In this work, micromagnetic simulations of writing and reading processes in a perpendicular system including a single pole head and recording media with soft underlayer (SUL) have been performed. The noise contribution from the recording layer increased with increasing grain size distribution of the recording layer but that from soft underlayer remained almost a constant at a given linear density. Details of the noise from the soft underlayer will be discussed. Also thermal decay over a long time scale of the recorded bits was investigated by the Langevin equation and the time-temperature scaling method. It was found that at the linear density of 1058 kfci narrower grain size distribution in the recording layer even in the same average grain size is very important in the point of thermal decay than expectation.