The binary reflected Gray code is optimal for M-PSK

Agrell, Erik,1965Chalmers tekniska högskola,Chalmers University of Technology (author)

This paper is concerned with the problem of selecting a binary labeling for the signal constellation in an M-PSK communication system. A good starting point is labelings having the Gray property, but this is not altogether enough, since 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 (not only Gray), that will give the lowest possible average probability of bit errors. Under certain assumptions on the channel, the answer is that the labeling originally proposed by Gray, the binary reflected Gray code, is the optimal labeling for M-PSK systems, which has, surprisingly, never been proved before.

Lassing, Johan,1973Chalmers tekniska högskola,Chalmers University of Technology(Swepub:cth)lassing (author)
Ström, Erik,1965Chalmers tekniska högskola,Chalmers University of Technology(Swepub:cth)estrom (author)
Ottosson Gadd, Tony,1969Chalmers tekniska högskola,Chalmers University of Technology(Swepub:cth)tonyo (author)
Chalmers tekniska högskola (creator_code:org_t)

In:Proc. IEEE International Symposium on Information Theory, Chicago, Illinois, USA, s. 164-0780382803

By the author/editor: Agrell, Erik, 19 ...; Lassing, Johan, ...; Ström, Erik, 196 ...; Ottosson Gadd, T ...

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