On the Capacity of the Precision-Resolution System

Arguably, the most prominent constrained system in storage applications is the $(d,k)$-run-length limited (RLL) system, where every binary sequence obeys the constraint that every two adjacent 1's are separated by at least $d$ consecutive ${\bf 0}$'s and at most $k$ consecutive ${\bf 0}$'s, namely, runs of ${\bf 0}$'s are length limited. The motivation for the RLL constraint arises mainly from the physical limitations of the read and write …