Gray coding for multilevel constellations in Gaussian noise

IEEE Transactions on Information Theory

Volumn 53, Issue 1, 2007, Pages 224-235

  Agrell, Erik ^a   Lassing, Johan ^b   Ström, Erik G ^a   Ottosson, Tony ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^b Qamcom Research and Technology   (Sweden)

Author keywords

Binary reflected Gray code; Bit error probability (BEP); Bit error rate; Constellation labeling; Digital modulation; Gray mapping; Optimal labeling; Phase shift keying (PSK); Pulse amplitude modulation (PAM); Quadrature amplitude modulation (QAM)

Indexed keywords

BINARY CODES; BIT ERROR RATE; COMMUNICATION CHANNELS (INFORMATION THEORY); ENCODING (SYMBOLS); PHASE SHIFT KEYING; PROBABILITY; PULSE AMPLITUDE MODULATION; QUADRATURE AMPLITUDE MODULATION;

BINARY REFLECTED GRAY CODE; BIT-ERROR PROBABILITY (BEP); CONSTELLATION LABELING; DIGITAL MODULATION; GRAY MAPPING; OPTIMAL LABELING;

GAUSSIAN NOISE (ELECTRONIC);

EID: 33846119606     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2006.887070     Document Type: Article

References (16)

1. J. G. Proakis, Digital Communications, 3rd ed. New York: McGraw-Hill, 1995.
2. R. D. Wesel, X. Liu, J. M. Cioffi, and C. Komninakis, "Constellation labeling for linear encoders," IEEE Trans. Inf. Theory, vol. 47, no. 6, pp. 2417-2431, Sep. 2001.
3. F. Gray, "Pulse Code Communications," U.S. Patent 2632058, Mar. 1953.
4. G. Takahara, F. Alajaji, N. C. Beaulieu, and H. Kuai, "Constellation mappings for two-dimensional signaling of nonuniform sources," IEEE Trans. Commun., vol. 51, no. 3, pp. 400-408, Mar. 2003.
5. E. Agrell, J. Lassing, E. G. Ström, and T. Ottosson, "On the optimality of the binary reflected Gray code," IEEE Trans. Inf. Theory, vol. 50, no. 12, pp. 3170-3182, Dec. 2004.
6. S. Verdú, Multiuser Detection. Cambridge, U.K.: Cambridge Univ. Press, 1998.
7. J. Lassing, E. G. Ström, T. Ottosson, and E. Agrell, "Computation of the exact bit error rate of coherent M-ary PSK with Gray code bit mapping," IEEE Trans. Commun., vol. 51, no. 11, pp. 1758-1760, Nov. 2003.
8. C. E. Shannon, "Probability of error for optimal codes in a Gaussian channel," Bell Syst. Tech. J., vol. 38, pp. 611-656, May 1959.
9. J. Lassing, E. G. Ström, T. Ottosson, and E. Agrell, "The exact symbol and bit error probabilities of coherent M-ary PSK," in Proc. IEEE Int. Symp. Information Theory, Yokohama, Japan, Jun./Jul. 2003, p. 11.
10. M. K. Simon and M. S. Alouini, Digital Communications Over Fading Channels. A Unified Approach to Performance Analysis. New York: Wiley, 2000.
11. K. Cho and D. Yoon, "On the general BER expression of one- and two-dimensional amplitude modulations," IEEE Trans. Commun., vol. 50, no. 7, pp. 1074-1080, Jul. 2002.
12. G. S. Bhat and C. D. Savage, "Balanced Gray codes," Electron. J. Comb., vol. 3, no. 1, 1996, paper R25.
13. D. E. Knuth, The Art of Computer Programming. Reading, MA: Addision-Wesley, 2005, vol. 4, fascicle 2.
14. C. Savage, "Comments by the second author on R25 of volume 3 (1), 1996," Electron. J. Comb., 2005.
15. J. Lassing, "On the Labeling of Signal Constellations," Ph.D. dissertation, Dept. Signals and Systems, Chalmers Univ. Technol., Göteborg, Sweden, Jan. 2005.
16. L.-L. Yang and L. Hanzo, "A recursive algorithm for the error probability evaluation of M-QAM," IEEE Commun. Lett., vol. 4, no. 10, pp. 304-306, Oct. 2000.