Closed-form timing function for 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. In this article, the closed-form timing function of the Muller and Mueller’s phase detector is derived in the presence of the partial erasure under the assumption that the transition shift has been precompensated. The derived timing function is a weighted combination of two odd functions. One of these two functions is identical to that of a magnetic recording channel in the absence of the nonlinear distortions, and the other is itself a suitable candidate for a timing function. In addition, the weighting coefficients are functions of the reduction parameters. The timing function in the presence of the partial erasure is thus a suitable timing function. The timing functions for both the partial response class IV (PR4) and the extended partial response class IV (EPR4) are explicitly derived, and computer simulations are given to verify the derived results. The closed-form timing function for the nonlinear magnetic recording channel is obtained and discussed; in summary, the slope of the timing function at the origin roughly decreases as the partial erasure effect is prominent.