The combined constraints for perpendicular recording channels

The maximum transition run (MTR) and running digital sum (RDS) constraints have a wide variety of applications in magnetic recording systems. The property of an MTR constraint is to eliminate long runs of transitions so that certain common error events can be eliminated. The property of an RDS constraint is desirable for achieving high-density recording for recording channels exhibiting low frequency components, such as perpendicular recording channels. It is very common to implement more than one constraint in practice to achieve the desired effect in the recording channel. In this paper, the labeled graph representations of RDS and MTR [or the time-varying MTR (TMTR)] constraints are combined to obtain new classes of constraints: RDS-MTR and RDS-TMTR constraints. The capacity of a combined constraint is slightly lower than that of its constituent constraints. The spectra of RDS-MTR and RDS-TMTR constraints show the suppression of low frequency contents compared to the conventional MTR and TMTR constraints. A method for designing block codes is proposed to implement the properties of RDS, MTR (or TMTR), the run-length-limited (RLL) (0,k), and twin constraints. The cardinalities of block codes are maximized over various situations of codeword boundaries. The code design methodology is demonstrated via a rate 100/108 RDS-TMTR block code based on a rate 20/21 RDS-TMTR mother code.