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Aperiodic correlation constraints on large binary sequence sets

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2 Author(s)

The existence of binary sequences with specific aperiodic autocorrelation and cross correlation properties is investigated. Relationships are determined among the size of a sequence set, the length of the sequences n, the maximum autocorrelation sidelobe magnitude \alpha , and the maximum cross correlation magnitude \beta . The principal result is the proof of the existence of sequence sets characterized by certain combinations of n, \alpha , and \beta . The proof makes use of a new lower bound to the expected size of sequence sets constructed according to an explicit "random coding" procedure. For large n , the sequence set size is controlled primarily by the cross correlation constraint \beta . Two consequences of the existence theorem are 1) a demonstration that large sequence sets exist for which the maximum autocorrelation sidelobe and cross correlation magnitudes vanish almost as fast as the inverse square root of the sequence length (l/\sqrt {n}); 2) a new proof of the Gilbert bound of coding theory.

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Information Theory, IEEE Transactions on  (Volume:21 ,  Issue: 1 )