Signal to noise ratio scaling and density limit estimates in longitudinal magnetic recording

A simplified general expression is given for SNR for digital magnetic recording for transition noise dominant systems. High density media are assumed in which the transition parameter scales with the in-plane grain diameter. At a fixed normalized code density, the SNR varies as the square of the bit spacing times the read track width divided by the grain diameter cubed. This scaling law is shown to be quite general and useful for error rate analysis. Density optimization argues for track width narrowing rather than bit length reduction, limited by edge track considerations. Utilization of Arrhenius thermal signal decay yields limiting density estimates, neglecting electronics noise, in the range 50-100 Gbit/in² increasing with an increase in medium thickness/grain diameter ratio