Determination of the merit factor of Legendre sequences
IEEE Transactions on Information Theory
Digital and Analog Communication Systems
Digital and Analog Communication Systems
A memetic algorithm for the low autocorrelation binary sequence problem
Proceedings of the 9th annual conference on Genetic and evolutionary computation
A note on low autocorrelation binary sequences
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
A survey of the merit factor problem for binary sequences
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
Evolutionary search for low autocorrelated binary sequences
IEEE Transactions on Evolutionary Computation
A new search for skewsymmetric binary sequences with optimal merit factors
IEEE Transactions on Information Theory
Sieves for low autocorrelation binary sequences
IEEE Transactions on Information Theory
The merit factor of long low autocorrelation binary sequences (Corresp.)
IEEE Transactions on Information Theory
| Hi-index | 0.00 |
Low autocorrelation binary sequences (LABS) are very important for communication applications. And it is a notoriously difficult computational problem to find binary sequences with low aperiodic autocorrelations. The problem can also be stated in terms of finding binary sequences with minimum energy levels or maximum merit factor defined by M.J.E. Golay, F=N^22E, N and E being the sequence length and energy respectively. Conjectured asymptotic value of F is 12.32 for very long sequences. In this paper, a theorem has been proved to show that there are finite number of possible energy levels, spaced at an equal interval of 4, for the binary sequence of a particular length. Two more theorems are proved to derive the theoretical minimum energy level of a binary sequence of even and odd length of N to be N2 and N-12 respectively, making the merit factor equal to N and N^2N-1 respectively. The derived theoretical minimum energy level successfully explains the case of N=13, for which the merit factor (F=14.083) is higher than the conjectured value. Sequence of lengths 4, 5, 7, 11, 13 are also found to be following the theoretical minimum energy level. These sequences are exactly the Barker sequences which are widely used in direct-sequence spread spectrum and pulse compression radar systems because of their low autocorrelation properties. Further analysis shows physical reasoning in support of the conjecture that Barker sequences exists only when N=