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This paper proposes an improved receiver for the Tomlinson-Harashima precoder (THP). In this paper we demonstrate that most of the capacity loss associated with conventional THP is due to the suboptimal receiver, which is a simple modulo operation. We then demonstrate how this loss can can be avoided with the optimization of the receiver. In the suboptimal receiver the modulo operation ignores the dependency between the implicitly added sequence of symbols removed by it. We then implement a THP with quantized outputs. The quantized outputs enable to implement a Maximum A-Posteriori Probability (MAP) receiver that exploits the dependency between the received symbols. The MAP receiver is named Enhanced MODulo operation (EMOD), and operates as an inner decoder within an iterative scheme, either with outer Low Density Parity Check (LDPC) code or outer Turbo Code. Simulation results show considerable gains relative to coded conventional THP, and also relative to the Turbo-Equalizer (TE) (which does not use a precoder in the transmitter).