Threshold-Based One-Bit Soft Forwarding for a Network Coded Multi-Source Single-Relay System

In this paper, we propose a threshold-based one-bit soft forwarding (TOB-SF) protocol for a multi-source relaying system with network coding, where two sources communicate with the destination with the help of a relay. Specifically in the TOB-SF protocol, the relay calculates the log-likelihood ratio (LLR) value of each network coded symbol, compares this LLR value with a pre-optimized threshold, and determines whether to transmit or keep silent. We are interested in optimizing the TOB-SF protocol in fading channels, and consider both the uncoded and low-density parity check coded systems. In the uncoded system, we first derive the bit error rate (BER) expressions at the destination, based on which, we derive the optimal threshold. Then we theoretically prove that the system can achieve the full diversity gain by using this threshold. Further, we optimize the power allocation at the relay to achieve a higher coding gain. In the coded system, we first optimize the LLR threshold. Then we develop a methodology to track the BER evolution at the destination by using Gaussian approximations. Based on the BER evolution, we further optimize the power allocation at the relay which minimizes the system BER. Simulation results show that the proposed TOB-SF protocol outperforms other conventional relaying protocols in terms of error performance.