Accession Number:

AD0684180

Title:

SOME GENERAL RESULTS OF CODING THEORY WITH APPLICATIONS TO THE STUDY OF CODES FOR THE CORRECTION OF SYNCHRONIZATION ERRORS,

Descriptive Note:

Corporate Author:

PARKE MATHEMATICAL LABS INC CARLISLE MASS

Personal Author(s):

Report Date:

1968-11-01

Pagination or Media Count:

30.0

Abstract:

Codes have been considered to combat different noise effects, e.g. substitution errors, synchronization errors, erasures, etc.. A unified theory treating arbitrary patterns of errors of any nature is sketched here by giving suitably general definitions of error-correcting, decodable with abounded delay, and error-limiting or synchronizable codes and by establishing the usual implications. As a by-product the essence of those notions is brought out with great clarity. Some auxiliary notions and results are used also for two interesting applications. One is a generalization of a previous result, giving sufficient conditions for a code to be decodable with bounded delay and hence also error-correcting with respect to certain patterns of up to e substitution or synchronization errors. The second is an extension of the basic Hamming Theorem and solves an open problem a block code of word length n has Levenshtein distance or 2e 1 between any two distinct words with 2e n if and only if it can correct up to e substitution errors in every word or up to e substitution and synchronization errors in the whole message. Author

Subject Categories:

  • Cybernetics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE