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Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/240BC38D-0B75-4578-9FBA-F85D2FD1E5C1 | ||
| Year | 2010 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
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| Bibliographic Citation | G. N. Karystinos and A. P. Liavas, “Efficient computation of the binary vector that maximizes a rank-deficient quadratic form,” IEEE Transactions on Information Theory, vol. 56, no. 7, pp. 3581 - 3593, Jul. 2010. doi: 10.1109/TIT.2010.2048450 https://doi.org/10.1109/TIT.2010.2048450 | ||
| Appears in Collections |
The maximization of a full-rank quadratic form over the binary alphabet can be performed through exponential-complexity exhaustive search. However, if the rank of the form is not a function of the problem size, then it can be maximized in polynomial time. By introducing auxiliary spherical coordinates, we show that the rank-deficient quadratic-form maximization problem is converted into a double maximization of a linear form over a multidimensional continuous set, the multidimensional set is partitioned into a polynomial-size set of regions which are associated with distinct candidate binary vectors, and the optimal binary vector belongs to the polynomial-size set of candidate vectors. Thus, the size of the candidate set is reduced from exponential to polynomial. We also develop an algorithm that constructs the polynomial-size candidate set in polynomial time and show that it is fully parallelizable and rank-scalable. Finally, we demonstrate the efficiency of the proposed algorithm in the context of adaptive spreading code design.
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