On the optimality of the binary reflected gray code

IEEE Transactions on Information Theory

Volumn 50, Issue 12, 2004, Pages 3170-3182

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

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Average distance spectrum; Binary reflected Gray code; Constellation labeling; Phase shift keying (PSK); Pulse amplitude modulation (PAM); Quadrature amplitude modulation (QAM)

Indexed keywords

ERROR ANALYSIS; PHASE SHIFT KEYING; PROBABILITY; PULSE AMPLITUDE MODULATION; QUADRATURE AMPLITUDE MODULATION; RECURSIVE FUNCTIONS;

AVERAGE DISTANCE SPECTRUM; BINARY REFLECTED GRAY CODE; BIT ERROR PROBABILITY; CONSTELLATION LABELING;

BINARY CODES;

EID: 10644221284     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2004.838367     Document Type: Article

References (14)

1. J. G. Proakis, Digital Communications, 3rd ed. New York: McGraw-Hill, 1995.
2. F. Gray, "Pulse Code Communications," U. S. Patent 2632058, Mar. 1953.
3. P. J. Lee, "Computation of the bit error rate of coherent M-ary PSK with Gray code bit mapping," IEEE Trans. Commun., vol. COM-34, pp. 488-491, May 1986.
4. M. I. Irshid and I. S. Salous, "Bit error probability for coherent M ary PSK systems," IEEE Trans. Commun., vol. 39, pp. 349-352, Mar. 1991.
5. M. K. Simon, S. M. Hinedi, and W. C. Lindsey, Digital Communication Techniques. Englewood Cliffs, NJ: Prentice-Hall, 1994.
6. J. Lu, K. B. Letaief, J. C.-I. Chuang, and M. L. Liou, " M-PSK and M-QAM BER computation using signal-space concepts," IEEE Trans. Commun., vol. 47, pp. 181-184, Feb. 1999.
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, pp. 1758-1760, Nov. 2003.
8. M. K. Simon and M. S. Alouini, Digital Communications Over Fading Channels - A Unified Approach to Performance Analysis. New York: Wiley, 2000.
9. E. N. Gilbert, "Gray codes and paths on the n-cube," Bell Syst. Tech. J., vol. 37, pp. 815-826, May 1958.
10. J. E. Ludman, "Gray code generation for MPSK signals," IEEE Trans. Commun., vol. COM-29, pp. 1519-1522, Oct. 1981.
11. C. E. Sundberg, "Bit error probability properties of Gray-coded M.P.S.K signals," IEE Electron. Lett., vol. 11, no. 22, pp. 542-544, Oct. 1975.
12. R. D. Wesel, X. Liu, J. M. Cioffi, and C. Komninakis, "Constellation labeling for linear encoders," IEEE Trans. Inform. Theory, vol. 47, pp. 2417-2431, Sept. 2001.
13. J. Gross and J. Yellen, Graph Theory and its Applications. Boca Raton, FL: CRC, 1999.
14. K. Cho and D. Yoon, "On the general BER expression of one- and two-dimensional amplitude modulations," IEEE Trans. Commun., vol. 50, pp. 1074-1080, July 2002.