Coding Gain - Bandwidth-limited Regime

In the bandwidth-limited regime (, i.e. the domain of non-binary signaling), the effective coding gain of a signal set at a given target error rate is defined as the difference in dB between the required to achieve the target with and the required to achieve the target with M-PAM or (M×M)-QAM (i.e. no coding). The nominal coding gain is defined as

This definition is normalized so that for M-PAM or (M×M)-QAM. The UBE becomes

where is the average number of nearest neighbors per two dimensions.