Mitigating error propagation in two-way relay channels with network coding

In relay networks, error propagation at the relay nodes degrades the performance of the system. To combat that effect, it has been suggested to implement a reliability threshold at the relay to control error propagation. Specifically, the relay calculates log-likelihood ratio (LLR) values for the bits sent from the source. These values are subjected to a threshold to selectively forward bits that are most reliable and discard bits that are less so, resulting in less errors propagating to the destination. We investigate the application of this technique to a network-coded two-way relay channel where the relay is assisting two sources simultaneously. We first consider network-coded systems without channel coding, and then consider network-channel coded systems. We examine two modes of thresholding, one based on the individual bits, and the other based on the combined bits. We provide the full analysis for the bit-error rate (BER) performance of both thresholding modes and optimize the thresholds accordingly. We demonstrate that the optimum thresholds based on both modes give similar performances and are far better than the case of no thresholding. We also consider the performance of the proposed thresholding techniques for network-channel coded systems. We present several numerical examples that illustrate the efficacy of employing thresholding at the relay nodes (for networks with and without channel coding).