is well known that among all systematic codes with k information bits, Berger codes are optimal unordered codes with r = [log(2)(k + 1)] check bits. This paper introduces a new class of systematic unordered codes with variable length check symbols whose average redundancy is r approximate to (1/2) log(2)(pi ek/2) = (1/2) log(2) k +1.04709 ... Such new codes are shown to be optimal in the class of systematic AUED codes with fixed length information symbols and variable length check symbols.