On the Use and Performance of Error-Voiding and Error-Marking Codes

Abstract

In contrast to payroll or inventory data, which must reach the recipient in its entirety, there is another class of data that includes radar-tracking data, remote-sensory data or control data, etc., for which the requirement of completeness is not so stringent. Error control for this class of data may be accomplished by forward-acting error-correcting codes which void or mark any detected errors that they do not correct. In order to evaluate these error-voiding methods, the error rates for such codes are estimated in this paper using the error statistics of the Alexander-Gryb-Nast study. A class of 18 (about 50 percent redundant) cyclic codes capable of correcting from one to five errors and having block lengths from 15 to 47 bits is examined. Only bounded-distance decoding is evaluated, but each code is assigned each possible decoding radius up to the maximum permissible radius determined by the capability of the code. Since interleaving generally reduces error rates, the error rates for this class of codes are estimated for interleaving constants from 50 to 300 in steps of 50. It is concluded that: (i) If voids are permissible (at a rate of about 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> ) then low undetected-error rates may be achieved by a code capable of correcting many errors but used to correct only two or three errors. Such a code might be about 50 percent redundant and have a block length between 25 and 50 bits. (ii) It is impractical to obtain low void rates. If voids are not tolerable, then retransmission is required to obtain low error rates. (iii) Interleaving is more effective with codes correcting three (or more) errors than with those correcting only single or double errors.