By introducing gain/loss perturbation into periodic refractive index modulation, the unified coupled-mode equations and their close-form analytical solutions of complex long-period-grating-assisted-coupler (LPGAC) are deduced. Characteristics of power coupling are investigated and results show that unidirectional nonreciprocal signal transferring can be achieved by matching gain/loss with the refractive index modulation. Utilizing the feature of complex LPGAC, a novel optical signal buffer is proposed and its structure is examined in detail.