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A crucial issue for bit patterned media recording is write-errors. This is an essential concern for media whose individual bits are represented by single switching units (dots) due to the insufficient writing field gradient at high areal densities. In this paper a statistical approach to clarify the write error rate for a system with a switching field distribution and a head field gradient is established using binomial distribution modeling. Then, two approaches to reduce the write error rate are presented. The first is multi-dot recording with a bit patterned structure, in which the error rate is reduced due to the averaging effect of recording on several dots. The switching field distribution can also be reduced if exchange coupling is introduced between the dots. The second possible approach is the combination of bit patterned media and temperature gradient recording. This effectively improves the writing gradient. The minimum bit length and achievable areal density is estimated taking into account the switching field distribution and writing field gradient.