Owing to the high sensitivity of quantum mechanical systems to even small perturbations, means of error protection are essential for any computation or communication process based on quantum mechanics. After a short introduction to quantum registers and operations as well as quantum channels, different approaches to the problem of protecting quantum information are presented.

The crisscross error model in data arrays is considered, where the corrupted symbols are confined to a prescribed number of rows or columns (or both). Under the additional assumption that the corrupted entries are uniformly distributed over the channel alphabet, and by allowing a small decoding error probability, a coding scheme is presented where the redundancy can get close to one half the re...

T HIS PAPER is concerned with the decoding problem for error-correcting cyclic codes with relatively high redundancy r/n. The general decoding algorithms for the Bose-Chaudhuri codes given by Peterson’ are well known. Also, other interesting decoding methods have been given by Meggitt,’ Prange3 and Zierler.4 The decoding scheme described here is rather simple in principle’ and is appropriate fo...

A probabilistic procedure is suggested for the automatic correction of spelling and typing errors in printed English texts. The heart of the procedure is a probabilistic model for the generation of the garbled word from the correct word. The garbler can delete or insert symbols in the word or substitute one or more symbols by other symbols. An expression is derived for P(Y I X), the probability...