Analog network coding in nonlinear chains

The problem of characterizing the optimal rate achievable with analog network coding (ANC) for a unicast communication over general wireless relay networks is computationally hard. A relay node performing ANC scales and forwards its input signals. The source-destination channel in such communication scenarios is, in general, an intersymbol interference (ISI) channel which leads to the single-letter characterization of the optimal rate in terms of an optimization problem with nonconvex, non closed-form objective function and non-convex constraints. For a special class of such networks, called layered networks, a few key results and insights are however available. To gain insights into the nature of the optimal solution and to construct low-complexity schemes to characterize the optimal rate for general wireless relay networks, we need (1) network topologies that are regular enough for analysis, yet general enough to capture essential characteristics of general wireless relay networks, and (2) schemes to approximate the objective function in closed-form without significantly compromising the performance. Towards these two goals, this work proposes (1) nonlinear chain networks, and (2) two approximation schemes. We show that their combination allows us to tightly characterize the optimal ANC rate with low computational complexity for a much larger class of general wireless relay networks than possible with existing schemes.