Asymptotically Optimal Codebooks in Regard to the Welch Bound with Characters

2020 ◽  
Vol E103.A (11) ◽  
pp. 1292-1295
Author(s):  
Gang WANG ◽  
Min-Yao NIU ◽  
Lin-Zhi SHEN ◽  
You GAO
Keyword(s):  
Asymptotically Optimal ◽  
Welch Bound

scholarly journals New Constructions of Asymptotically Optimal Codebooks via Cyclotomic Classes of Order 8

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Wanfeng Qi ◽  
Yueying Song ◽  
Rui Ma ◽  
Lingli Tang ◽  
Qian Wang
Keyword(s):  
Finite Fields ◽  
Difference Sets ◽  
Good Alternative ◽  
Asymptotically Optimal ◽  
Welch Bound ◽  
New Class ◽  
Almost Difference Sets

Asymptotically optimal codebooks are a family of codebooks that can approach an optimal codebook meeting the Welch bound when the lengths of codewords are large enough. They can be constructed easily and are a good alternative for optimal codebooks in many applications. In this paper, we construct a new class of asymptotically optimal codebooks by using the product of some special finite fields and almost difference sets, which are composed of cyclotomic classes of order eight.

scholarly journals Constructions of asymptotically optimal codebooks with respect to Welch bound and Levenshtein bound

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Gang Wang ◽  
Deng-Ming Xu ◽  
Fang-Wei Fu
Keyword(s):  
Code Division Multiple Access ◽  
Communication Systems ◽  
Multiple Access ◽  
Cross Correlation ◽  
Hadamard Matrices ◽  
Circulant Matrices ◽  
Asymptotically Optimal ◽  
Welch Bound ◽  
Construction Methods ◽  
Code Division Multiple

<p style='text-indent:20px;'>Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in code division multiple access communication systems. In this paper, several classes of codebooks are introduced, whose maximum cross-correlation amplitudes asymptotically achieve the corresponding Welch bound and Levenshtein bound. Specially, a class of optimal codebooks with respect to the Levenshtein bound is obtained. These classes of codebooks are constructed by selecting certain rows deterministically from circulant matrices, Fourier matrices and Hadamard matrices, respectively. The construction methods and parameters of some codebooks provided in this paper are new.</p>

scholarly journals Four Constructions of Asymptotically Optimal Codebooks via Additive Characters and Multiplicative Characters

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1144 ◽  
Author(s):  
Xia Wu ◽  
Wei Lu
Keyword(s):  
Cross Correlation ◽  
Irreducible Polynomials ◽  
Asymptotically Optimal ◽  
Welch Bound ◽  
Multiplicative Characters ◽  
Special Case

In this paper, we present four new constructions of complex codebooks with multiplicative characters, additive characters, and quadratic irreducible polynomials and determine the maximal cross-correlation amplitude of these codebooks. We prove that the codebooks we constructed are asymptotically optimal with respect to the Welch bound. Moreover, we generalize the result obtained by Zhang and Feng and contain theirs as a special case. The parameters of these codebooks are new.

scholarly journals Asymptotically optimal cubature formulas on manifolds for prefixed weights

2021 ◽  
pp. 105632
Author(s):  
Martin Ehler ◽  
Ujué Etayo ◽  
Bianca Gariboldi ◽  
Giacomo Gigante ◽  
Thomas Peter
Keyword(s):  
Asymptotically Optimal ◽  
Cubature Formulas

Large Families of Asymptotically Optimal Two-Dimensional Optical Orthogonal Codes

2012 ◽  
Vol 58 (2) ◽  
pp. 1163-1185 ◽  
Author(s):  
Reza Omrani ◽  
Gagan Garg ◽  
P. Vijay Kumar ◽  
Petros Elia ◽  
Pankaj Bhambhani
Keyword(s):  
Two Dimensional ◽  
Asymptotically Optimal ◽  
Optical Orthogonal Codes ◽  
Orthogonal Codes ◽  
Large Families

ON THE AVERAGE CASE CIRCUIT DELAY OF DISJUNCTION

1995 ◽  
Vol 05 (02) ◽  
pp. 275-280 ◽  
Author(s):  
BEATE BOLLIG ◽  
MARTIN HÜHNE ◽  
STEFAN PÖLT ◽  
PETR SAVICKÝ
Keyword(s):  
Lower Bounds ◽  
Wide Class ◽  
Time Complexity ◽  
Upper And Lower Bounds ◽  
Average Case ◽  
Asymptotically Optimal ◽  
Circuit Delay ◽  
Suitable Measure

For circuits the expected delay is a suitable measure for the average case time complexity. In this paper, new upper and lower bounds on the expected delay of circuits for disjunction and conjunction are derived. The circuits presented yield asymptotically optimal expected delay for a wide class of distributions on the inputs even when the parameters of the distribution are not known in advance.

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