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We propose and design a practical modulation-coded (MC) physical-layer network coding (PNC) scheme to approach the capacity limits of Gaussian and fading two-way relay channels (TWRCs). In the proposed scheme, an irregular repeat–accumulate (IRA) MC over $\textrm{GF}(q)$ with the same random coset is employed at two users, which directly maps the message sequences into coded PAM or QAM symbol sequences...
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