Correlation Functions for Storage Data and Nonreturn-to-Zero-Inverted Modulated Data of a High-Density Magnetic Recording Channel with Partial Erasure Effect

As magnetic recording densities grow, the nonlinear distortions, known as transition shift and partial erasure, arise and limit the performance of the detector. Despite that the transition shift can be compensated by a write current technique, the effect of partial erasure complicates the evaluation of the correlation functions for the storage data and the nonreturn-to-zero-inverted modulated data. In this article, we observe the dependence between the partial erasure effect and storage data, and derive the correlation functions for storage data and nonreturn-to-zero-inverted modulated data in a high density magnetic recording channel. The closed-form of the correlation functions are obtained, these results are applied to verify the timing function of the Muller & Mueller's phase detector in a partial response class IV channel via computer simulations.