Achieving AWGN channel capacity with lattice Gaussian coding

IEEE Transactions on Information Theory

Volumn 60, Issue 10, 2014, Pages 5918-5929

  Ling, Cong ^a   Belfiore, Jean Claude ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b TELECOM PARISTECH   (France)

Author keywords

Channel capacity; flatness factor; lattice coding; lattice Gaussian distribution; MMSE

Indexed keywords

FLATNESS FACTOR; GAUSSIANS; LATTICE CODING; MMSE;

CHANNEL CAPACITY;

EID: 84907192661     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2014.2332343     Document Type: Article

References (27)

1. G. Poltyrev, "On coding without restrictions for the AWGN channel," IEEE Trans. Inf. Theory, vol. 40, no. 2, pp. 409-417, Mar. 1994.
2. U. Erez and R. Zamir, "Achieving 1/2 log (1+SNR) on the AWGN channel with lattice encoding and decoding," IEEE Trans. Inf. Theory, vol. 50, no. 10, pp. 2293-2314, Oct. 2004.
3. Y. Yan, C. Ling, and X. Wu, "Polar lattices: Where Arkan meets Forney," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Istanbul, Turkey, Jul. 2013, pp. 1292-1296.
4. N. di Pietro, J. J. Boutros, G. Zémor, and L. Brunel, "New results on low-density integer lattices," in Proc. Inf. Theory Appl. (ITA) Workshop, San Diego, CA, USA, Feb. 2013.
5. N. di Pietro, G. Zémor, and J. J. Boutros, "New results on construction A lattices based on very sparse parity-check matrices," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Istanbul, Turkey, Jul. 2013, pp. 1675-1679.
6. N. Sommer, M. Feder, and O. Shalvi, "Low-density lattice codes," IEEE Trans. Inf. Theory, vol. 54, no. 4, pp. 1561-1585, Apr. 2008.
7. M.-R. Sadeghi, A. H. Banihashemi, and D. Panario, "Low-density paritycheck lattices: Construction and decoding analysis," IEEE Trans. Inf. Theory, vol. 52, no. 10, pp. 4481-4495, Oct. 2006.
8. C. E. Shannon, "Systems which approach the ideal as P/N?," in Miscellaneous Writings, N. J. A. Sloane and A. D. Wyner, Eds. Murray Hill, NJ, USA: Mathematical Sciences Research Center, 1993. [Online]. Available: https://archive.org/details/ShannonMiscellaneous Writings
9. S. Shamai, "Old and new: An information-estimation perspective," in Proc. Elect. Eng. IDSE Seminar, Oct. 2012.
10. Y. Wu and S. Verdú, "The impact of constellation cardinality on Gaussian channel capacity," in Proc. 48th Allerton Conf. Commun., Control, Comput., Allerton, IL, USA, Sep./Oct. 2010, pp. 14-21.
11. G. D. Forney, Jr. and L.-F. Wei, "Multidimensional constellations. I. Introduction, figures of merit, and generalized cross constellations," IEEE J. Sel. Areas Commun., vol. 7, no. 6, pp. 877-892, Aug. 1989.
12. F. R. Kschischang and S. Pasupathy, "Optimal nonuniform signaling for Gaussian channels," IEEE Trans. Inf. Theory, vol. 39, no. 3, pp. 913-929, May 1993.
13. R. Zamir, Lattice Coding for Signals and Networks. Cambridge, U.K.: Cambridge Univ. Press, Aug. 2014.
14. R. Zamir, "Lattice coding for signals and networks: Application and design," in Proc. ISIT, 2012.
15. N. Palgy and R. Zamir, "Dithered probabilistic shaping," in Proc. IEEE 27th Conv. Elect. Electron. Eng. Israel, Eilat, Israel, Nov. 2012, pp. 1-5.
16. C. Ling, L. Luzzi, J.-C. Belfiore, and D. Stehlé, "Semantically secure lattice codes for the Gaussian wiretap channel," IEEE Trans. Inf. Theory, to be published. [Online]. Available: http://arxiv.org/abs/1210.6673
17. J.-C. Belfiore, "Lattice codes for the compute-and-forward protocol: The flatness factor," in Proc. ITW, Paraty, Brazil, 2011.
18. J. Conway and N. J. A. Sloane, Sphere Packings, Lattices, and Groups, 3rd ed. New York, NY, USA: Springer-Verlag, 1998.
19. G. D. Forney, M. D. Trott, and S.-Y. Chung, "Sphere-bound-achieving coset codes and multilevel coset codes," IEEE Trans. Inf. Theory, vol. 46, no. 3, pp. 820-850, May 2000.
20. D. Micciancio and O. Regev, "Worst-case to average-case reductions based on Gaussian measures," in Proc. Ann. Symp. Found. Comput. Sci., Rome, Italy, Oct. 2004, pp. 372-381.
21. W. Banaszczyk, "New bounds in some transference theorems in the geometry of numbers," Math. Ann., vol. 296, no. 1, pp. 625-635, 1993.
22. H.-A. Loeliger, "Averaging bounds for lattices and linear codes," IEEE Trans. Inf. Theory, vol. 43, no. 6, pp. 1767-1773, Nov. 1997.
23. O. Regev, "On lattices, learning with errors, random linear codes, and cryptography," J. ACM, vol. 56, no. 6, pp. 34-1-34-40, 2009.
24. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York, NY, USA: Wiley, 1991.
25. M. R. Bloch and J. N. Laneman, "Strong secrecy from channel resolvability," IEEE Trans. Inf. Theory, vol. 59, no. 12, pp. 8077-8098, Dec. 2013, doi: 10.1109/TIT.2013.2283722.
26. R. Zamir and M. Feder, "On lattice quantization noise," IEEE Trans. Inf. Theory, vol. 42, no. 4, pp. 1152-1159, Jul. 1996.
27. G. D. Forney, Jr., "Coset codes. I. Introduction and geometrical classification," IEEE Trans. Inf. Theory, vol. 34, no. 5, pp. 1123-1151, Sep. 1988.