Finite-word-length and nonrecursive implementation of Tomlinson-Harashima precoding

In this paper finite-word-length implementation of Tomlinson-Harashima precoding is considered. At first, the quantization errors of additions and multiplications performed in two's complement representation are reviewed. Then, quantization effects at the precoder are investigated in two steps: on the one hand, finite-word-length restriction on the precoder coefficients is studied, and on the other hand, quantization of data at precoder is regarded. The effect of quantization noise taking effect at the decoder input is described analytically. Examples and simulation results demonstrate the validity of these expressions. Additionally, an alternative, nonrecursive structure of Tomlinson-Harashima precoding is presented, which is implementable without any quantization noise. Finally, the application of both structures to DC-free channels is discussed.