  A space-time physical-layer network coding (ST- PNC) method is presented for
information exchange among multiple users over fully-connected multi-way relay
networks. The method involves two steps: i) side-information learning and ii)
space-time relay transmission. In the first step, different sets of users are
scheduled to send signals over networks and the remaining users and relays
overhear the transmitted signals, thereby learning the interference patterns.
In the second step, multiple relays cooperatively send out linear combinations
of signals received in the previous phase using space-time precoding so that
all users efficiently exploit their side-information in the form of: 1) what
they sent and 2) what they overheard in decoding. This coding concept is
illustrated through two simple network examples. It is shown that ST-PNC
improves the sum of degrees of freedom (sum-DoF) of the network compared to
existing interference management methods. With ST-PNC, the sum-DoF of a general
multi-way relay network without channel knowledge at the users is characterized
in terms of relevant system parameters, chiefly the number of users, the number
of relays, and the number of antennas at relays. A major implication of the
derived results is that efficiently harnessing both transmit- ted and overheard
signals as side-information brings significant performance improvements to
fully-connected multi-way relay networks.
