New M-Ary Sequence Families With Low Correlation From the Array Structure of Sidelnikov Sequences

作者：Kim Young Tae^*; Kim Dae San; Song Hong Yeop

来源：IEEE Transactions on Information Theory, 2015, 61(1): 655-670.

DOI：10.1109/TIT.2014.2371461

• Sidelnikov sequences
• polyphase sequences
• non-binary sequences
• sequences for GNSS
• family of sequences with good crosscorrelation
• cyclotomic cosets

In this paper, we extend the construction by Yu and Gong for families of M-ary sequences of period q-1 from the array structure of an M-ary Sidelnikov sequence of period q(2)-1, where q is a prime power and M vertical bar q-1. The construction now applies to the cases of using any period q(d)-1 for 3 <= d<(1/2)(root q-(2/root q) + 1) and q>27. The proposed construction results in a family of M-ary seqeunces of period q-1 with: 1) the correlation magnitudes, which are upper bounded by (2d-1)root q+1 and 2) the asymptotic size of (M-1) q(d-1)/d as q increases. We also characterize some subsets of the above of size similar to(r-1) q(d-1)/d but with a tighter upper bound (2d-2)root q +2 on its correlation magnitude. We discuss reducing both time and memory complexities for the practical implementation of such constructions in some special cases. We further give some approximate size of the newly constructed families in general and an exact count when d is a prime power or a product of two distinct primes. The main results of this paper now give more freedom of tradeoff in the design of M-ary sequence family between the family size and the correlation magnitude of the family.

• 出版日期2015-1