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This paper considers relaying techniques that increase the achievable throughput in multi-hop wireless networks by taking advantage of the bi-directional traffic flow. Such a relaying technique is termed relaying with Bi-directional Amplification of Throughput (BAT-relaying). The BAT-relaying is utilizing the concept of anti-packets, defined for bi-directional traffic flows. The relay node combines the anti-packets that are destined for different nodes and broadcasts the combined packet. Two BAT-relaying techniques have been proposed previously, Decode-and-Forward (DF) BAT-relaying and Amplify-and-Forward (AF) BAT-relaying. While in DF the relay node combines the packets by an XOR operation, AF BAT-relaying utilizes the inherent packet combining provided by the multiple access channel. In an errorless channel, AF has always higher achievable throughput than DF, but in noisy channels the noise amplification can severely degrade the performance of AF. In this paper we introduce a new scheme for BAT-relaying, termed Denoise-And-Forward (DNF) BAT-Relaying. The DNF BAT-relaying also makes use of the combining provided by the multiple access channel, but it removes the noise from the combined anti-packets before broadcasting to the destinations. While in the noiseless channel DNF and AF offer the same throughput performance which is superior to DF BAT-relaying, in large regions of the lower SNR values DNF BAT-relaying has the best throughput performance of all three schemes. Due to the unconventional nature of the BAT-relaying schemes, there are many open issues for further investigation. The design of a practical DNF scheme concerns several protocol layers, including modulation and coding.