Capacity of M-ary multitrack RLL codes for storage channels

This paper introduces M-ary multitrack runlength limited (RLL) (d,k) constrained codes for data storage systems. We calculate the capacities and densities of the codes. We have derived a general form of the state transition matrix for M-ary n-track (d,k) codes. Using the largest eigenvalue of the transition matrix, we calculate the capacity and density. The capacity approaches to the limit with a small k constraint compared to single-track codes. One can design some practical M-ary multitrack codes applying the same algorithms for single-track codes.