Joint multilevel RLL and error correction coding

Runlength-limited (RLL) codes, also known as (d,k) RLL codes, are used in digital magnetic recording and have potential use in soliton optical communication. We show how our approach to RLL coding can naturally incorporate multilevel error correction coding. It allows us not only to correct shift errors but also insertions and deletions of zeros. The main method for achieving this is to use Lee-metric codes. The component codes of the multilevel block code are chosen such that this code has a large minimum Lee distance and such that the (d,k) RLL code combined with the error correction multilevel code provides the highest possible rate. We emphasize that multilevel (d,k) RLL coding combined with multilevel block coding for error correction is well suited to multistage decoding. We also show that for an appropriate choice of the normalised thresholds of these parallel codes, the rate of the corresponding (d,k) RLL code converges to the capacity of the (d,k) constraint, as the dimension of each of the parallel codes goes to infinity.