LDPC code design for half-duplex decode-and-forward relaying

We propose LDPC code designs for the half-duplex relay channel. Our designs mimic 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 that can be decoded by belief propagation. The optimization of relay LDPC code profiles presents unique challenges, which are met by using the density evolution algorithm with additional constraints for relaying. To speed up our 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 within 0.4 dB of the achievable lower bound for decode-and-forward relaying.