Abstract-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. Bidirectional or two-way communication between two nodes was first studied by Shannon himself in [1] . Nowadays the two-way communication where an additional node acting as a relay is supporting the exchange of information between the two nodes is attracting increasing attention. Some achievable rate regions for the two-way relay channel using different strategies at the relay, such as decode-and-forward, compress-and-forward and amplify-and-forward, have been analyzed in [2] . The capacity region of the so called broadcast two-way half-duplex relay channel, i.e. assuming that the communication takes places in two hops and the relay is decoding the received messages completely, was recently characterized in [3] . Network coding type techniques have been proposed by [4] , [5] , [6] (and others) in order to improve the transmission rate. While inferior to traditional routing at low signal-to-noise-ratios (SNR), it was shown in [7] that network coding achieves twice the rate of routing at high SNR. Similarly, in [8] the half-duplex two-way relay channel where the channel gains are all equal to one is investigated. It was shown that a combination of a decodeand-forward strategy using lattice codes and a joint decoding strategy is asymptotically optimal. Indeed, by using lattice codes it was shown in [9] that for some cases rates within less than one bit to the capacity can be achieved. So far, the main focus is however so far on the one-way relay channel, which was introduced by [10] and further investigated in [11] . In general, cooperative communication schemes are particulary important when reliable communication can not be guaranteed by using a conventional point-
REF comes up with a deterministic approach to approximate the capacity of the two-way relay channel.
Approximate capacity of the two-way relay channel: A deterministic approach
2008 46th Annual Allerton Conference on Communication, Control, and Computing
2008 46th Annual Allerton Conference on Communication, Control, and Computing
Computer Science Mathematics