Approximate capacity of a class of multi-source Gaussian relay networks

We study K-user M-hop Gaussian relay networks with K_m nodes in the m-th layer, where M is even and K = K₁ = K_M+1. We observe that the time-varying nature of wireless channels (fading) can be exploited to mitigate the inter-user interference. The proposed block Markov encoding and relaying scheme exploits such channel variations and works for any isotropically distributed channels including Rayleigh fading. We show a general achievable degrees of freedom (DoF) region of this class of Gaussian relay networks, which coincides with the cut-set outer bound if M/K_min is an integer, where K_min = min_m {K_m}. Therefore, we completely characterize the DoF region for the case where M/K_min is an integer.