Maximum a posteriori estimation using ARCH models and burst error correcting array codes for burst-erasure recording channels

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.