Nested block decodable runlength-limited codes

Consider a (d₁, k₁)-runlength-limited (RLL) constraint that is contained in a (d₂, k₂)-RLL constraint, where k₁⩾2d₁ and d₂>0, and fix a codeword length q>k₂. 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 (d₁, k₁ )-RLL constrained word is decoded by first using a block decoder of the (d₂, k₂)-RLL encoder, and then applying a certain function to the output of that decoder