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On the optimality of the binary reflected Gray code

Erik Agrell (Institutionen för signaler och system, Kommunikationssystem) ; Johan Lassing (Institutionen för signaler och system, Kommunikationssystem) ; Erik G. Ström (Institutionen för signaler och system, Kommunikationssystem) ; Tony Ottosson (Institutionen för signaler och system, Kommunikationssystem)
IEEE Transactions on Information Theory (0018-9448 ). Vol. 50 (2004), 12, p. 3170-3182.
[Artikel, refereegranskad vetenskaplig]

This paper concerns the problem of selecting a binary labeling for the signal constellation in M-PSK, M-PAM, and M-QAM communication systems. Gray labelings are discussed and the original work by Frank Gray is analyzed. As is noted, the number of distinct Gray labelings that result in different bit-error probability grows rapidly with increasing constellation size. By introducing a recursive Gray labeling construction method called expansion, the paper answers the natural question of what labeling, among all possible constellation labelings, will give the lowest possible average probability of bit errors for the considered constellations. Under certain assumptions on the channel, the answer is that the labeling proposed by Gray, the binary reflected Gray code, is the optimal labeling for all three constellations, which has, surprisingly, never been proved before.

Nyckelord: error-control, linear-mod



Denna post skapades 2006-09-12. Senast ändrad 2016-04-28.
CPL Pubid: 15207

 

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Institutioner (Chalmers)

Institutionen för signaler och system, Kommunikationssystem

Ämnesområden

Information Technology

Chalmers infrastruktur