Linear block codes for error detection

辰一 小島

Gérard Cohen, Philippe Godlewski

Tadao Kasami, Torleiv Kløve, Shu Lin

The probability of undetected error of linear block codes for use on a binary symmetric channel is investigated. Upper hounds are derived. Several classes of linear block codes are proved to have good error-detecting capability.

Giuliano G. La Guardia

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.

Sat Narain Gupta, Anusha Malhotra

Linear codes having a sub-block structure are discussed. A substitute method of constructing codes capable of detecting and correcting combinations of error patterns in various sub-blocks is given. Codes where error-correction capabilities are determined in terms of various sub-blocks of the word length are introduced.