Abstract
A fixed-length binary code is called t-unidirectional error detecting if no codeword can be transformed into another codeword by at most t unidirectional errors. In this paper we consider the problem of mapping information sequences of length k into code-words of a t-unidirectional error detecting code of length k+p. In case of systematic codes we show that the parameters p and i must satisfy the relation t≤2p −2p/2+1+p. Moreover, we give a simple systematic encoding to map information sequences into codewords of a t-unidirectional error detecting code. In case of non-systematic codes, we give a method to design t-unidirectional error detecting codes in which the number p of check bits must satisfy the inequality t≤2p−p−1. The encoding and decoding algorithms require time linear in the number k of information bits.
The work of the last two authors was partially supported by the National Council of Research (CNR) under grant 90.0071.3.PF69 and 90.01552.CT12.
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References
S. Al-Bassan and B. Bose, “On Balanced Codes”, IEEE Int. Symp. Inform. Theory, Japan, June 1988.
S. Al-Bassan and B. Bose “Design of Efficient Balanced Codes”, 19th Int. Symp. on Fault-Tolerant Computing, Chicago, Ill., 1989.
J. M. Berger, “A Note on Error Detecting Codes for Asymmetric Channel”, Information and Control, vol. 4, pp. 68–73, 1961.
J. M. Borden, “Optimal Asymmetric Error Detecting Codes”, Information and Control, vol. 53, pp. 66–73, 1982.
B. Bose, “On Unordered Codes”, 17th Int. Symp. on Fault-Tolerant Computing, Pittsburgh, Penn., pp. 102–107, 1987.
B. Bose and D. J. Lin, “Systematic Unidirectional Error-Detecting Codes”, IEEE Trans. Comp., vol. C-34, pp. 1026–1032, 1985.
R. M. Capocelli, L. Gargano, G. Landi and U. Vaccaro, “Improved Balanced Encodings”, IEEE International Symposium on Information Theory, San Diego, USA, 1990.
R. M. Capocelli, L. Gargano and U. Vaccaro, “An Efficient Algorithm to Test Immutability of Variable Length Codes”, IEEE Trans. Inform. Theory, vol. IT-35, pp. 1310–1314, 1989.
R. M. Capocelli, L. Gargano and U. Vaccaro, “Efficient q-ary Immutable Codes”, Discrete Applied Math., to appear.
R. W. Cook, W. H. Sisson, T. G. Stoney, and W. N. Toy, “Design of Self-Checking Microprogram Control”, IEEE Trans. Comput., vol. C-22, pp. 255–262, 1973.
C. V. Freiman, “Optimal Error Detecting Codes for Completely Asymmetric Binary Channels”, Information and Control, vol. 5, pp. 64–71, 1962.
P. Godlewski and G. D. Cohen “Some Cryptographic Aspects of Womcodes”, Proceedings of CRYPTO '85, Lecture Notes in Computer Science, Springer Verlag, 1985.
J. R. Griggs, “Saturated Chains of Subsets and a Random Walk”, Journal of Combinatorial Theory, Series A, vol. 47, pp. 262–283, 1988.
D. E. Knuth, The Art of Computer Programming, Vol. 1, pp. 70 and 486, Addison-Wesley, Reading, Mass., 1968.
D. E. Knuth, “Efficient Balanced Codes”, IEEE Trans. Inform. Theory, vol. IT-32, pp. 51–53, 1986.
E. L. Leiss, “Data Integrity on Digital Optical Discs”, IEEE Trans. Computers, vol. C-33, pp. 818–827, 1984.
E. L. Leiss, “On Codes which are Unchangeable under Given Subversions”, J. Combin. Inform. & Syst. Sci., vol. 10, pp. 91–109, 1985.
E. L. Leiss, “On Testing for Immutability of Codes”, IEEE Trans. Inform. Theory, vol. IT-33, pp. 934–938, 1987.
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© 1991 Springer-Verlag Berlin Heidelberg
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Cohen, G.D., Gargano, L., Vaccaro, U. (1991). Unidirectional error detecting codes. In: Cohen, G., Charpin, P. (eds) EUROCODE '90. EUROCODE 1990. Lecture Notes in Computer Science, vol 514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54303-1_122
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DOI: https://doi.org/10.1007/3-540-54303-1_122
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