Improving capacity for physical network coding with lattice strategies in two‐way fading channels

In this study, the capacity problem in a two‐way fading channel is considered. The authors propose amplify‐and‐forward with lattice codes (AF&LC), exploiting a modulo operation at the relay. Without destroying the construct of codebook, the modulo operation reduces the power of the received signals, and thus achieves a larger power‐scaled gain than the amplified‐and‐forward with random codes (AF&RC). It is proved that AF&LC outperforms AF&RC in the high signal‐to‐noise ratio (SNR) regime by employing theoretical analyses. By simulating one‐dimension lattice codes, AF&LC achieves about 1.5 dB SNR gain over AF&RC with error probability 10 −2 . Compared with decode‐and‐forward with lattice codes (DF&LC) and fixed modulo‐and‐forward (FMF), AF&LC achieves larger rate region which is closer to upper bound in some scenarios. Moreover, AF&LC can work in fading two‐way channels without feedback schemes, which is easier to be implemented than DF&LC, FMF and compress‐and‐forward.