Al-hashimi, B.M.

Nicolici, N.

English

Southampton (e-Prints Soton)

1426 IEEE TRANSACTIONS ON COMPUTERS,  VOL.  47,  NO.  12,  DECEMBER  1998Correction to the Proof of Theorem 2 in“Parallel Signature Analysis Design withBounds on Aliasing”Nicola Nicolici and Bashir M. Al-Hashimi————————   F   ————————IN [1], Saxena and McCluskey have reported parallel signaturedesign techniques and simple bounds on the aliasing probability.In the proof of Theorem 2 on p.436, it was stated that:111111 1 210 210 21vLvv v pppLppL k ov vkkLkm mm+  =+--+ - -- å ,, , K K 162716. (1)The exponent of the numerator in the second term on the righthand side of (1) should be L + 1 instead of L. The correct result isobtained as follows. By integrating the multinomial expansiontreating  pk as auxiliary variable, we have:pp p d p oLkpmk++ + =- 1 21 0L 49p vLvv v pp kk ov vm mm 11 1 210 210 21+ - -- å ,, , K K .        (2)By applying the substitution rule:pu iim=-å =021.               (3)This yields:ud u LpLLpkLk 1111111 -+= + --+27.( 4 )From (2) and (4) we obtain:111111 1 210 2110 21vLvv v pppLppL k ov vkkLkm mm+   =+--+ - -+- å ,, , K K 162716. (5)Now, note that the exponent of the numerator in the second termon the right hand side of equation (5) is L + 1. It should be notedthat this term is ignored in the original paper [1] and does not haveany impact on the final result.ACKNOWLEDGMENTThe authors would like to thank Nirmal Saxena for his feedbackand encouragement on the presented work.REFERENCE[1] N. Saxena and E.J. McCluskey, “Parallel Signature Analysis De-sign with Bounds on Aliasing,” IEEE Trans. Computers, vol. 46, no. 4,pp. 425-438, Apr. 1997.0018-9340/98/$10.00 © 1998 IEEE²²²²²²²²²²²²²²²²· The authors are with the VLSI Processing Group, School of Engineeringand Advanced Technology, Staffordshire University, Beaconside, Stafford,ST18 0AD, U.K. E-mail: nicola@bss10a.staffs.ac.uk.Manuscript received 27 Apr. 1998.For information on obtaining reprints of this article, please send e-mail to:tc@computer.org, and reference IEEECS Log Number 106761.

Correction to the proof of theorem 2 in "Parallel signature analysis design with bounds on aliasing"

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