An Extended Tanner Graph Approach to Decoding LDPC Codes over Decode-and-Forward Relay Channels

This paper reexamines the decoding problem for LDPC-coded relay channels applying the decode-and-forward protocol. The error-free decoding process at the relay is typically assumed by the conventional MRC based decoder at the destination. However, in practice, the unsuccessful decoding at the relay is unavoidable and the resultant error propagation may become a performance bottleneck. In this paper, we propose a new Tanner graph error representation to accurately characterize the relay decoding errors. Based on the proposed error representation, we derive a new message passing decoder which is implemented on an extended Tanner graph of the system. It is empirically verified that the new decoder can outperform existing decoders, and achieve promising performance improvement in the scenario of symmetric links. Moreover, the proposed error representation allows us to conduct density evolution to analyze the threshold performance of the new decoder for LDPC-coded relay channels.