Optimized markers for balancing runlength-limited sequences in optical recording

A well-known method for balancing binary sequences, in the sense of forcing them to have as many zeroes as ones, was proposed by Knuth. It is based on the inversion of all bits beyond a certain balancing index, and communicating this index via a prefix. This principle has also been applied to balance runlength-limited (RLL) sequences. Another Knuth-based approach exploits the insertion of a marker in the RLL sequence causing a deliberate runlength violation at the position of the balancing index. This marker method has an advantage over the prefix method, since its redundancy does not grow with the length of the source blocks. In this paper, the markers are optimized with respect to their length and the severeness of the runlength violation, for possible application in future (optical) recording systems.