Publisher : The Korean Institute of Information and Commucation Engineering
DOI : 10.6109/jkiice.2016.20.4.715
Title & Authors
Design of 3-Dimensional Cross-Lattice Signal Constellations with Increased Compactness Li, Shuang; Kang, Seog Geun;
In this paper, a method to design 3-dimensional (3-D) cross-lattice signal constellations with increased compactness is presented and analyzed. Here, the symbols located at the outermost sides in the conventional lattice constellation are moved symmetrically to fill in empty sides and sunken corners. While the minimum Euclidean distance (MED) among adjacent symbols remains unchanged, the presented cross-lattice constellations have 3~5% reduced average power and upto 25% reduced total volume as compared with the conventional ones. Due to the increase compactness, average power of the new 3-D constellations is lower than that of the conventional ones. As a result, computer simulation verifies that the presented cross-lattice constellations can improve symbol error performance of a digital transmission system about 0.4 [dB]. Hence, the proposed 3-D cross-lattice constellations are appropriate for low-power and high-quality digital communication systems.
Digital communications;Lattice;Minimum Euclidean distance;Shaping gain;Signal constellation;
R. W. Hamming, "Error detecting and error correcting codes," Bell System Tech. J., vol. 24, no. 2, pp. 147-160, Apr. 1961.
R. G. Gallager, "Low-density parity-check codes," IRE Trans. Inform. Theory, vol. 8, no. 1, pp. 21-28, Jan. 1962.
H. G. Batshon, I. Djordjevic, L. Xu, and T. Wang, "Multidimensional LDPC-coded modulation for beyond 400 Gb/s wavelength transmission," IEEE Photon. Technol. Lett., vol. 21, no. 16, pp. 1139-1141, Aug. 2008.
G. Ungerboeck, "Trellis-coded modulation with redundant signal set - Part 2: State of the art," IEEE Commun. Mag., vol. 25, no. 2, pp. 12-21, Feb. 1987.
J. G. Proakis and M. Salehi, Digital Communications, 5th ed., McGraw-Hill, Singapore, 2008.
G. Stepniak, "Comparison of efficiency of N-dimensional CAP modulations," J. Lightwave Technol., vol. 32, no. 14, pp. 2516-2523, July 2014.
N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, and J. H. Conway, "Minimal-energy clusters of hard spheres," Discrete Comput. Geom., vol. 14, pp. 237-259, Oct. 1995.
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, New York, N.Y., 1988.
J.-E. Porath and T. Aulin, "Design of multidimensional signal constellations," IEE Proc.-Commun., vol. 150, no. 5, pp. 317-323, Oct. 2003.
Z. Chen and S. G. Kang, "Three-dimensional modulation formats with constant power for optical communications," Opt. Express, vol. 19, no. 23, pp. 22358-22363, Nov. 2011.
S. G. Kang, Z. Chen, J. Y. Kim, J. S. Bae, and J.-S. Lim, "Construction of higher-level 3-D signal constellations and their accurate symbol error probabilities in AWGN," IEEE Trans. Signal Process., vol. 59, no. 12, pp. 6267-6273, Dec. 2011.