In this paper, one of new maximum a posteriori (MAP) estimation methods is introduced for signal detection in a magnetic recording channel with burst erasures. In signal detection for the recoded data sequence on the recording media, it needs to consider that there exists a fluctuation range for the variance of media noise according to the specific recorded bit patterns. Most of conventional signal estimation techniques assume to use the constant and invariant variance of media noise within the specified data fields. But, the readback signals happen to be faded in consequence of media defects or thermal asperities in several time intervals. These physical distortions cause burst erasures in magnetic recording. From a view point of signal estimation problem, the estimation technique is based on nonstationary time series analysis for a stochastic process is effective for attenuated signal sequences caused by burst errors. In this paper, it is shown that the estimation problem for burst erasures is solved by maximum a posteriori estimation with an autoregressive conditional heteroscedastic (ARCH) process (model) and burst error correcting non-binary array codes for 4K block sectors. For the given non-binary array coding system, the error rate performance using proposed channel predicting MAP estimation method is superior to the performance using the conventional MAP estimation.

A number of multitrack recording systems with multiple-head arrays have been developed for the future high density magnetic recoding systems. In this recording system, the signal detection scheme is needed to estimate the received sequence with media noise, intersymbol interference and inter-track interference. From the recent trend of high density magnetic recording, it is indispensable for any signal processing scheme to mitigate or reduce the effect of media noise such as mixture signal-dependent transition noise and colored Gaussian thermal noise. This paper proposes the statistical inference using the cointegrated process based on vector autoregressive (VAR) models for such a finite mixture of known number of noise and interference components. Our signal detection scheme is applied to maximum a posteriori (MAP) detection with the cointegrated VAR processes. Furthermore, a high rate low-density parity-check (LDPC) code is used for the error correcting code which satisfies the specific run-length limited condition in the proposed multitrack recording system. We show that the proposed multi-track system of error correcting and signal detection scheme is effective to estimate degraded signal sequences and improve the error rate performances with respect to the conventional multitrack system which has the LDPC coding scheme and MAP detector employing the BCJR algorithm.