Analysis of recurrent codes
- 1 July 1963
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 9 (3), 143-156
- https://doi.org/10.1109/tit.1963.1057831
Abstract
A definition of a recurrent code is given in a framework which renders it amenable to mathematical analysis. Recurrent codes for both independent and burst errors are considered, and a necessary and sufficient condition for either type of error correction is established. For burst-error-correcting codes, the problem treated is (for a fixed burst length and redundancy) the minimization of the error-free distance ("guard space") required between bursts. A lower bound is obtained on the guard space, and in certain cases, codes which realize this bound are given. A general code which is close to the lower bound in many cases is also given. For independent errors, a code which will correct any error, provided that no consecutive "n" positions have more than "e" digits in error, is discussed. Fore = 1, a necessary and sufficient condition onnis derived; fore > 1, a lower bound onnis obtained, and for the case of redundancy1/2, an upper bound onnis also derived.Keywords
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