Constrained equalizers and precoding for magnetic storage channels

The nonlinear write process of magnetic recording allows to write the symbols ±1 only. The magnetic channel is a differentiating channel. The locations of the transitions from +1 to -1 and vice versa in the input signal to the magnetic channel are important for the received waveform. This paper defines a noise enhancement constrained, finite dimensional equalizer. This equalizer trades some misequalization of the data signal for less noise enhancement after the equalizer. In a second step the misequalization is decreased by the precoding. Precoding shapes the communication signal before entering the communication channel. Since precoding works on the noise-free signal, there is no noise enhancement. Since precoding in magnetic channels is limited to shifting the positions of the transitions around, precoding does not allow for full equalization at the receiver. Therefore the equalizer in the receiver and the precoder are optimized. In order to find the optimal transition positions a linearized representation of the transition shift is produced. This representation leads to a constrained optimization problem