A hybrid EF/DF protocol with rateless coded network code for two-way relay channel

In this paper, we investigate a rateless code design for a two-way relay channel (TWRC) where a network coding operation is employed at the relay. Rateless codes are used at both two users and the relay nodes as it can cope with various channel conditions. We propose a hybrid estimate and forward (EF)/decode and forward (DF) protocol with rateless codes for the TWRC. In the proposed scheme, the relay uses a joint belief propagation (BP) decoding process to decode the messages of two users. Depending on whether the relay recovers both users´ messages, only one user´s message or no users´ messages, the relay will generate three different types of signals, namely, network code (NC), soft network code (SNC) or soft physical-layer network code (SPNC), respectively. We design the degree distribution of the rateless codes for the three nodes of the TWRC, to make it suitable not only for decoding at two users at high SNR, but also for decoding at the relay at low SNR. We show that the proposed hybrid EF/DF protocol with the designed rateless codes outperforms other schemes significantly in terms of bit error rate (BER) performance.