Error-Correcting Codes That Nearly Saturate Shannon's Bound

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Efficient information transmission plays a central role in modern society, taking a variety of forms, from telephone and satellite communication to storing and retrieving information on disk-drives. Error-correcting codes are commonly used in most methods of information transmission to compensate for noise corrupting the data during transmission; they require the use of additional information t...

On the Hamming bound for nonbinary localized-error-correcting codes

For nonbinary codes it is proved that the Hamming bound is asymptotically sharp in some range of the code rate.

Kolmogorov complexity and the asymptotic bound for error-correcting codes

The set of all error-correcting block codes over a fixed alphabet with q letters determines a recursively enumerable set of rational points in the unit square with coordinates (R, δ):= (relative transmission rate, relative minimal distance). Limit points of this set form a closed subset, defined by R ≤ αq(δ), where αq(δ) is a continuous decreasing function called the asymptotic bound. Its exist...

Synchronizable Error-Correcting Codes

A new technique for correcting synchronization errors in the transmission of discrete-symbol information is developed. The technique can be applied to any t-additive-error-correcting Bose-Chaudhuri-Hocquenghem code, to provide protection against synchronization errors. The synchronization error is corrected at the first complete received word after the word containing the synchronization error,...

Parallel error correcting codes