مرکز منطقه ای اطلاع رساني علوم و فناوري

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. For $e = 1$ , a necessary and sufficient condition on $n$ is derived; for $e > 1$ , a lower bound on $n$ is obtained, and for the case of redundancy $1/2$ , an upper bound on $n$ is also derived.

Keywords :

Burst-correcting codes; Convolutional codes; Bismuth; Decoding; Error correction; Error correction codes; Error probability; Feedback; Parity check codes; Redundancy; Transmitters; Upper bound;