Nonlinear turbo equalization using context trees

In this paper, we study adaptive nonlinear turbo equalization to model the nonlinear dependency of a linear minimum mean square error (MMSE) equalizer on soft information from the decoder. To accomplish this, we introduce piecewise linear models based on context trees that can adaptively choose both the partition regions as well as the equalizer coefficients in each region independently, with the computational complexity of a single adaptive linear equalizer. This approach is guaranteed to asymptotically achieve the performance of the best piecewise linear equalizer that can choose both its regions as well as its filter parameters based on observing the whole data sequence in advance.