In recent signal processing schemes of various high density digital magnetic storage systems, it needs to detect signal sequences with signal-dependent media noise and colored Gaussian noise, and so on. The more the areal recording density of storage systems gets increasingly, the more it seems increasingly difficult for any signal processing system to reduce or cancel the effects caused by noise and interference because total noise for which several different distributions are mixed occurs frequently in recording channels. High areal density recording needs not only the severe demand for signal detection, but also comes in predisposed to trend for recording by a large-sector size instead of a single sector which consists of 512 information 8-bit bytes. From this trend, nonbinary low-density parity check (LDPC) codes will be important for future recording systems. For these future problems, this paper proposes the signal estimation method based on statistical inference for such a finite mixture model with known number of noise components. Our signal detection scheme with vector (multivariate) autoregressive (AR) models for total noise is applied to maximum a posteriori probability sequence detection. Furthermore, burst error correcting nonbinary low-density generator matrix (LDGM) codes are used for an error correcting code which satisfies the specific run-length limited condition in the proposed signal processing system. We show that the scheme of these error correcting and signal detection methods are effective to estimate signal sequences degraded by a mixture of noise and improve the error rate performances with respect to the conventional scheme using binary LDGM codes and univariate AR models.