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We provide achievable rate regions for two-way relay channels (TRC). At first, for a binary TRC, we show that the subspace-sharing of linear codes can achieve the capacity region. And, for a Gaussian TRC, we propose the subset-sharing of lattice codes. In some cases, the proposed lattice coding scheme can achieve within 1/2-bit the capacity and is asymptotically optimal at high signal-to-noise ratio (SNR) regimes.

Abstract-This paper considers a broadband cellular orthogonal frequency-division multiple-access (OFDMA) system with relay nodes operating in decode-and-forward and half-duplex mode. Two transmit resource allocation problems for sum-rate maximization are formulated for such a system. The first one is the optimization of subcarrier allocation with predetermined power assignment for each subcarrier, and the other is the joint optimization of power and subcarrier allocation. Since these problems can't be solved easily in direct forms, we make continuous relaxation and solve the dual problems using a subgradient method. Numerical results show that a remarkable increment in sum-rate is achieved, with the aid of relay nodes and sophisticated resource allocation, compared to a system without relay nodes.

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In this paper, a class of relay networks is considered. We assume that, at a node, outgoing channels to its neighbors are orthogonal, while incoming signals from neighbors can interfere with each other. We are interested in the multicast capacity of these networks. As a subclass, we first focus on Gaussian relay networks with interference and find an achievable rate using a lattice coding scheme. It is shown that there is a constant gap between our achievable rate and the information theoretic cut-set bound. This is similar to the recent result by Avestimehr, Diggavi, and Tse, who showed such an approximate characterization of the capacity of general Gaussian relay networks. However, our achievability uses a structured code instead of a random one. Using the same idea used in the Gaussian case, we also consider linear finite-field symmetric networks with interference and characterize the capacity using a linear coding scheme. Index TermsWireless networks, multicast capacity, lattice codes, structured codes, multiple-access networks, relay networks I. INTRODUCTION Characterizing the capacity of general relay networks has been of great interest for many years. In this paper, we confine our interest to the capacity of single source multicast relay networks, which is still an open problem. For instance, the capacity of single relay channels is still unknown except for some special cases [1]. However, if we confine the class of networks further, there are several cases in which the capacity is characterized.Recently, in [2], the multicast capacity of wireline networks was characterized. The capacity is given by the max-flow min-cut bound, and the key ingredient to achieve the bound is a new coding technique called network coding. Starting from this seminal work, many efforts have been made to incorporate wireless effects in the network model, such as broadcast, interference, and noise. In [3], the broadcast nature was incorporated into the network model by requiring each relay node to send the same signal on all outgoing channels, and the unicast capacity was determined. However, the model assumed that the network is deterministic (noiseless) and has no interference in reception at each node. In [4], the work was extended to multicast capacity. In [5], the interference nature was also incorporated, and an achievable multicast rate was computed. This achievable rate has a cut-set-like representation and meets the information theoretic cut-set bound [27] in some special cases. To incorporate the noise, erasure networks with broadcast or interference only were considered in [7], [8]. However, the network models in [7], [8] assumed that the side information on the location of all erasures in the network is provided to destination nodes. Noisy networks without side information at destination nodes were considered in [12] and [13] for finite-field additive noise and erasure cases, respectively.