Probability estimates for fading and wiretap channels from ideal class zeta functions

Advances in Mathematics of Communications

Volumn 9, Issue 4, 2015, Pages 391-413

  Karpuk, David ^a   Ernvall, Anne Maria Hytönen ^b   Hollanti, Camilla ^a   Viterbo, Emanuele ^c  

^a AALTO UNIVERSITY   (Finland)

^b UNIVERSITY OF HELSINKI   (Finland)

^c MONASH UNIVERSITY   (Australia)

Author keywords

Ideal lattices; Inverse norm sum; Lattice codes; Rayleigh fading channel; Zeta functions

Indexed keywords

EID: 84947798997     PISSN: 19305346     EISSN: 19305338     Source Type: Journal    
DOI: 10.3934/amc.2015.9.391     Document Type: Article

References (19)

1. SAGE open source mathematics software system, http: //www.sagemath.org/.
2. J.-C. Belfiore and F. Oggier, Lattice code design for the rayleigh fading wiretap channel, IEEE International Conference on Communications, (2011), 1-5.
3. J.-C. Belfiore and F. Oggier, An error probability approach to mimo wiretap channels, IEEE Trans. on Comm., 61 (2013), 3396-3403.
4. J.-C. Belfiore and F. Oggier, Secrecy gain: A wiretap lattice code design, IEEE International Symposium on Information Theory and its Applications, (2010), 174-178.
5. J.-C. Belfiore and P. Solé, Unimodular lattices for the gaussian wiretap channel, IEEE Information Theory Workshop, (2010), 1-5.
6. J. Ducoat and F. Oggier, An analysis of small dimensional fading wiretap lattice codes, IEEE International Symposium on Information Theory, (2014), 966-970.
7. A.-M. Ernvall-Hytönen and C. Hollanti, On the Eavesdropper's Correct Decision in Gaussian and Fading Wiretap Channels Using Lattice Codes, IEEE Information Theory Workshop, 2011.
8. C. Hollanti and E. Viterbo, Analysis on Wiretap Lattice Codes and Probability Bounds from Dedekind Zeta Functions, IEEE International Congress on Ultra-Modern Telecommunications and Control Systems and Workshops, 2011.
9. C. Hollanti, E. Viterbo and D. Karpuk, Nonasymptotic probability bounds for fading channels exploiting Dedekind zeta functions, preprint, arXiv: 1303.3475.
10. S. Lang, Algebraic Number Theory, Second edition. Graduate Texts in Mathematics, 110. Springer-Verlag, New York, 1994.
11. S. Leung-Yan-Cheong and M. Hellman, The Gaussian wire-tap channel, IEEE Trans. on Inf. Theory, 24 (1978), 451-456.
12. F. Oggier, P. Solé and J.-C. Belfiore, Lattice codes for the wiretap gaussian channel: Construction and analysis, Information Theory, IEEE Tran, pp (2015), p1, arXiv: 1103.4086 (2013).
13. F. Oggier and E. Viterbo, Algebraic number theory and code design for rayleigh fading channels, Foundations and Trends in Communications and Information Theory, 1 (2004), 333- 416.
14. S. Ong and F. Oggier, Wiretap lattice codes from number fields with no small norm elements, Designs, Codes, and Cryptography, 73 (2014), 425-440.
15. R. Vehkalahti and H.-F. Lu, An algebraic look into MAC-DMT of lattice space-time codes, IEEE International Symposium on Information Theory, (2011), 2831-2835.
16. R. Vehkalahti and H.-F. Lu, Diversity-multiplexing gain tradeoff: A tool in algebra?, IEEE Information Theory Workshop, (2011), 135-139.
17. R. Vehkalahti, H.-F. Lu and L. Luzzi, Inverse Determinant Sums and Connections Between Fading Channel Information Theory and Algebra, IEEE Trans. on Inf. Theory, 59 (2013), 6060-6082.
18. R. Vehkalahti and L. Luzzi, Connecting DMT of division algebra space-time codes and point counting in lie groups, IEEE International Symposium on Information Theory, (2012), 3038- 3042.
19. A. Wyner, The wire-tap channel, Bell Syst. Tech. Journal, 54 (1975), 1355-1387.