Off-track bit error rate modeling

Abstract

Traditionally, channel generated bit error rates (BERs) at a certain signal to noise ratio (SNR) have been modeled by a Gaussian distribution function. This approach has been suitable for a peak detection channel as the analysis is performed in only one bit. In the case of a partial response maximum likelihood (PRML) channel, one data bit is determined by multiple code bits. There is a burst of errors detected if any one of the involved code bits gives an error. The chi-square distribution function, which is a sum of several independent Gaussian-squared distributions, is another method to model BERs of a PRML channel. Particularly, different PRML codes could be modeled by a chi-square distribution with different degrees of freedom. In this paper, the relationship of SNR to BER is generated using the chi-square method. The measured on-track rms SNR, read sensitivity function, and media magnetization are the input parameters. Old data and adjacent track interference are considered as random variables. At specified track pitch and read write misregistration, the probability distributions of these random variables are defined by the read sensitivity function and media magnetization. For a given interference, the off-track SNR is calculated. Error rate at a given interference is then derived from off-track SNR by using the SNR to BER relationship defined by a chi-square distribution. The BER at a specific track pitch and read–write misregistration is computed by integrating the error rate at a given interference with the probability distribution of the interference. This model describes the statistical nature of the BER in magnetoresistance head applications and provides very good correlation to experimental data.