Rate-Compatible Protograph-based LDPC Codes for Inter-Symbol Interference Channels

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.