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As a promising technology, non-orthogonal multiple access (NOMA) enhances spectral efficiency and system capacity by allocating the same resource to multiple users. Network coding (NC) has the advantages of compressing data and high spectral efficiency, and it plays a crucial role in two-way relay networks. However, conventional two-way relay networks suffer from throughput limitations due to the use of OMA scheme. In this paper, we utilize a hybrid concept to design a two-way relaying system (namely Hybrid-TWRS) which combines NOMA and NC. Furthermore, we investigate the size-mismatch problem caused by asymmetric channel in the NOMA scheme and propose a bit-match scheme and a symbol-match scheme based on the Hybrid-TWRS. Theoretical derivation and numerical results demonstrate that the proposed method distinctly outperforms both (i) traditional two-way relaying system with OMA in …