  In this paper, we derive the capacity of a special class of mesh networks. A
mesh network is defined as a heterogeneous wireless network in which the
transmission among power limited nodes is assisted by powerful relays, which
use the same wireless medium. We find the capacity of the mesh network when
there is one source, one destination, and multiple relays. We call this channel
the single source multiple relay single destination (SSMRSD) mesh network. Our
approach is as follows. We first look at an upper bound on the information
theoretic capacity of these networks in the Gaussian setting. We then show that
the bound is achievable asymptotically using the compress-forward strategy for
the multiple relay channel. Theoretically, the results indicate the value of
cooperation and the utility of carefully deployed relays in wireless ad-hoc and
sensor networks. The capacity characterization quantifies how the relays can be
used to either conserve node energy or to increase transmission rate.
