nach oben

Cryptography and Communications

Erschienen in:

02.10.2018

Two constructions of asymptotically optimal codebooks

verfasst von: Gaojun Luo, Xiwang Cao

Erschienen in: Cryptography and Communications | Ausgabe 4/2019

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

Codebooks with low-coherence have wide applications in many fields such as direct spread code division multiple access communications, compressed sensing, signal processing and so on. In this paper, we propose two constructions of complex codebooks from the operations of certain sets. The complex codebooks produced by these constructions are proved to be asymptotically optimal with respect to the Welch bound. In addition, the parameters of the complex codebooks presented in this paper are new and flexible in some cases.

Vorheriger Artikel Construction of a Near-Optimal Quasi-Complementary Sequence Set from Almost Difference Set

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Candes, E., Wakin, M.: An introduction to compressive sampling. IEEE Signal Process. 25(2), 21–30 (2008)CrossRef

Conway, J., Harding, R., Sloane, N.: Packing lines, planes, etc.: Packings in Grassmannian spaces. Exp. Math. 5(2), 139–159 (1996)MathSciNetMATHCrossRef

Cao, X., Chou, W., Zhang, X.: More constructions of near optimal codebooks associated with binary sequences. Adv. Math. Commun. 11(1), 187–202 (2017)MathSciNetMATHCrossRef

Ding, C.: Complex codebooks from combinatorial designs. IEEE Trans. Inform. Theory 52(9), 4229–4235 (2006)MathSciNetMATHCrossRef

Ding, C., Feng, T.: A generic construction of complex codebooks meeting the Welch bound. IEEE Trans. Inform. Theory 53(11), 4245–4250 (2007)MathSciNetMATHCrossRef

Delsarte, P., Goethals, J., Seidel, J.: Spherical codes and designs. Geometriae Dedicate. 67(3), 363–388 (1997)MathSciNetMATH

Fickus, M., Mixon, D., Tremain, J.: Steiner equiangular tight frames. Linear Algebra Appl. 436(5), 1014–1027 (2012)MathSciNetMATHCrossRef

Fickus, M., Mixon, D.: Tables of the existence of equiangular tight frames. arXiv:1504.00253v2 (2016)

Fickus, M., Mixon, D., Jasper, J.: Equiangular tight frames from hyperovals. IEEE Trans. Inf. Theory 62(9), 5225–5236 (2016)MathSciNetMATHCrossRef

10.

Fickus, M., Jasper, J, Mixon, D., Peterson, J.: Tremain equiangular tight frames. arXiv:1602.03490v1 (2016)

11.

Hu, H., Wu, J.: New constructions of codebooks nearly meeting the Welch bound with equality. IEEE Trans. Inf. Theory 60(2), 1348–1355 (2014)MathSciNetMATHCrossRef

12.

Hong, S., Park, H., Helleseth, T., Kim, Y.: Near optimal partial Hadamard codebook construction using binary sequences obtained from quadratic residue mapping. IEEE Trans. Inf. Theory 60(6), 3698–3705 (2014)MathSciNetMATHCrossRef

13.

Heng, Z., Ding, C., Yue, Q.: New constructions of asymptotically optimal codebooks with multiplicative characters. IEEE Trans. Inf. Theory 63(10), 6179–6187 (2017)MathSciNetMATHCrossRef

14.

Heng, Z.: Nearly optimal codebooks based on generalized Jacobi sums. Dis. Appli. Math. https://doi.org/10.1016/j.dam.2018.05.017 (2018)

15.

Li, C., Yue, Q., Huang, Y.: Two families of nearly optimal codebooks. Des. Codes Cryptogr. 75(1), 43–57 (2015)MathSciNetMATHCrossRef

16.

Love, D., Heath, R., Strohmer, T.: Grassmannian beamforming for multiple-input multiple-output wireless systems. IEEE Trans. Inf. Theory 49(10), 2735–2747 (2003)MathSciNetMATHCrossRef

17.

