Signal Sets From Functions With Optimum Nonlinearity

Ding, Cunsheng; Yin, Jianxing

doi:10.1109/tcomm.2007.894113

Cited by 59 publications

(58 citation statements)

References 23 publications

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“…For the case of M being too large to fulfill (4), the bound in (7) is targeted by Mutually Unbiased Bases (MUBs) in [21], [45]. MUBs consist of multiple N dimensional bases for which all inner products across their elements are of the same magnitude 1/ √ N [45], [46].…”

Section: Algorithms Aiming For Optimal Coherencementioning

confidence: 99%

Coherence Optimization and Best Complex Antipodal Spherical Codes

Zorlein¹,

Bossert²

2015

IEEE Trans. Signal Process.

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Vector sets with optimal coherence according to the Welch bound cannot exist for all pairs of dimension and cardinality. If such an optimal vector set exists, it is an equiangular tight frame and represents the solution to a Grassmannian line packing problem. Best Complex Antipodal Spherical Codes (BCASCs) are the best vector sets with respect to the coherence. By extending methods used to find best spherical codes in the real-valued Euclidean space, the proposed approach aims to find BCASCs, and thereby, a complex-valued vector set with minimal coherence. There are many applications demanding vector sets with low coherence. Examples are not limited to several techniques in wireless communication or to the field of compressed sensing. Within this contribution, existing analytical and numerical approaches for coherence optimization of complex-valued vector spaces are summarized and compared to the proposed approach. The numerically obtained coherence values improve previously reported results. The drawback of increased computational effort is addressed and a faster approximation is proposed which may be an alternative for time critical cases.

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Section: Algorithms Aiming For Optimal Coherencementioning

confidence: 99%

Coherence Optimization and Best Complex Antipodal Spherical Codes

Zorlein¹,

Bossert²

2015

IEEE Trans. Signal Process.

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“…These codebooks can constructed from binary Kerdock codes [2,31,33], perfect nonlinear functions [10,31], bent functions [36], Z 4 -Kerdock codes [2], and Z 4 -valued quadratic forms [15]. It is interesting to construct optimal codebooks achieving the Levenstein Bound with different parameters from different methods.…”

Section: Introductionmentioning

confidence: 99%

Codebooks from generalized bent Z4-valued quadratic forms

Mesnager

Tang

2020

Discrete Mathematics

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“…Since then MUBs have been used in quantum key distribution protocols [3], [21], and can be used to construct signal sets for communications systems [1], [7].…”

Section: Introductionmentioning

confidence: 99%

Mutually unbiased bases as submodules and subspaces

Hall

Šťovíček

2012

2012 IEEE International Symposium on Information Theory Proceedings

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Mutually unbiased bases (MUBs) have been used in several cryptographic and communications applications. There has been much speculation regarding connections between MUBs and finite geometries. Most of which has focused on a connection with projective and affine planes. We propose a connection with higher dimensional projective geometries and projective Hjelmslev geometries. We show that this proposed geometric structure is present in several constructions of MUBs.

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Signal Sets From Functions With Optimum Nonlinearity

Cited by 59 publications

References 23 publications

Coherence Optimization and Best Complex Antipodal Spherical Codes

Coherence Optimization and Best Complex Antipodal Spherical Codes

Codebooks from generalized bent Z4-valued quadratic forms

Mutually unbiased bases as submodules and subspaces

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