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Design of 3-Dimensional Cross-Lattice Signal Constellations with Increased Compactness

조밀도가 증가된 3차원 십자격자형 신호성상도의 설계

  • Li, Shuang (Department of Electrical and Electronic Engineering, Gyeongsang National University) ;
  • Kang, Seog Geun (Department of Semiconductor Engineering, Gyeongsang National University)
  • Received : 2016.02.11
  • Accepted : 2016.03.12
  • Published : 2016.04.30

Abstract

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.

본 논문에서는 조밀도가 증가된 3차원 십자격자형 신호성상도의 설계 방법을 제시하고 분석한다. 우수한 성형이득을 얻기 위하여 여기서는 기존 성상도에서 최외곽에 위치한 심볼들을 빈 면과 움푹 들어간 모서리로 이동시킨다. 제시된 신호성상도는 심볼 간 최소 유클리드 거리를 동일하게 유지하면서도 기존 성상도에 비하여 크기에 따라 3~5% 감소된 평균전력과 최대 25%까지 감소된 체적을 가지는 것으로 나타났다. 이와 같은 조밀도의 증가로 인하여 새로운 성상도는 기존 성상도에 비하여 감소된 평균전력을 가진다. 그 결과, 제시된 십자격자형 신호성상도는 디지털 전송시스템의 심볼오류성능을 0.4 [dB] 가량 향상시킬 수 있는 것으로 확인되었다. 따라서 제안된 3차원 격자형 신호성상도는 저전력 및 고신뢰성이 요구되는 디지털 통신시스템에 적합한 것으로 사료된다.

Keywords

References

  1. R. W. Hamming, "Error detecting and error correcting codes," Bell System Tech. J., vol. 24, no. 2, pp. 147-160, Apr. 1961.
  2. R. G. Gallager, "Low-density parity-check codes," IRE Trans. Inform. Theory, vol. 8, no. 1, pp. 21-28, Jan. 1962. https://doi.org/10.1109/TIT.1962.1057683
  3. 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.
  4. 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. https://doi.org/10.1109/MCOM.1987.1093541
  5. J. G. Proakis and M. Salehi, Digital Communications, 5th ed., McGraw-Hill, Singapore, 2008.
  6. G. Stepniak, "Comparison of efficiency of N-dimensional CAP modulations," J. Lightwave Technol., vol. 32, no. 14, pp. 2516-2523, July 2014. https://doi.org/10.1109/JLT.2014.2329141
  7. 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. https://doi.org/10.1007/BF02570704
  8. J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, New York, N.Y., 1988.
  9. J.-E. Porath and T. Aulin, "Design of multidimensional signal constellations," IEE Proc.-Commun., vol. 150, no. 5, pp. 317-323, Oct. 2003. https://doi.org/10.1049/ip-com:20030652
  10. 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. https://doi.org/10.1364/OE.19.022358
  11. 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. https://doi.org/10.1109/TSP.2011.2165062

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