In a bi-directional relay channel, a pair of nodes wish to exc hange independent messages over a shared wireless half-duplex channel with the help of relays. Recent work has mostly considered information theoretic limits of the bi-directional relay channel with t wo terminal nodes (or end users) and one relay. In this work we consider bi-directional relaying with one base station, multiple terminal nodes and one relay, all of which operate in half-duplex modes. We assume that each terminal node communicates with the base-station in a bi-directional fashion through t he relay and do not place any restrictions on the channels between the users, relays and base-stations; t hat is, each node has a direct link with every other node. Our contributions are three-fold: 1) the introd uction of four new temporal protocols which fully exploit the two-way nature of the data and outperform simple routing or multi-hop communication schemes by carefully combining network coding, random binning and user cooperation which exploit over-heard and own-message side information, 2) derivations of inner and outer bounds on the capacity region of the discrete-memoryless multi-pair two-way network, and 3) a numerical evaluation of the obtained achievable rate regions and outer bounds in Gaussian noise which illustrate the performance of the proposed protocols compared to simpler schemes, to each other, to the outer bounds, which highlight the relative gains achieved by network coding, random binning and compress-and-forward-type cooperation between terminal nodes.
@math In @cite_42 multiple bi-directional pairs communicate over a shared relay in the absence of a direct link between end nodes. Under a linear deterministic channel interaction model, an interesting equation-forwarding strategy is shown to be capacity-achieving. This intuition is transfered to the two-pair full-duplex bi-directional Gaussian relay network in @cite_10 , where a carefully constructed superposition scheme of random and lattice codes was used to achieved rates within 2 bits of the outer cut-set bound.
@cite_42 @cite_10
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We study the capacity of the Gaussian two-pair fullduplex directional (or two-way) relay network with a single-relay supporting the communication of the pairs. This network is a generalization of the well known bidirectional relay channel, where we have only one pair of users. We propose a novel transmission technique which is based on a specific superposition of lattice codes and random Gaussian codes at the source nodes. The relay attempts to decode the Gaussian codewords and the superposition of the lattice codewords of each pair. Then it forwards this information to all users. We analyze the achievable rate of this scheme and show that for all channel gains it achieves to within 2 bits sec Hz per user of the cut-set upper bound on the capacity region of the two-pair bidirectional relay network. We study the capacity of the full-duplex bidirectional (or two-way) relay channel with two nodes and one relay. The channels in the forward direction are assumed to be different (in general) than the channels in the backward direction, i.e. channel reciprocity is not assumed. We use the recently proposed deterministic approach to capture the essence of the problem and to determine a good transmission and relay strategy for the Gaussian channel. Depending on the ratio of the individual channel gains, we propose to use either a simple amplify-and-forward or a particular superposition coding strategy at the relay. We analyze the achievable rate region and show that the scheme achieves to within 3 bits the cut-set bound for all values of channel gains. In this paper, a Gaussian two-way relay channel, where two source nodes exchange messages with each other through a relay, is considered. We assume that all nodes operate in full-duplex mode and there is no direct channel between the source nodes. We propose an achievable scheme composed of nested lattice codes for the uplink and structured binning for the downlink. Unlike conventional nested lattice codes, our codes utilize two different shaping lattices for source nodes based on a three-stage lattice partition chain, which is a key ingredient for producing the best gap-to-capacity results to date. Specifically, for all channel parameters, the achievable rate region of our scheme is within 1 2 bit from the capacity region for each user and its sum rate is within log3 2 bit from the sum capacity. We consider a state-dependent three-terminal full-duplex relay channel with the channel states noncausally available at only the source, that is, neither at the relay nor at the destination. This model has application to cooperation over certain wireless channels with asymmetric cognition capabilities and cognitive interference relay channels. We establish lower bounds on the channel capacity for both discrete memoryless (DM) and Gaussian cases. For the DM case, the coding scheme for the lower bound uses techniques of rate-splitting at the source, decode-and-forward (DF) relaying, and a Gel'fand-Pinsker-like binning scheme. In this coding scheme, the relay decodes only partially the information sent by the source. Due to the rate-splitting, this lower bound is better than the one obtained by assuming that the relay decodes all the information from the source, that is, full-DF. For the Gaussian case, we consider channel models in which each of the relay node and the destination node experiences on its link an additive Gaussian outside interference. We first focus on the case in which the links to the relay and to the destination are corrupted by the same interference; and then we focus on the case of independent interferences. We also discuss a model with correlated interferences. For each of the first two models, we establish a lower bound on the channel capacity. The coding schemes for the lower bounds use techniques of dirty paper coding or carbon copying onto dirty paper, interference reduction at the source and decode-and-forward relaying. The results reveal that, by opposition to carbon copying onto dirty paper and its root Costa's initial dirty paper coding (DPC), it may be beneficial in our setup that the informed source uses a part of its power to partially cancel the effect of the interference so that the uninformed relay benefits from this cancellation, and so the source benefits in turn.