Nested block decodable runlength limited codes

Consider a (d₁,k₁)-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, the respective decoders are combined: 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