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In a high-density magnetic recording channel, non-linear effects such as transition shift and partial erasure arise, and these effects limit detector performance. The transition shift can be precompensated by using an appropriate write current; however, partial erasure still degrades detector performance. In this study, the authors obtained the correlation functions of the stored data in the presence of partial erasure under the assumption that the transition shift has been precompensated. The correlation functions are applied in designing a minimum mean squared error equaliser for both the linear partial response and the non-linear partial response, and the corresponding partial response maximum likelihood (PRML) sequence detector, realised by the Viterbi decoder, is also examined. Computer simulations indicate that the mean squared error of the proposed equaliser can be improved and the bit error rate of the PRML sequence detector is also reduced as compared with the conventional one in the presence of partial erasure.