Cointegrated vector autoregressive models for multitrack systems in digital magnetic recording

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.