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Design of Self-Testing Checkers for Borden Codes
April 1996 (vol. 45 no. 4)
pp. 461-469

Abstract—The optimal codes C(n, t) capable of detecting t-unidirectional errors in an n-bit vector were defined by Borden. Unidirectional errors have been observed in modern digital devices such as PLA's, ROM's, and compact laser disks. In this paper, a new approach to designing self-testing checkers (STCs) for Borden codes is proposed. The new STC is built of a self-testing code-disjoint translator of the Borden code into the 1-out-of-z code (z≥ 2) and—if z = 3 or 4—an STC for the 1-out-of-z code. The translator is built of two multi-output threshold circuits with $\lfloor n/2 \rfloor$ and $\lceil n/2 \rceil$ inputs and a merging network. Compared to existing STC's for Borden codes the new checker generally uses significantly less hardware. It also enjoys a modular and highly regular structure which makes it attractive for VLSI implementation.

[1] D.K. Pradhan and J.J. Stiffler,"Error-Correcting Codes and Self-Checking Circuits," Computer, vol. 13, pp. 27-37, Mar. 1980.
[2] G.P. Mak et al., "The Design of PLAs with Concurrent Error Detection," Digest of Papers 12th Int'l FTC Symp., pp. 303-310,Santa Monica, Calif. June 1982.
[3] M. Nicolaidis and M. Boudjit,"New Implementations, Tools, and Experiments for Decreasing Self-Checking PLAs Overhead," Proc. ICCD'91, pp. 275-281.
[4] E.L. Leiss,"Data Integrity in Digital Optical Disks," IEEE Trans. Computers, vol. 33, no. 9, pp. 818-827, Sept. 1984.
[5] E. Fujiwara and D.K. Pradhan,"Error-Control Coding in Computers," Computer, vol. 23, pp. 63-72, July 1990.
[6] J.M. Berger,"A Note on Error Detection Codes for Asymmetric Binary Channels," Information Control, vol. 4, pp. 68-73, Mar. 1961.
[7] C.V. Freiman,"Optimal Error Detection Codes for Completely Asymmetric Binary Channels," Information Control, vol. 5, pp. 64-71, Mar. 1962.
[8] J.M. Borden,"Optimal Asymmetric Error Detecting Codes," Information Control, vol. 53, pp. 66-73, Apr. 1982.
[9] N.K. Jha,"A Totally Self-Checking Checker for Borden's Code," IEEE Trans. Computer Aided Design, vol. 8, pp. 731-736, July 1989.
[10] E. Fujiwara and M. Yoshikawa,"A Design Method for Cost-Effective Self-Testing Checker for Optimal d-Unidirectional Error Detecting Codes," IEICE Trans. Information and Systems, vol. E75-D, pp. 771-777, Nov. 1992.
[11] W.C. Carter and P.R. Schneider,"Design of Dynamically Checked Computers," Proc. IFIP Conf., pp. 878-883,Edinburgh, Aug. 1968.
[12] D.A. Anderson and G. Metze,"Design of Totally Self-Checking Check Circuits for m-out-of-n Codes," IEEE Trans. Computers, vol. 22, pp. 263-269, Mar. 1973.
[13] S.J. Piestrak,"Design Method of Totally Self-Checking Checkers for m-out-of-n Codes," Digest of Papers 13th Int'l FTC Symp., pp. 162-168, June28-30, Milan.
[14] S.J. Piestrak,"The Minimal Test Set for Sorting Networks and the Use of Sorting Networks in Self-Testing Checkers for Unordered Codes," Digest of Papers 20th Int'l FTC Symp., Newcastle upon Tyne, U.K. pp. 457-464, June 1990.
[15] S.J. Piestrak,"The Minimal Test Set for Multi-Output Threshold Circuits Implemented as Sorting Networks," IEEE Trans. Computers, vol. 42, no. 6, pp. 700-712, June 1993.
[16] D. Knuth, The Art of Computer Programming, vol. 3: Sorting and Searching. Addison-Wesley, 1973.
[17] V. Rabara,"Design of Self-Checking Checker for 1-out-of-n Code (n > 3)," Proc. Fourth Int'l Conf. Fault-Tolerant Systems and Diagnostics, pp. 234-240,Brno, Czechoslovakia, Sept.28-30, 1981.
[18] P. Golan,"Design of Totally Self-Checking Checker for 1-out-of-3 Code," IEEE Trans. Computers, vol. 33, no. 3, p. 285, Mar. 1984.
[19] S.J. Piestrak,"Design of Residue Generators and Multioperand Adders modulo-3 Built of Multi-Output Threshold Circuits," IEEE Proc. Computers and Digital Technology, vol. 141, pp. 129-134, Mar. 1994.

Index Terms:
Borden code, concurrent error detection, easily-testable circuit, multioutput threshold circuit, optimal t-unidirectional error detecting code, self-testing checker, unidirectional errors, unidirectional error detecting code.
Citation:
Stanislaw J. Piestrak, "Design of Self-Testing Checkers for Borden Codes," IEEE Transactions on Computers, vol. 45, no. 4, pp. 461-469, April 1996, doi:10.1109/12.494103
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