Nested block decodable runlength-limited codes

Consider a (d(1), k(1))-runlength-limited (RLL) constraint that is contained in a (d(2), k(2))-RLL constraint, where k(1) greater than or equal to 2d(1) and d(2) > 0, and fix 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, Specifically, a (d(1), k(1))-RLL constrained word is decoded by first using a block decoder of the (d(2), k(2))-RLL encoder, and then applying a certain function to the output of that decoder.