Linear MMSE-Optimal Turbo Equalization Using Context Trees

TL;DR

This paper introduces a novel adaptive turbo equalizer using context trees to model nonlinear soft information dependence, achieving near-optimal performance with manageable complexity.

Contribution

It proposes a piecewise linear model based on context trees for adaptive turbo equalization, capturing nonlinear soft information effects efficiently.

Findings

Asymptotic performance matches the best piecewise linear equalizer.

MSE converges to the linear MMSE estimator as data length increases.

Computational complexity remains comparable to traditional linear equalizers.

Abstract

Formulations of the turbo equalization approach to iterative equalization and decoding vary greatly when channel knowledge is either partially or completely unknown. Maximum aposteriori probability (MAP) and minimum mean square error (MMSE) approaches leverage channel knowledge to make explicit use of soft information (priors over the transmitted data bits) in a manner that is distinctly nonlinear, appearing either in a trellis formulation (MAP) or inside an inverted matrix (MMSE). To date, nearly all adaptive turbo equalization methods either estimate the channel or use a direct adaptation equalizer in which estimates of the transmitted data are formed from an expressly linear function of the received data and soft information, with this latter formulation being most common. We study a class of direct adaptation turbo equalizers that are both adaptive and nonlinear functions of the soft information from the decoder. We introduce piecewise linear models based on context trees that can adaptively approximate the nonlinear dependence of the equalizer on the soft information such that it can choose both the partition regions as well as the locally linear equalizer coefficients in each region independently, with computational complexity that remains of the order of a traditional direct adaptive linear equalizer. This approach is guaranteed to asymptotically achieve the performance of the best piecewise linear equalizer and we quantify the MSE performance of the resulting algorithm and the convergence of its MSE to that of the linear minimum MSE estimator as the depth of the context tree and the data length increase.