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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 magnitudealpha, and the maximum cross correlation magnitudebeta. The principal result is the proof of the existence of sequence sets characterized by certain combinations ofn, alpha, andbeta. 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 largen, the sequence set size is controlled primarily by the cross correlation constraintbeta. 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.

Published in:

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

Date of Publication:

Jan 1975

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