Constructions of codes correcting burst asymmetric errors

Abstract

A class of q-ary systematic codes correcting burst asymmetric errors is proposed. These codes have approximately b+log_q(q−1)k+log_q log_q k check symbols, where b is the maximal length of correctable burst asymmetric errors and k is the number of information symbols. The codes have less check symbols than ordinary burst-error-correcting codes if log_q(q−1)k+log_q log_q k<b. A decoding algorithm for the codes is also presented. Encoding and decoding of the codes are very easy. Further, this paper gives some types of codes obtained by modifications of these codes: codes correcting random errors and burst asymmetric errors, and codes correcting random and burst asymmetric errors. Furthermore, more efficient q-ary burst-asymmetric-error-correcting codes are presented. When q=2, these codes have approximately b+log₂ k+1/2 log₂ log₂ k check bits.

This work was presented in part at the 1990 IEICE National Conference, Tokyo, Japan, March 1990, at the meeting of Technical Group on Information Theory, Yokohama, Japan, March 1990, and in Electronics Letters, vol. 26, no. 5, pp. 286–287, March 1990.