Bounds and constructions for binary block codes correcting asymmetric or unidirectional errors

Abdullah A. Hashim

J. Martin Borden

We study binary error-correcting and error-detecting codes suitable for use on a completely asymmetric or Z channel. This channel accepts inputs of 0 and 1 and reproduces these faithfully as outputs, except that occasionally the input of a 1 will erroneously result in the output of a 0. We construct block codes protecting against this error and bound the performance of the best possible codes.

Yijun, Luo -, Jin Jin +1 more

Jos H. Weber, Cornelis de Vroedt, Dick E. Boekee

Necessary and sufficient conditions are given for block codes to be capable of correcting up to t/sub 1/ symmetric errors, up to t/sub 2/ unidirectional errors, and up to t/sub 3/ asymmetric errors, as well as detecting from t/sub 1/+1 up to d/sub 1/ symmetric errors that are not of the unidirectional type, from t/sub 2/+1 up to d/sub 2/ unidirectional errors that are not of the asymmetric type, and from t/sub 3/+1 up to d/sub 3/ asymmetric errors. Many known conditions on block codes concerning error correction and/or detection appear as special cases of this general result. Further, some codes turn out to have stronger error correcting/detection capabilities than they were originally designed for.>

Bruce L. Montgomery

This dissertation investigates the complexity of minimum-distance decoding (MDD) algorithms for general binary linear block codes, and also investigates the use of such codes in constructing error correcting/detecting codes that are effective against both random and unidirectional errors. A new MDD algorithm is proposed, and its complexity is analyzed and compared to that of other such algorithms. The question of whether all good codes satisfy certain properties required for efficient implementation of the algorithm is also considered. The performance of decoding algorithms, with the information bit error rate as the criterion instead of the block error rate, is also studied. New decoding rules which can yield lower information bit error rates than the MDD rule are proposed and evaluated. A new class of binary codes is developed which corrects random errors and detects all unidirectional errors. These codes are obtained by appending a suffix to each codeword of a linear block code. To evaluate the efficiency of the new codes, a thorough comparison with the best previously obtained codes is made.

Robert Stephen Cunningham