THE TRADEOFF FUNCTION FOR A CLASS OF RLL(d, k)CONSTRAINTS

摘要

A reverse concatenation coding scheme for storage systems in which the information is encoded first by a modulation (constraint) code and then by a systematic error-correcting code is considered. In this scheme, the output of the modulation coding stage has certain positions left "unconstrained" in the sense that any way of filling them with bits results in a sequence that satisfies the constraint. These positions are then used to store the parity-check bits of the error-correcting code so that the result is a valid constrained sequence. The tradeoff function defines the maximum overall rate of the encoding scheme for a given density of unconstrained positions. This function is determined for two families of run length limited (RLL) constraints: RLL(d, ∞) and RLL(d, 2d + 2). For RLL(d, 2d+2), a curious dichotomy in the shape of the tradeoff function between different ranges of values of d is shown to exist.