Abstract
A generalization of the run-length-limited (RLL) code has been studied for multilevel recording systems where more than one kind of mark is used to record information. The run-length constraints have been generalized to include the spacing in addition to the minimum and maximum run-length constraints. The ratic of the minimum run length to the detection window has become arbitrarily adjustable. This provides the flexibility to design the modulation codes which match with the resolution and jitter characteristics of the recording system. The method of the calculus of variations has been applied to the asymptotic behavior of the amount of information stored in a sufficiently long code sequence. The formulation has been obtained for the code characteristics, which include the maximum density ratio, the maximum amount of information contained in the detection window, the average rate of appearance for individual run lengths, etc. The effect of the multilevel recording scheme depends on the number of the levels, the minimum and maximum run length, and the spacing. The optimum selection of these parameters can realize a large recording capacity close to the intrinsic potential of the multilevel recording system.
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