Optimal precompensation in high density magnetic recording

Abstract

In high-density magnetic recording, the readback signal is corrupted by signal-dependent nonlinearities. Possibly, the best known method is to precompensate for them when writing bits. While there exist many precompensation schemes in the literature, the optimal scheme is unknown. In this work, we seek such an optimal solution. We intitiate our study with a simple optimality criterion, namely the mean-square error (MSE) of the nonlinear signal with a desired linear one. We start off by proposing a dynamic programming approach, which requires known nonlinear channel characteristics. We study various dynamic programming techniques that apply to our problem. We find the optimal solution to be complicated, and go on to propose a suboptimal approximation. In practice, the nonlinear channel characteristics are typically unknown, and we study other dynamic programming based methods which do not require this said knowledge. Finally, we perform computer simulations, and point out current limitations of our methods.