LDPC Code-Design for the Relay Channel

We propose LDPC code designs for the half-duplex relay channel. Our designs are derived from the information theoretic random coding scheme for decode-and-forward relaying. An important advantage of our scheme is that it is built entirely of single-user codes. The optimization of relay LDPC code profiles presents unique challenges, which are met by modifying the density evolution algorithm by introducing additional constraints for relaying. To speed up optimization, we use a Gaussian approximation of density evolution that converts the infinite dimensional code profile optimization into a simple linear programming problem. The thresholds of the discovered relay code profiles are a fraction of a dB from the achievable lower bound for decode-and-forward relaying.