A study on the implications of grain density distribution over the granular media model for TDMR

Two dimensional magnetic recording (TDMR) technology aims at achieving recording densities as high as 10 Tb/in² with the current interest in achieving >1 Tb/in². In TDMR, the size of a bit is reduced to the order of the size of magnetic grains. The effects of this are two-fold: a) increased interference in cross-track as well as down-track directions and b) ultra high jitter noise due to irregular grain positions. Channel models that include the grain distributions on the medium give a more accurate jitter noise characteristics than the first order linear approximations of the jitter noise. Signal detection for 2D-ISI channels is well known to be NP-hard. JTED algorithm, proposed in [3], is proved to iteratively achieve maximum aposterior (MAP) performance. Partial response maximum likelihood (PRML) detection is a well known technique for reducing signal detection complexity by using a linear equalizer before maximum likelihood (ML) detection. The linear equalizer allows partial ISI as seen at the input of the ML detector. At high areal densities, the jitter noise is the dominant component of the noise observed in the read back signal. Noise predictive maximum likelihood (NPML) detection improves upon the PRML detection by decorrelating the noise. In this paper, we study the effects of grain density (average number of grains per channel bit) and jitter noise using a low complexity 2D NPML detector recently proposed in [2] over the granular media model. By using correlation properties of the jitter noise, we could achieve >1 .5dB gain in SNR at a chosen grain density. Gains in channel bit densities (CBD) of up to 10% are also observed.