Low complexity network error correction based on nonbinary LDPC codes over matrix channels

This paper presents a low-complexity network error correction (NEC) code for wireless relay networks (WRN), where the non-binary low density parity check (LDPC) code is jointly designed with a random network code. We give different transmission schemes under which the decoding complexity of the network code can be much reduced by dividing the transfer matrix into smaller decodable sub-matrices. We also propose a complexity optimization algorithm to the non-binary LDPC code based on an upper bound of message error probability. Simulations show that the complexity optimized codes can outperform the threshold optimized codes in higher SNR regime.