Lattice Index Coding

IEEE Transactions on Information Theory

Volumn 61, Issue 12, 2015, Pages 6505-6525

  Natarajan, Lakshmi ^a   Hong, Yi ^a   Viterbo, Emanuele ^a  

^a MONASH UNIVERSITY   (Australia)

Author keywords

Chinese remainder theorem; Gaussian broadcast channel; index coding; lattice codes; principal ideal domain; side information

Indexed keywords

BROADCASTING; GAUSSIAN DISTRIBUTION; INFORMATION USE; SENSOR NETWORKS; SIGNAL RECEIVERS; WIRELESS SENSOR NETWORKS;

CHINESE REMAINDER THEOREM; GAUSSIAN BROADCAST CHANNEL; INDEX CODING; LATTICE CODES; PRINCIPAL IDEAL DOMAIN; SIDE INFORMATION;

CODES (SYMBOLS);

EID: 84959420436     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2015.2491924     Document Type: Article

References (33)

1. Y. Birk and T. Kol, "Informed-source coding-on-demand (ISCOD) over broadcast channels," in Proc. 17th Annu. Joint Conf. IEEE Comput. Commun. Soc. (INFOCOM), vol. 3. Mar./Apr. 1998, pp. 1257-1264.
2. Z. Bar-Yossef, Y. Birk, T. S. Jayram, and T. Kol, "Index coding with side information," IEEE Trans. Inf. Theory, vol. 57, no. 3, pp. 1479-1494, Mar. 2011.
3. N. Alon, E. Lubetzky, U. Stav, A. Weinstein, and A. Hassidim, "Broadcasting with Side Information," in Proc. 49th IEEE Symp. Found. Comput. Sci. (FOCS), Oct. 2008, pp. 823-832.
4. S. El Rouayheb, A. Sprintson, and C. Georghiades, "On the index coding problem and its relation to network coding and matroid theory," IEEE Trans. Inf. Theory, vol. 56, no. 7, pp. 3187-3195, Jul. 2010.
5. A. Blasiak, R. Kleinberg, and E. Lubetzky. (2010). "Index coding via linear programming." [Online]. Available: http://arxiv.org/abs/1004.1379
6. S. Unal and A. B. Wagner, "General index coding with side information: Three decoder case," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Jul. 2013, pp. 1137-1141.
7. Y. Wu, "Broadcasting when receivers know some messages a priori," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Jun. 2007, pp. 1141-1145.
8. G. Kramer and S. Shamai, "Capacity for classes of broadcast channels with receiver side information," in Proc. IEEE Inf. Theory Workshop (ITW), Sep. 2007, pp. 313-318.
9. L.-L. Xie, "Network coding and random binning for multi-user channels," in Proc. 10th Can. Workshop Inf. Theory (CWIT), Jun. 2007, pp. 85-88.
10. T. J. Oechtering, C. Schnurr, I. Bjelakovic, and H. Boche, "Broadcast capacity region of two-phase bidirectional relaying," IEEE Trans. Inf. Theory, vol. 54, no. 1, pp. 454-458, Jan. 2008.
11. T. J. Oechtering, M. Wigger, and R. Timo, "Broadcast capacity regions with three receivers and message cognition," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Jul. 2012, pp. 388-392.
12. J. W. Yoo, T. Liu, and F. Xue, "Gaussian broadcast channels with receiver message side information," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Jun. 2009, pp. 2472-2476.
13. J. Sima and W. Chen, "Joint network and Gelfand-Pinsker coding for 3-receiver Gaussian broadcast channels with receiver message side information," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Jun. 2014, pp. 81-85.
14. B. Asadi, L. Ong, and S. J. Johnson, "The capacity of three-receiver AWGN broadcast channels with receiver message side information," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Jun. 2014, pp. 2899-2903.
15. E. Tuncel, "Slepian-Wolf coding over broadcast channels," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1469-1482, Apr. 2006.
16. L. Xiao, T. E. Fuja, J. Kliewer, and D. Costello, Jr., "Nested codes with multiple interpretations," in Proc. 40th Annu. Conf. Inf. Sci. Syst. (CISS), Mar. 2006, pp. 851-856.
17. Y. Ma, Z. Lin, H. Chen, and B. Vucetic, "Multiple interpretations for multi-source multi-destination wireless relay network coded systems," in Proc. IEEE 23rd Int. Symp. Pers. Indoor Mobile Radio Commun. (PIMRC), Sep. 2012, pp. 2253-2258.
18. F. C. Barbosa and M. H. M. Costa, "A tree construction method of nested cyclic codes," in Proc. IEEE Inf. Theory Workshop (ITW), Oct. 2011, pp. 302-305.
19. Y.-C. Huang, "Lattice index codes from algebraic number fields," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Jun. 2015, pp. 2485-2489.
20. L. Natarajan, Y. Hong, and E. Viterbo, "Index codes for the Gaussian broadcast channel using quadrature amplitude modulation," IEEE Commun. Lett., vol. 19, no. 8, pp. 1291-1294, Aug. 2015.
21. L. Natarajan, Y. Hong, and E. Viterbo, "Capacity of coded index modulation," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Jun. 2015, pp. 596-600.
22. K. H. Rosen, Elementary Number Theory and Its Application. Reading, MA, USA: Addison-Wesley, 2005.
23. G. Ungerboeck, "Channel coding with multilevel/phase signals," IEEE Trans. Inf. Theory, vol. 28, no. 1, pp. 55-67, Jan. 1982.
24. J. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups. New York, NY, USA: Springer-Verlag, 1999.
25. G. D. Forney, Jr., "Coset codes. I. Introduction and geometrical classification," IEEE Trans. Inf. Theory, vol. 34, no. 5, pp. 1123-1151, Sep. 1988.
26. R. Zamir, S. Shamai, and U. Erez, "Nested linear/lattice codes for structured multiterminal binning," IEEE Trans. Inf. Theory, vol. 48, no. 6, pp. 1250-1276, Jun. 2002.
27. H. Cohn and A. Kumar, "Optimality and uniqueness of the Leech lattice among lattices," Ann. Math., vol. 170, no. 3, pp. 1003-1050, Nov. 2009.
28. N. Jacobson, Basic Algebra I. San Francisco, CA, USA: Freeman, 1974.
29. J. Proakis, Digital Communications. New York, NY, USA: McGraw-Hill, 2001.
30. Y.-C. Huang, K. R. Narayanan, and N. E. Tunali. (2014). "Multistage compute-and-forward with multilevel lattice codes based on product constructions." [Online]. Available: http://arxiv.org/abs/1401.2228
31. J. H. Conway and D. Smith, On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry. Natick, MA, USA: A K Peters, 2003.
32. J. Uspensky and M. Heaslet, Elementary Number Theory. New York, NY, USA: McGraw-Hill, 1939.
33. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York, NY, USA: Wiley, 2012.