A Soft-Network-Coded Multilevel Forwarding Scheme for Multiple-Access Relay Systems

This paper proposes the novel technique of multilevel-threshold-based soft quantization (MLT-SQ) for a multiple-access relay system (MARS). The scheme is suitable for systems using binary phase-shift keying (BPSK) and network coding at the relay. In the proposed MLT-SQ protocol, the relay evaluates the reliabilities, which are expressed as log-likelihood ratios (LLRs), of the received signals from the two sources. It then computes the LLRs of the network-coded packet and quantizes these using a set of optimized multilevel thresholds, forwarding the resulting "quantized soft symbols" to the destination. We provide the derivation for the bit error rate (BER) at the destination, and based on this, we optimize the multilevel thresholds to minimize the BER. Simulation results are provided for the proposed MLT-SQ system, both without coding and for the case where low-density parity-check (LDPC) coding is employed. The proposed system achieves full diversity order. Compared with competing schemes, the performance of our system is superior in terms of BER when the same amount of channel state information (CSI) is exploited.