Unidirectional error correcting/detecting codes

An extensive theory of symmetric error control coding has been developed in the last few decades. The recently developed VLSI circuits, ROM, and RAM memories have given an impetus to the extension of error control coding to include asymmetric and unidirectional types of error control. The maximal numbers of unidirectional errors which can be detected by systematic codes using r checkbits are investigated. They are found for codes with k, the number of information bits, being equal to 2[superscript r] and 2[superscript r] + 1. The importance of their characteristic in unidirectional error detection is discussed. A new method of constructing a systematic t-error correcting/all-unidirectional error detecting(t-EC/AUED) code, which uses fewer checkbits than any of the previous methods, is developed. It is constructed by appending t + 1 check symbols to a systematic t-error correcting and (t+l)-error detecting code. Its decoding algorithm is developed. A bound on the number of checkbits for a systematic t-EC/AUED code is also discussed. Bose-Rao codes, which are the best known single error correcting/all-unidirectional error detecting(SEC/AUED) codes, are completely analyzed. The maximal Bose-Rao codes for a fixed weight and for all weights are found. Of course, the base group and the group element which make the Bose-Rao code maximal are found, too. The bounds on the size of SEC/AUED codes are discussed. Nonsystematic single error correcting/d-unidirectional error detecting codes are constructed. Three methods for constructing the systematic t-error correcting/d-unidirectional error detecting(t-EC/d-UED) codes are developed. From these, simple and efficient t-EC/(t+2)-UED codes are derived. The decoding algorithm for one of these methods, which can be applied to the other two methods with slight modification, is described. A lower bound on the number of checkbits for a systematic t-EC/d-UED code is derived. Finally, future research efforts are proposed