  A novel solution is proposed to undertake a frequent task in wireless
networks, which is to let all nodes broadcast information to and receive
information from their respective one-hop neighboring nodes. The contribution
is two-fold. First, as each neighbor selects one message-bearing codeword from
its unique codebook for transmission, it is shown that decoding their messages
based on a superposition of those codewords through the multiaccess channel is
fundamentally a problem of compressed sensing. In the case where each message
consists of a small number of bits, an iterative algorithm based on belief
propagation is developed for efficient decoding. Second, to satisfy the
half-duplex constraint, each codeword consists of randomly distributed on-slots
and off-slots. A node transmits during its on-slots, and listens to its
neighbors only through its own off-slots. Over one frame interval, each node
broadcasts a message to neighbors and simultaneously decodes neighbors'
messages based on the superposed signals received through its own off-slots.
Thus the solution fully exploits the multiaccess nature of the wireless medium
and addresses the half-duplex constraint at the fundamental level. In a network
consisting of Poisson distributed nodes, numerical results demonstrate that the
proposed scheme often achieves several times the rate of slotted ALOHA and CSMA
with the same packet error rate.