Luo, G., Cao, X.: Two constructions of asymptotically optimal codebooks via the hyper Eisenstein sum. IEEE Trans. Inf. Theory. https://doi.org/10.1109/TIT.2017.2777492 (2017)

18.

Lidl, R., Niederreiter, H.: Finite Fields. Cambridge University Press, Cambridge (1997)MATH

19.

Mukkavilli, K., Sabharwal, A., Erkip, E., Aazhang, B.: On beamforming with finite rate feedback in multiple antenna systems. IEEE Trans. Inf. Theory 49(10), 2562–2579 (2003)MathSciNetMATHCrossRef

20.

Massey, J., Mittelholzer, T.: Welch Bound and Sequence Sets for Code-Division Multiple-Access Systems. Sequences II, pp 63–78. Springer, New York (1999)MATH

21.

Rahimi, F.: Covering graphs and equiangular tight frames. Ph.D. Thesis, University of Waterloo, Ontario. (available at http://hdl.handle.net/10012/10793) (2016)

22.

Renes, J., Blume-Kohout, R., Scot, A., Caves, C.: Symmetric informationally complete quantum measurements. J. Math. Phys. 45(6), 2171–2180 (2004)MathSciNetMATHCrossRef

23.

Sarwate, D.: Meeting the Welch Bound with Equality. Sequences and their Applications, pp 79–102. Springer, London (1999)MATHCrossRef

24.

Strohmer, T., Heath, R.: Grassmannian frames with applications to coding and communication. Appl. Comput. Harmonic Anal. 14, 257–275 (2003)MathSciNetMATHCrossRef

25.

Tsiligianni, E., Kondi, L., Katsaggelos, A.: Construction of incoherent unit norm tight frameswith application to compressed sensing. IEEE Trans. Inform. Theory 60(4), 2319–2330 (2014)MathSciNetMATHCrossRef

26.

Tan, P., Zhou, Z., Zhang, D.: A construction of codebooks nearly achieving the Levenshtein bound. IEEE Signal Process. Lett. 23(10), 1306–1309 (2016)CrossRef

27.

Welch, L.: Lower bounds on the maximum cross correlation of signals. IEEE Trans. Inform. Theory 20(3), 397–399 (1974)MATHCrossRef

28.

Xia, P., Zhou, S., Giannakis, G.: Achieving the Welch bound with difference sets. IEEE Trans. Inform. Theory 51(5), 1900–1907 (2005)MathSciNetMATHCrossRef

29.

Yu, N.: A construction of codebooks associated with binary sequences. IEEE Trans. Inf. Theory 58(8), 5522–5533 (2012)MathSciNetMATHCrossRef

30.

Zhang, A., Feng, K.: Two classes of codebooks nearly meeting the Welch bound. IEEE Trans. Inf. Theory 58(4), 2507–2511 (2012)MathSciNetMATHCrossRef

31.

Zhang, A., Feng, K.: Construction of cyclotomic codebooks nearly meeting the Welch bound. Des. Codes Cryptogr. 63(2), 209–224 (2013)MathSciNetMATHCrossRef

32.

Zhou, Z., Tang, X.: New nearly optimal codebooks from relative difference sets. Adv. Math. Commun. 5(3), 521–527 (2011)MathSciNetMATHCrossRef

Titel: Two constructions of asymptotically optimal codebooks
verfasst von: Gaojun Luo
Xiwang Cao
Publikationsdatum: 02.10.2018
Verlag: Springer US
Erschienen in: Cryptography and Communications / Ausgabe 4/2019
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-018-0331-4

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 4/2019

Frequency-hopping sequence sets with good aperiodic Hamming correlation property

Construction of a Near-Optimal Quasi-Complementary Sequence Set from Almost Difference Set

Hadamard partitioned difference families and their descendants

Periodic state-space representations of periodic convolutional codes

Complete weight enumerators of a class of two-weight linear codes

Settling the mystery of Zr = r in RC4