The @math -user additive white Gaussian noise multiway relay channel is investigated, where @math users exchange information at the same rate through a single relay. A new achievable rate region, based on the functional-decode-forward coding strategy, is derived. For the case where there are three or more users, and all nodes transmit at the same power, the capacity is obtained. For the case where the relay power scales with the number of users, it is shown that both compress-forward and functional-decode-forward achieve rates within a constant number of bits of the capacity at all SNR levels; in addition, functional-decode-forward outperforms compress-forward and complete-decode-forward at high SNR levels.
The MWRC is an extension of the two-way relay channel (TWRC), i.e., @math . Since there is an embedded relay channel from user 1 to user 2 via the relay, and vice versa, coding strategies proposed for relay networks @cite_9 @cite_11 , i.e., complete-decode-forward, This coding strategy is commonly known as decode-forward. We modify the name to distinguish this coding strategy and the functional-decode-forward coding strategy to be discussed next. compress-forward, and amplify-forward, have been modified for the TWRC @cite_6 @cite_20 .
@cite_9 @cite_20 @cite_6 @cite_11
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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 @math with the same random coset is employed at two users, which directly maps the message sequences into coded PAM or QAM symbol sequences. The relay chooses appropriate network coding coefficients and computes the associated finite-field linear combinations of the two users' message sequences using an iterative belief propagation algorithm. For a symmetric Gaussian TWRC, we show that, by introducing the same random coset vector at the two users and a time-varying accumulator in the IRA code, the MC-PNC scheme exhibits symmetry and permutation-invariant properties for the soft information distribution of the network-coded message sequence (NCMS). We explore these properties in analyzing the convergence behavior of the scheme and optimizing the MC to approach the capacity limit of a TWRC. For a block fading TWRC, we present a new MC linear PNC scheme and an algorithm used at the relay for computing the NCMS. We demonstrate that our developed schemes achieve near-capacity performance in both Gaussian and Rayleigh fading TWRCs. For example, our designed codes over GF(7) and GF(3) with a code rate of 3 4 are within 1 and 1.2 dB of the TWRC capacity, respectively. Our method can be regarded as a practical embodiment of the notion of compute-and-forward with a good nested lattice code, and it can be applied to a wide range of network configurations. We study the application of convolutional codes to two-way relay networks (TWRNs) with physical-layer network coding (PNC). When a relay node decodes coded signals transmitted by two source nodes simultaneously, we show that the Viterbi algorithm (VA) can be used by approximating the maximum likelihood (ML) decoding for XORed messages as two-user decoding. In this setup, for given memory length constraint, the two source nodes can choose the same convolutional code that has the largest free distance in order to maximize the performance. Motivated from the fact that the relay node only needs to decode XORed messages, a low complexity decoding scheme is proposed using a reduced-state trellis. We show that the reduced-state decoding can achieve the same diversity gain as the full-state decoding for fading channels. We derive the capacity of the binary multi-way relay channel, in which multiple users exchange messages at a common rate through a relay. The capacity is achieved using a novel functional-decode-forward coding strategy. In the functional-decode-forward coding strategy, the relay decodes functions of the users' messages without needing to decode individual messages. The functions to be decoded by the relay are defined such that when the relay broadcasts the functions back to the users, every user is able to decode the messages of all other users. This paper investigates the iterative decoding for spectrally efficient two-way relay (TWR) communications in which two end nodes exchange information through a relay (R). With the use of physical-layer network coding (PNC), information exchange throughput can be significantly improved as only two orthogonal time slots (TS) are required to realize both the multiple access (MAC) and the broadcast (BC) transmissions. During the MAC stage, transmitted symbols from the end nodes are superimposed at R which decodes the exclusive-or (XOR) information of the two end nodes. However, with a high order modulation, symbol superposition will cause demapping ambiguity. This paper proposes a TWR communication system that employs the bit-interleaved coded modulation (BICM). The iterative decoding, namely, the BICM-ID, is introduced to dissolve the demapping ambiguity. With iterative decoding, the transmitted symbol pair probabilities can be better estimated so that the demapper can provide better coded bit information for the decoder. The proposed work generalizes the iterative demapping-decoding approach for TWR channels. Our simulation results demonstrate significant iterative decoding gains can be achieved with a tendency of approaching the XOR-decoding bound.