Bilayer LDPC Convolutional Codes for Half-Duplex Relay Channels

In this paper we present regular bilayer LDPC convolutional codes for half-duplex relay channels. For the binary erasure relay channel, we prove that the proposed code construction achieves the capacities for the source-relay link and the source-destination link provided that the channel conditions are known when designing the code. Meanwhile, this code enables the highest transmission rate with decode-and-forward relaying. In addition, its regular degree distributions can easily be computed from the channel parameters, which significantly simplifies the code optimization. Numerical results are provided for the codes with finite node degrees over binary erasure channels. We can observe that the gaps between the decoding thresholds and the Shannon limits are impressively small.