# How does BER performance depend on gray or natural binary?

I read that BER performance would be improved if Gray code is used in 16 QAM rather than natural binary coding. I think that it should not depend on the coding used. 16 QAM simply assigns to each of the 16 combinations of 4 bits, one particular sinusoidal signal with fixed frequency but different amplitude and phase. When this is transmitted and detected properly at the receiver we can get the 4 bit group transmitted. The error depends on the detection capability and the noise in the system. Any arbitrary assignment between the signals and the group of 4 bits should give the same BER as long as the detection performance is the same. Where am I going wrong?