Abstract
Unidirectional error control codes have been studied extensively for application to VLSI memories. Also, studies on multiple-valued logic and memories received considerable attention since by employing multi-valued (m-ary) symbol representation, one can drastically reduce the interconnection area in VLSI chips as compared to the binary representation which requires more than 70% chip area for interconnection. In this context, m-ary unidirectional error control codes will be of great importance in improving reliability of such multiple-valued logic and memory systems.
In this paper, we propose a new construction method for m-ary t-unidirectional error correcting and all-unidirectional error discriminating (-UEC & all-UEDis)codes. We first show that a t-UEC & all-UEDis code can be characterized as a t-asymmetric error correcting (t-AEC) code with an added capability for discriminating errors between positive errors and negative errors. Noting this fact, we propose a simple construction method for t-UEC & all-UEDis codes starting from m-ary t-AEC codes.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
T.R.N. Rao and E. Fujiwara: Error-Control Coding for Computer Systems, Prentice Hall, 1989.
T. Murase: “256QAM 400Mb/s Microwave Radio System,” Japan Telecommunications Review, vol.30, No.2, pp.23–30, April 1988
J. T. Butler: “Multiple-Valued Logic,” Computer, vol.21-4, pp.13–15, April 1988
K. C. Smith: “Multiple-Valued Logic: A Tutorial and Appreciation,” Computer, vol.21-4, pp.17–27, April 1988
R.R. Varshamov: “A Class of Codes for Asymmetric Channels and Problem from Additive Theory of Numbers,” IEEE Trans. on Information Theory, vol.IT-19, pp.92–95, January 1973.
R.J. McEliece: “A Comment on A Class of Codes for Asymmetric Channels and a Problem from the Additive Theory of Numbers,” IEEE Trans. on Information Theory, vol.IT-3, p.137, January 1973.
P.H. Delsarte and P.H. Piret: “Spectral Enumerators for Certain Additive-Error-Correcting Codes over Integer Alphabets,” Information and Control, vol.48, pp.193–210, March 1981.
K. Sakaniwa, T.N. Ahn and T.R.N. Rao: “A Construction Method for m-ary Error Correcting and Discriminating Codes,” Proc. The 11th Symposium on Information Theory and Its Applications (SITA '88), pp.137–142, Dec. 1988 (in Japanese)
B. Bose and D.K. Pradhan: “Optimal Unidirectional Error Detecting/Correcting Codes,” IEEE Trans. on Computers, vol.C-31, no.6, pp.564–568, June 1982
E.R. Berlekamp: Algebraic Coding Theory, McGraw-Hill, NY, 1968
K. Sakaniwa, T.N. Ahn and T.R.N. Rao: “A New Theory of m-ary Error Correcting/Discriminating Codes (Part-I, II, III and IV),” IEICE (the Institute of Electronics, Information and Communication Engineers of Japan) Technical Report, CS88-64, Nov. 1988, CS88-65, Nov. 1988, CS88-98, Jan. 1989, CS89-53, July 1989 (in Japanese)
L.P. To and K. Sakaniwa: “Theory and Construction of m-ary Error Discriminating Codes,” Proc. The 11th Symposium on Information Theory and Its Applications (SITA'89), pp.121–125, Dec. 1989 (in Japanese)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ahn, T.N., Sakaniwa, K., Rao, T.R.N. (1991). A construction method for m-ary unidirectional error control codes. In: Sakata, S. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1990. Lecture Notes in Computer Science, vol 508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54195-0_40
Download citation
DOI: https://doi.org/10.1007/3-540-54195-0_40
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54195-0
Online ISBN: 978-3-540-47489-0
eBook Packages: Springer Book Archive