  This letter produces a family of rate-compatible protograph-based LDPC codes
approaching the independent and uniformly distributed (i.u.d.) capacity of
inter-symbol interference (ISI) channels. This problem is highly nontrivial due
to the joint design of structured (protograph-based) LDPC codes and the state
structure of ISI channels. We describe a method to design nested high-rate
protograph codes by adding variable nodes to the protograph of a lower rate
code. We then design a family of rate-compatible protograph codes using the
extension method. The resulting protograph codes have iterative decoding
thresholds close to the i.u.d. capacity. Our results are supported by numerical
simulations.
