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By taking advantage of the additional information provided by a transmitter precoder, semi-blind approaches are proposed for identification and equalization of the so-called LTI-ZMNL-LTI nonlinear channels, which consist of two linear time invariant (LTI) filters separated by a polynomial type zero memory nonlinearity (ZMNL). Identification of the linear subsystems relies on the output second order cyclostationary/stationary statistics, induced in the transmit data by non-redundant periodically time-varying and/or redundant block precoders. It is shown that identification of linear subsystems is robust to channel order overestimation errors, location of channel zeros, and color of additive noise. Assuming that the ZMNL is a one-to-one map, transmitter precoding allows also exact zero-forcing (ZF) linear equalization of LTI-ZMNL-LTI channels, without restrictions on the zeros of the linear subsystems and channel order overestimation errors.