## 2 Two-Way Relaying System Model and Related Works
In [21], [PERSON] and [PERSON], the inventors of PNC, further develop their PNC idea. The authors integrate network coding and channel coding through the appropriate application of a channel code, called the Repeat Accumulate (RA) code [22], at the two end nodes. Thanks to this solution, based on the samples received by the relay, the modulo-2 addition of both received source packets can be calculated efficiently. The authors assume that the relay does not need to detect individual packets from both end nodes, but it is only interested in decoding its modulo-2 sum. The authors redesign the belief propagation decoding algorithm of the RA code to suit the needs of the PNC multiple access channel. However, one can notice that the simulation system model used in experimental investigations is oversimplified, and confirmation of usability of the proposed solutions would require a much more sophisticated model. In [23], convolutional codes in two-way relay networks with rate diverse network coding are considered. In this arrangement, for a given memory length constraint, two source nodes can adopt convolutional codes of different lengths and use a reduced-state trellis to reduce decoding complexity. The authors claim that the proposed approach can improve system throughput significantly. It offers increased reliability and reduces the complexity of decoding of the applied convolutional code. However, one can notice that the application of the reduced-state trellis in the decoding algorithm results in performance deterioration. Codes other than convolutional ones have also been studied for application in PNC. In [24], the authors compare the performance of a two-way relaying network employing PNC with three types of error-correcting codes used at the source and destination nodes. These are iteratively decodable low-density parity check codes (LDPC), turbo codes, and bit-interleaved coded modulation with iterative decoding (BICM-ID). The research reported in [24] indicates that, when applied in PNC, the performance of LDPC codes is degraded more than in the case of other codes due to the sum-product decoding algorithm which is less robust to unreliable symbols broadcast from the relay. However, it is worth stressing that other factors can also influence channel code selection, such as introduced decoding delay, simplicity of decoder implementation, etc. The authors assumed a very idealized transmission model analogous to that used in [14]. The signals received by the relay are an ideal sum of constellation symbols and additive AWGN noise. Moreover, the relay performs hard-decision decoding, determining the signal constellation of modulo-2 sum bits carried by both signals reaching the relay. We must admit that the reference system model reported in our paper in Section 3.1 is much more realistic, taking into account possible different attenuations and phase shifts of the signals arriving to the relay. Another proposal associated with iteratively decodable codes is shown in [25]. In this paper, a novel joint channel and physical layer network decoding scheme for a two-way relaying communication system is presented. The proposed decoding scheme can be viewed as a serial concatenated decoding scheme with the source codes, not necessarily the same, treated as the outer codes, and the physical network coding as the inner code. The drawback of the authors' approach is similar to that in [24]. Namely, they assume an ideal PNC scheme, in which the signal received by the relay is a sum of equally attenuated and co-phased BPSK signals transmitted by both end nodes. This assumption is not realistic. Again, our model shown in Section 3.1 seems to be much better. Bandwidth-efficient coded modulation schemes for PNC with high-order modulations are also a topic of interest. In [26], several soft-decision iterative decoding schemes for PNCoperated with coded modulations and bit-interleaved coded modulations are presented. The authors consider network coding-based channel decoding and multi-user complete decoding for PNC.