Optimization and implementation of an equalized maximum likelihood receiver for a simple partial erasure model

Abstract

In a high-density magnetic recording channel, nonlinear effects such as transition shift and partial erasure arise, and these effects limit the detector performance. The transition shift can be precompensated by using an appropriate write current; however, partial erasure still degrades the detector performance. To mitigate this problem, the partial response maximum likelihood (PRML) receiver with a specific target response is widely used; it has acceptable performance for a reasonable realization complexity. Furthermore, the equalized maximum likelihood (EML) receiver is proposed, and its performance is improved because of the optimized target response. However, the conventional design for optimization often ignores nonlinear effects or minimizes the cost function in the sense of least-squared error because of lacking a closed-form expressions of the correlation functions. Herein, we apply the closed-form correlation functions for a simple partial erasure model (SPEM) to jointly optimize the coefficients of the partial equalizer and the target response to minimize the mean squared error (MSE) between the outputs of the partial equalizer and the target response. The corresponding Viterbi decoder (VD) with a nonlinear trellis diagram is realized. Computer simulations indicate that the EML receiver yields a smaller bit error rate (BER); in fact, it outperforms the conventional PRML receiver by around 1.5 dB when the BER is lower than 10 − 4 .