Nested block decodable runlength-limited codes

Abstract

Consider a (d 1 ; k 1)-RLL constraint that is contained in a (d 2 ; k 2)-RLL constraint, where k 1 2d 1 and d 2 > 0, and x a codeword length q > k 2. It is shown that whenever there exist block decodable encoders with codeword length q for those two constraints, there exist such encoders where one is a subgraph of the other; furthermore, both encoders can be decoded by essentially the same decoder. Speci cally, a (d 1 ; k 1)-RLL constrained word is decoded by rst using a block decoder of the (d 2 ; k 2)-RLL encoder, and then applying a certain function to the output of that decoder.