  We investigate the multipath fading relay channel in the limit of a large
bandwidth, and in the non-coherent setting, where the channel state is unknown
to all terminals, including the relay and the destination. We propose a
hypergraph model of the wideband multipath fading relay channel, and show that
its min-cut is achieved by a non-coherent peaky frequency binning scheme. The
so-obtained lower bound on the capacity of the wideband multipath fading relay
channel turns out to coincide with the block-Markov lower bound on the capacity
of the wideband frequency-division Gaussian (FD-AWGN) relay channel. In certain
cases, this achievable rate also meets the cut-set upper-bound, and thus
reaches the capacity of the non-coherent wideband multipath fading relay
channel.
