Effect of precoding on the convergence of turbo equalization for partial response channels

Abstract—The effect of the precoder on the convergence of turbo equalization for precoded partial response channels is studied. The idea is to consider the turbo decoding algorithm as a one-param-eter dynamical system and to study the effect of the precoder on the fixed points of the system. It is showed that precoding results in a loss in fidelity during the first iteration and that this loss de-pends on the precoder. Further, the rate at which the extrinsic in-formation increases with iterations is also dependent on the pre-coder. The net result of these two effects is used to explain several existing results in the literature about the performance of different precoders. A design criteria based on the convergence is then pro-posed, and the impact of precoding on the design of the outer code is then studied. Finally, the design of precoders in the presence of an error correcting code, such as a Reed–Solomon code, is studied. Index Terms—Convergence, density evolution, precoding, turbo equalization. I