Layered SEMS Decoding for Non-Binary LDPC-Coded PNC Systems

In this letter, a layered scaled extended min-sum (LSEMS) algorithm is proposed to decode non-binary low-density parity-check (LDPC) codes in physical-layer network coding (PNC) systems. The proposed LSEMS algorithm is developed for the joint channel decoding and physical-layer network coding (JCNC) over wireless fading channels. It proposes a sequential update of check nodes to decode the exclusive ORed (XORed) codewords that are generated by the non-binary LDPC codes. The LSEMS algorithm achieves almost the same decoding complexity as the scaled extended min-sum (SEMS) algorithm, while it benefits from much less complexity than the reliability-based layered BP (RLBP) algorithm. Simulation results show that the LSEMS algorithm outperforms the conventional SEMS algorithm by about 0.5 dB in non-binary LDPC-coded PNC for both q-level pulse amplitude modulation (q-PAM) and q-ary phase shift keying (q-PSK) modulations.