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This paper studies the transceiver design of the Gaussian two-pair two-way relay channel (TWRC), where two pairs of users exchange information through a common relay in a pairwise manner. Our main contribution is to show that the capacity of the Gaussian two-pair TWRC is achievable to within $\frac{1}{ 2}$ bit for arbitrary channel conditions. For the outer bound, we derive a genie-aided bound of the Gaussian two-pair TWRC, which is tighter than the cut-set bound. For the inner bound, we develop a hybrid coding scheme involving Gaussian random coding, nested lattice coding, superposition coding, and network-coded decoding. We further present a message-reassembling strategy to decouple the coding design for the user-to-relay and relay-to-user links, so as to provide flexibility to fully exploit the channel randomness. We show that judicious power allocation at the users and at the relay is necessary to approach the channel capacity under various channel conditions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a generalized channel decoding scheme for nonbinary physical-layer network coding (CD-NC) in two-way relay channels (TWRCs), where two source nodes A and B exchange their nonbinary symbols via a relay. The two sources use the same nonbinary low-density parity-check (LDPC) channel code over the integer ring $\mathbb {Z}_M$ and $M$ -pulse-amplitude modulation, respectively. The existing channel decoding schemes for nonbinary network coding suffer severe rate loss compared with the cut-set bound of TWRC, especially in the low-to-medium signal-to-noise ratio regime. The proposed CD-NC can decrease the rate loss. Our contributions are as follows: 1) We develop a generalized nonbinary sum product algorithm (G-SPA) for CD-NC according to the principle of virtual encoding of the superimposed symbols. Simulation results show that our CD-NC can achieve significant performance gains over the conventional nonbinary network coding for both additive white Gaussian noise and fading channels; and 2) We exploit two-dimensional fast-Fourier-transform-based belief propagation (2-D-FFT-BP) and extended min-sum (EMS) decoding algorithms to reduce the decoding complexity of G-SPA. Simulation results show that the 2-D-FFT-BP has the same performance as G-SPA, while EMS can greatly reduce the decoding complexity of G-SPA at the cost of slight performance degradation. [ABSTRACT FROM AUTHOR]

This paper studies and analyzes a multi-pair MIMO two-way relay (TWR) system from a principal-angle perspective. In this system, users are grouped into pairs and two users in each pair exchange information through a common relay. The transmission scheme consists of two phases. In the uplink phase, the relay’s receive signal space is divided into two subspaces for each pair: in one subspace, the signals of the two users are near-parallel, and physical-layer network coding (PNC) decoding is applied to retrieve network-coded messages; in the other subspace, the two user signals are near-orthogonal, and complete decoding (CD) is applied to retrieve individual user messages. In the downlink phase, the relay’s transmit signal space is split into orthogonal subspaces for each pair, and in each subspace a common message is broadcasted to the two users. Our main contribution is to establish a critical link between the transmission scheme and the concept of principal angle in linear algebra. In particular, principal angle quantizes the degree of orthogonality between the user signals and helps determining how to partition the relay’s receive signal space into PNC decoding subspace and CD decoding subspace. Building on that, we discuss the optimal design of user/relay precoders for both uplink and downlink phases to maximize the asymptotic sum-rate of the proposed scheme at high signal-to-noise ratio (SNR). The analysis and numerical results indicate that our scheme performs close to the cut-set outer bound and significantly outperforms the existing schemes in the literature. [ABSTRACT FROM AUTHOR]