On the optimality of the binary reflected Gray code
Journal article, 2004

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.

error-control

linear-mod

Author

Erik Agrell

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

Johan Lassing

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

Erik Ström

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

Tony Ottosson Gadd

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

IEEE Transactions on Information Theory

0018-9448 (ISSN)

Vol. 50 12 3170-3182

Subject Categories

Computer and Information Science

DOI

10.1109/TIT.2004.838367

More information

Latest update

3/29/2018