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 technologies in magnetic and optical storage systems. We revisit the rationale for the RLL system, reevaluate its relationship to the constraints of the physical media and propose a new framework that we call the Precision-Resolution (PR) system. Specifically, in the PR system there is a separation between the encoder constraints (which relate to the precision of writing information into the physical media) and the decoder constraints (which relate to its resolution, namely, the ability to distinguish between two different signals received by reading the physical media). We compute the capacity of a general PR system and compare it to the traditional RLL system.