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...y and forward mixed signals. Prior work in information theory has noted the potential for analog network coding and shown that, in theory, it doubles the capacity of the canonical 2-way relay network =-=[16, 22, 27, 28, 30]-=-. Prior work, however, focuses on capacity bounds and does not provide an algorithm for delivering the resulting throughput benefits. This is with the exception of [29], which describes an algorithm f...

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...stimehr, Diggavi, and Tse [10] and Perron [11] with a tighter gap to the cutset bound. We then show that noisy network coding can outperform other specialized schemes for two-way relay channels [12], =-=[13]-=- and interference relay channels [14], [15]. A. AWGN-multiple multicast network Theorem 4: Let D = D1 = ··· = DN . For any rate tuple (R1,...,RN) in the cutset outer bound, there exists (R′ 1 ,...,R′ ...

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...have more than one antenna. This scenario has been studied in detail in the literature [78]–[83]. For larger networks, the approach remains the same: each relay scales and retransmits its observation =-=[84]-=-. However, the noise build ups with each retransmission so the SNR requirement increases as the network grows [75]. We also note that, in some scenarios, it is advantageous to use the compress-andforw...

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...Nodes a and b are transmitting their signals to each other. To help the transmission of the two nodes, a relay node is located between two nodes, which is called the two-way relay channel (TRC) [10], =-=[2]-=-, [4], [9]. In [4], [5], lattice strategies were used to construct DF schemes. Our MF scheme is different from [4], Fig. 1. Two-way channel model [5] in that no decoding at the relay node for the latt...

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...er allocation problem to maximize the sum rate for a single antenna system. Reference [12] considered the rate of network coding but did not consider and compare with that of multi-hopping. Reference =-=[13]-=- investigated the achievable rates by classical multi-user information theory when a two stage scheme is used. In this scheme, the two source stations first transmit simultaneously to the relay, and t...

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...or rate because less information must be extracted from the received signal [1,2,6]. We highlight that PNC can be applied in a much wider range of scenarios than just the two way relay channel (TWRC) =-=[4,5]-=-. On the other hand, this paper will be focused on this setting because it is simple, includes all necessary elements of PNC, and enables to focus on signal processing issues. Two main approaches have...

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...tion as follows. First, both end-nodes send to the relay by multiaccess with successive cancelation as in classical multiaccess channel [9]; and then the relay broadcasts to both end nodes. Reference =-=[10]-=- investigated the achievable rates, [11] considered the MIMO case, and [12] considered the scaling. In [13] the sum-rate was considered for both the two-stage operation and a three-stage operation, an...

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...layer was proposed in [10] with power allocation, interference mitigation tanks to DPC and results on the total network throughput, nevertheless the full analysis is presented in this paper. Recently =-=[11]-=- studied AF with analog network coding and showed that joint relaying and network coding can enhance the network throughput. Our main contribution is to bring network coding, in an analog way, at the ...