Constructions of codes correcting burst asymmetric errors
- 182 Downloads
A class of q-ary systematic codes correcting burst asymmetric errors is proposed. These codes have approximately b+logq(q−1)k+logq logqk 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 logq(q−1)k+logq logqk<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+log2k+1/2 log2 log2k check bits.
Unable to display preview. Download preview PDF.
- M. Blaum, Systematic unidirectional burst detecting codes, IEEE Trans. Comput., 37 (1988) 453–457.Google Scholar
- B. Bose and T. R. N. Rao, Theory of unidirectional error correcting/detecting codes, IEEE Trans. Comput., C-31 (1982) 521–530.Google Scholar
- B. Bose, On unordered codes, in Dig. Papers 17th Int. Symp. Fault-Tolerant Comput. (1987) 102–107.Google Scholar
- D. E. Knuth, Efficient balanced codes, IEEE Trans. Inform. Theory, IT-32 (1986) 51–53.Google Scholar
- R. J. McEliece, Comment on “A class of codes for asymmetric channels and a problem from the additive theory of numbers”, IEEE Trans. Inform. Theory, IT-19 (1973) 137.Google Scholar
- B. Parhami and A. Avižienis, Detection of storage errors in mass memories using low-cost arithmetic error codes, IEEE Trans. Comput., C-27 (1978) 302–308.Google Scholar
- S. Park and B. Bose, Burst asymmetric/unidirectional error correcting/detecting codes, in Dig. Papers 20th Int. Symp. Fault-Tolerant Comput. (1990).Google Scholar
- W. W. Peterson and E. J. Weldon, Jr., Error-Correcting Codes, 2nd. ed. (The MIT Press, 1972).Google Scholar
- T. R. N. Rao and E. Fujiwara, Error-Control Coding for Computer Systems (Prentice Hall Int., New Jersey, 1989).Google Scholar
- Y. Saitoh, Design of asymmetric or unidirectional error control codes, Master's thesis, Division of Electrical and Computer Eng., Faculty of Eng., Yokohama National University, Yokohama, Japan (1990).Google Scholar
- R. R. Varshamov, A class of codes for asymmetric channels and a problem from the additive theory of numbers, IEEE Trans. Inform. Theory, IT-19 (1973) 92–95.Google Scholar