On the Use of Averaging to Estimate the Dibit Response

In the magnetics literature, the dibit response is typically estimated assuming knowledge of the written bit sequence and noiseless readback signal. However, magnetic recording systems suffer from various noise sources, and the readback signals are noisy. One way to obtain an estimate of the noiseless readback signal from noisy measurements is via spatial and temporal averaging. In this paper, transition position jitter and additive noise sources are considered in the readback signal. Using this model, we show that in the asymptotic regime of an infinite number of track locations and re-reads, the estimate formed via averaging has a bias. The effect of spatial and temporal averaging on the variance of the estimate is quantified without assuming an explicit distribution for the transition jitter and additive noise.