It has recently been recognized that the wireless networks represent a fertile ground for devising communication modes based on network coding. A particularly suitable application of the network coding arises for the two-way relay channels, where two nodes communicate with each other assisted by using a third, relay node. Such a scenario enables application of physical network coding, where the network coding is either done (a) jointly with the channel coding or (b) through physical combining of the communication flows over the multiple access channel. In this paper we first group the existing schemes for physical network coding into two generic schemes, termed 3-step and 2-step scheme, respectively. We investigate the conditions for maximization of the two-way rate for each individual scheme: (1) the Decode-and-Forward (DF) 3-step schemes (2) three different schemes with two steps: Amplify-and-Forward (AF), JDF and Denoise-and-Forward (DNF). While the DNF scheme has a potential to offer the best two-way rate, the most interesting result of the paper is that, for some SNR configurations of the source-relay links, JDF yields identical maximal two-way rate as the upper bound on the rate for DNF.

This paper introduces and analyzes relaying techniques that increase the achievable throughput in multi-hop wireless networks by applying network coding over bi-directional traffic flows. We term each such technique as Bi-directional Amplification of Throughput (BAT)-relaying. While network coding is normally performed by combining decoded packets, here we introduce a relaying method based on Amplify-and-Forward (AF), where the relay node utilizes the inherent combining of packets provided by simultaneous transmissions over a multiple access channel. Under low noise levels, AF BAT-relaying offers a superior throughput performance. The unconventionality of AF BAT relaying opens many possibilities for further research.Index Terms-Wireless network coding, wireless relay, bidirectional communication, amplify-and-forward, decode-andforward.

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In this paper, we propose a hybrid forwarding scheme for cooperative relaying in orthogonal frequency division multiplexing (OFDM) based networks. The proposed hybrid forwarding scheme changes the type of the forwarding scheme used by a relay terminal on a per sub-carrier basis. It adaptively decides to use either "Amplify and Forward (AF)" or "Decode and Forward (DF)" or "no relay" according to the instantaneous Signal to Noise Ratio (SNR) conditions between the source, relay and destination terminals. This decision is made based on analytically derived equations, which makes it possible to take into account all the link conditions in a relay network with low computational complexity. The bit error performance is presented for cooperative receive diversity with AF, with DF, with proposed hybrid forwarding scheme and for noncooperative transmission. Our results show that the proposed hybrid forwarding scheme significantly outperforms conventional cooperative relaying with AF and DF, and direct transmission schemes.