On ternary complementary sequences |
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Authors: | Gavish A Lempel A |
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Affiliation: | Dept. of Electr. Eng., Technion-Israel Inst. of Technol., Haifa; |
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Abstract: | A pair of real-valued sequences A=(a1,a2,...,aN) and B=(b1,b 2,...,bN) is called complementary if the sum R(·) of their autocorrelation functions RA(·) and RB(·) satisfies R(τ)=RA(τ)+R B(τ)=Σi=1N$ -τaiai+τ+Σj=1 N-τbjbj+τ=0, ?τ≠0. In this paper we introduce a new family of complementary pairs of sequences over the alphabet α3=+{1,-1,0}. The inclusion of zero in the alphabet, which may correspond to a pause in transmission, leads both to a better understanding of the conventional binary case, where the alphabet is α2={+1,-1}, and to new nontrivial constructions over the ternary alphabet α3. For every length N, we derive restrictions on the location of the zero elements and on the form of the member sequences of the pair. We also derive a bound on the minimum number of zeros necessary for the existence of a complementary pair of length N over α3. The bound is tight, as it is met by some of the proposed constructions, for infinitely many lengths |
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