On the Properties of Pseudo Noise Sequences with a Simple Proposal of Randomness Test
Maximal length sequences (m-sequences) are also
known as pseudo random sequences or pseudo noise sequences
for closely following Golomb-s popular randomness properties: (P1)
balance, (P2) run, and (P3) ideal autocorrelation. Apart from these,
there also exist certain other less known properties of such sequences
all of which are discussed in this tutorial paper. Comprehensive proofs
to each of these properties are provided towards better understanding
of such sequences. A simple test is also proposed at the end of
the paper in order to distinguish pseudo noise sequences from truly
random sequences such as Bernoulli sequences.
[1] R. J. McEliece, Finite Fields for Computer Scientists and Engineers.
Boston, MA: Kluwer Academic, 1987.
[2] S. Golomb, Shift Register Sequences, Revised edition. Laguna Hills, CA:
Aegean Park Press, 1982.
[3] S. Blackburn, "A Note on Sequences with the Shift and Add Property,"
Designs, Codes, and Crypt., vol. 9, pp. 251-256, 1996.
[4] F. J. MacWilliams and J. A. Sloane, "Pseudo-Random Sequences and
Arrays," Proc. IEEE, vol. 64, no. 12, pp. 1715-1729, Dec. 1976.
[5] S. A. Fredricsson, "Pseudo-Randomness Properties of Binary Shift
Register Sequences," IEEE Trans. Inform. Theory, vol. 21, pp. 115-120,
Jan. 1975.
[6] D. E. Knuth, The Art of Computer Progamming. Reading, MA: Addison-
Wesley, 1968.
[7] F. A. Feldman, "A New Spectral Test for Nonrandomness and the DES,"
IEEE Trans. Soft. Engg., vol. 16, no. 3, pp. 261-267, March 1990.
[8] E. R. Berlekamp, Algebraic Coding Theory. New York: McGraw-Hill,
1968.
[1] R. J. McEliece, Finite Fields for Computer Scientists and Engineers.
Boston, MA: Kluwer Academic, 1987.
[2] S. Golomb, Shift Register Sequences, Revised edition. Laguna Hills, CA:
Aegean Park Press, 1982.
[3] S. Blackburn, "A Note on Sequences with the Shift and Add Property,"
Designs, Codes, and Crypt., vol. 9, pp. 251-256, 1996.
[4] F. J. MacWilliams and J. A. Sloane, "Pseudo-Random Sequences and
Arrays," Proc. IEEE, vol. 64, no. 12, pp. 1715-1729, Dec. 1976.
[5] S. A. Fredricsson, "Pseudo-Randomness Properties of Binary Shift
Register Sequences," IEEE Trans. Inform. Theory, vol. 21, pp. 115-120,
Jan. 1975.
[6] D. E. Knuth, The Art of Computer Progamming. Reading, MA: Addison-
Wesley, 1968.
[7] F. A. Feldman, "A New Spectral Test for Nonrandomness and the DES,"
IEEE Trans. Soft. Engg., vol. 16, no. 3, pp. 261-267, March 1990.
[8] E. R. Berlekamp, Algebraic Coding Theory. New York: McGraw-Hill,
1968.
@article{"International Journal of Electrical, Electronic and Communication Sciences:64820", author = "Abhijit Mitra", title = "On the Properties of Pseudo Noise Sequences with a Simple Proposal of Randomness Test", abstract = "Maximal length sequences (m-sequences) are also
known as pseudo random sequences or pseudo noise sequences
for closely following Golomb-s popular randomness properties: (P1)
balance, (P2) run, and (P3) ideal autocorrelation. Apart from these,
there also exist certain other less known properties of such sequences
all of which are discussed in this tutorial paper. Comprehensive proofs
to each of these properties are provided towards better understanding
of such sequences. A simple test is also proposed at the end of
the paper in order to distinguish pseudo noise sequences from truly
random sequences such as Bernoulli sequences.", keywords = "Maximal length sequence, pseudo noise sequence,
punctured de Bruijn sequence, auto-correlation, Bernoulli sequence,
randomness tests.", volume = "2", number = "9", pages = "2089-6", }