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The authors study the design of network codes for M-source N-relay (M-N) wireless networks over slow-fading channels. Binary Frame-wise Network Coding (BFNC) based on cyclic-shifting matrices is developed to achieve full diversity and good coding gain. They develop a criterion in the context of BFNC that if satisfied guarantees to achieve full diversity gain. Based on this criterion, they propose an algorithm to design low-complexity encoders for a BFNC scheme by exploiting quasi-cyclic Low-Density Parity-Check (LDPC) code structures. They also design practical decoders based on the belief propagation decoding principle with a focus on large block lengths.
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