Some “goodness” properties of LDA lattices
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We study some structural properties of Construction-A lattices obtained from low density parity check codes over prime fields. Such lattices are called low density Construction-A (LDA) lattices, and permit low-complexity belief propagation decoding for transmission over Gaussian channels. It has been shown that LDA lattices achieve the capacity of the power constrained additive white Gaussian noise (AWGN) channel with closest lattice-point decoding, and simulations suggested that they perform well under belief propagation decoding. We continue this line of work and prove that these lattices are good for packing and mean squared error quantization and that their duals are good for packing. With this, we can conclude that codes constructed using nested LDA lattices can achieve the capacity of the power constrained AWGN channel, the capacity of the dirty paper channel, the rates guaranteed by the computeand-forward protocol, and the best known rates for bidirectional relaying with perfect secrecy.
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- 7.Baik, I.-J. and Chung, S.-Y., Network Coding for Two-Way Relay Channels Using Lattices, in Proc. IEEE Int. Conf. on Communications (ICC’08), Beijing, China, May 19–23, 2008, pp. 3898–3902.Google Scholar
- 17.di Pietro, N., On Infinite and Finite Lattice Constellations for the Additive White Gaussian Noise Channel, PhD Thesis, Inst. Math. Bordeaux, Univ. Bordeaux, Bordeaux, France, 2014. Available at https://tel.archives-ouvertes.fr/tel-01135575/document.Google Scholar
- 19.di Pietro, N., Boutros, J.J., Zémor, G., and Brunel, L., New Results on Low-Density Integer Lattices, in Proc. 2013 Information Theory and Applications Workshop (ITA’2013), San Diego, CA, Feb. 10–15, 2013, pp. 39–44.Google Scholar
- 20.di Pietro, N., Zémor, G., and Boutros, J.J., LDA Lattices without Dithering Achieve Capacity on the Gaussian Channel, arXiv:1603.02863 [cs.IT], 2016.Google Scholar
- 28.Bassalygo, L.A. and Pinsker, M.S., Complexity of an Optimum Nonblocking Switching Network without Reconnections, Probl. Peredachi Inf., 1973, vol. 9, no. 1, pp. 84–87 [Probl. Inf. Trans. (Engl. Transl.), 1973, vol. 9, no. 1, pp. 64–66].Google Scholar