New multivariate noise model and data detection using the expectation maximization algorithm

A signal sequence detector in a high areal density recording channel is required to provide robust compensation against unexpected error events. Primarily, a number of error events are caused by media noise and nonlinear distortion. The same problem of signal sequence detection remains to be solved in a future magnetic recording system that comes in predisposed to trend for recording by large-sector size instead of existing single-sector one that consists of 512 information 8-bits bytes. For the above problem, this paper shows the signal estimation method based on statistical inference for such a finite mixture model with known number of degraded noise components. Our signal detection scheme with multivariate autoregressive models for total noise and the expectation maximization algorithm is applied to maximum a posteriori estimation for multivariate mixtures of noise. Furthermore, a non-binary low-density parity-check (LDPC) code is used for an error-correcting code that satisfies the specific run-length limited condition in the proposed system. It shows that the proposed error-correcting and signal detection methods are effective in estimating signal sequences degraded by media noise and in improving the error rate performances with respect to the conventional system using the binary LDPC code and univariate autoregressive model.