Randomness properties of partial γ - β planes as LSI test inputs and their implementations

  • Yukihiro Kamiya
  • Takayuki Miki
  • Yoshihiro Iwadare
Submitted Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 948)


In testing LSI circuits, it is sometimes important to generate sequences with strong randomness properties with simple implementations as test inputs, since they can avoid time consuming test pattern generations for each fault assumed in each circuit under test (CUT). Randomness properties of test inputs are also useful when there are some unknown, variable or variety factors in CUT, since in these cases, it is impossible to generate efficient test inputs, and the above sequences would provide reasonable results in the sense of ”average behaviors”. M sequences are well known to have strong randomness properties, and they are often used as these test inputs. However, it sometimes is required to have additional elaborations. For example, when parallel independent inputs are required to test CUT with large number of input terminals k, the total length 2k−1 of an M sequence is too long. Therefore, only some partial sequences from entire M sequences can be applicable to the circuit. In these cases, randomness properties assured for entire sequences no longer hold. Still, the resulting sequences are required to have sufficient randomness properties. Randomness properties of three kinds of sequences, sequences from partial two-dimensional M sequences (γ - β plane), vertically-s-shifted sequences, and horizontally-cyclic 1-shifted sequences, all derived from the same original one dimensional M sequence as parallel test inputs to LSIs, are performed and compared in this paper. The results show that sequences from partial γ - β plane are satisfactory as parallel random input sequences for large CUT. Then, the implementations of γ - β plane are discussed. It is seen that simple methods of implementation do exist, and partial sequences from γ - β planes axe also promising from this point of view.


Input Sequence Input Pattern Test Input Plane Sequence Randomness Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    P.H.Bardell and W.H.McAnny, ”Pseudorandom arrays for built-in tests”, IEEE Trans. Computer, vol.C-35, pp.653–658, July,1986.Google Scholar
  2. [2]
    H.Hanai and Y.Horii, ”Randomness of sequence pattern generators for BIST” presented at the 27th FTC Conference, held in Toyama, Japan, July,1992.Google Scholar
  3. [3]
    T.Nomura,H.Miyakawa,H.Imai and A.Fukuda, ”A theory of two-dimensional linear recurring arrays”, IEEE Trans. Inform. Theory, vol.IT-18,6, pp.775–785, November,1972.Google Scholar
  4. [4]
    H.Imai,”A theory of two-dimensional cyclic codes”, Information and Control, vol.34, pp.1–22, May,1977.Google Scholar
  5. [5]
    H.Kashiwagi and H.Harada,”On cyclotomic phase of M-sequences”,Transactions of the Society of Instrument and Control Engineers, vol18, pp.999–1004, October,1982.Google Scholar
  6. [6]
    H.Kashiwagi, T.Kohashi and H.Harada, ”Evaluation of partial randomness of Msequence” Transactions of the Society of Instrument and Control Engineers, vol.23, pp.812–815, August,1988.Google Scholar
  7. [7]
    H.Harada and H.Kashiwagi,”Evaluation of resemblance of partial properties of M-sequences”,Transactions of the Society of Instrument and Control Engineers, vol.23, pp.816–820, August,1988.Google Scholar
  8. [8]
    F.J.Macwilliams and N.J.A.Sloane,”Pseudo-random sequences and arrays”, Proceedings of IEEE, vol.64, pp.1715–1728, December,1976.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Yukihiro Kamiya
    • 1
  • Takayuki Miki
    • 2
  • Yoshihiro Iwadare
    • 2
  1. 1.KDDJapan
  2. 2.Department of Information Engineering, Faculty of EngineeringNagoya UniversityNagoyaJapan

Personalised recommendations