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...nal transmission schemes [1]. Due to its remarkable potential, PNC has received considerable research attention in recent years, with a particular focus on two-way relay systems [2]. In a recent work =-=[3]-=-, Nazer and Gastpar extended PNC from two-way relay systems to general network scenarios. Their approach allows each relay to map an interfering signal into some linear combination of transmitted mess...

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...l compared to traditional transmission schemes [1]. Due to its remarkable potential, PNC has received considerable research attention in recent years, with a particular focus on two-way relay systems =-=[2]-=-. In a recent work [3], Nazer and Gastpar extended PNC from two-way relay systems to general network scenarios. Their approach allows each relay to map an interfering signal into some linear combinati...

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...e apply our framework for PNC to a Gaussian relay network and demonstrate its advantage over conventional PNC schemes. I. INTRODUCTION Physical-layer network coding (PNC) was proposed by Zhang et al. =-=[1]-=- to embrace interference in wireless networks. In a nutshell, each relay in the network maps an interfering signal into an XOR combination of simultaneously transmitted codewords. Surprisingly, this s...

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.... In fact, we set v` = 0 for ` = 1, . . . , L. In other words, we remove all the dithers. This is because the dither v` is just a tactic to simplify some proof, but is not actually needed in practice =-=[8]-=-. We apply the Tomlinson-Harashima shaping as suggested in [7], which is a special case of the shaping operations defined in Sec. III-C. As a result, our encoder E is identical to that used in [7]. 3)...

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...lattice shaping [7] may be used such that additional 1.53 dB of shaping gain can be potentially obtained. Another candidate of practical, high coding gain lattices is low density lattice codes (LDLC) =-=[9]-=-. It has recently been reported that a 100-dimensional LDLC 5 10 15 20 25 300 0.2 0.4 0.6 0.8 SNR (dB) N et w or ksTh ro ug hp uts(1 00 %) ←s8.3dB gain Signal Codes 9−QAM Fig. 3. Comparison of achieva...

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...8.3dB gain Signal Codes 9−QAM Fig. 3. Comparison of achievable throughput of PNC schemes using signal codes and uncoded QAM. using nested lattice shaping can be made only 3.6 dB from the sphere bound =-=[10]-=-. This makes it very attractive to be used in our framework. VI. CONCLUSION In this paper, we have followed the framework of Nazer and Gastpar [3] towards the design of PNC schemes via lattice partiti...

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...tices to produce a Z[i]-lattice Λ with sublattice Λ′, which is however very difficult to implement in practice. In contrast, we use existing practical, high coding gain lattices, such as signal codes =-=[7]-=-. Signal codes are a special class of Z[i]-lattices whose generator matrix is given by G k×(k+m) Λ = 1 f1 · · · fm 0 · · · 0 0 0 1 · · · fm−1 fm · · · 0 0 . . . . . . · · · ... ... · · · ... .....