This Article 
 Bibliographic References 
 Add to: 
Analysis of Checksums, Extended-Precision Checksums, and Cyclic Redundancy Checks
July 1990 (vol. 39 no. 7)
pp. 969-975

The effectiveness of extended-precision checksums is thoroughly analyzed. It is demonstrated that the extended-precision checksums most effectively exploit natural redundancy occurring in program codes. Honeywell checksums and cyclic redundancy checks are compared to extended-precision checksums. Two's complement, unsigned, and one's complement arithmetic checksums are treated in a unified manner. Results are also extended to any general radix-p arithmetic checksum. Asymptotic and closed-form formulas of aliasing probabilities for the various error models are derived.

[1] D. P. Siewiorek and R. S. Swarz,The Theory and Practice of Reliable System Design. Bedford, MA: Digital, 1982.
[2] Jacket al., "Coverage analysis of self-check techniques in semiconductor memories," Honeywell Corp. Tech. Rep. MR12399, Minneapolis, MN, 1975.
[3] A. M. Usas, "Checksum versus residue codes for multiple error detection," inProc. FTCS-8, 1978, p. 224.
[4] J. Wakerly,Error Detecting Codes, Self-Checking Circuits and Applications. New York: North-Holland, 1978.
[5] S. C. Tzou Chen and G. S. Fang, "A closed-form expression for the probability of checksum violation,"IEEE Trans. Syst., Man, Cybern., vol. SMC-10, no. 7, pp. 407-410, July 1980.
[6] J. G. Fletcher, "An arithmetic checksum for serial transmissions,"IEEE Trans. Commun., vol. COM-30, no. 1, pp. 247-252, Jan. 1982.
[7] A. Mahmood and E. J. McCluskey, "Concurrent error detection using watchdog processors--A survey,"IEEE Trans. Comput., vol. C-37, no. 2, pp. 160-174, Feb. 1988.
[8] J. C. Huck, "Comparative analysis of computer architectures," Stanford Ph.D. dissertation, Stanford, CA, Mar. 1983.
[9] R. L. Graham, D. E. Knuth, and O. Patashnik,Concrete Mathematics: A Foundation for Computer Science, Research Problem 7.56. Reading, MA: Addison-Wesley, 1988, p. 366.
[10] HP 3000/930 and HP 9000/840 Computers.Precision Architecture and Instruction Reference Manual, Hewlett-Packard Co., 2nd ed., June 1987.
[11] N. R. Saxena and J. P. Robinson, "Accumulator compression testing,"IEEE Trans. Comput., vol. C-35, no. 4, pp. 317-321, Apr. 1986.

Index Terms:
checksums; extended-precision checksums; cyclic redundancy checks; program codes; radix-p arithmetic checksum; closed-form formulas; error correction codes; error detection codes.
N.R. Saxena, E.J. McCluskey, "Analysis of Checksums, Extended-Precision Checksums, and Cyclic Redundancy Checks," IEEE Transactions on Computers, vol. 39, no. 7, pp. 969-975, July 1990, doi:10.1109/12.55701
Usage of this product signifies your acceptance of the Terms of Use.