  We investigate the binary-symmetric parallel-relay network where there is one
source, one destination, and multiple relays in parallel. We show that
forwarding relays, where the relays merely transmit their received signals,
achieve the capacity in two ways: with coded transmission at the source and a
finite number of relays, or uncoded transmission at the source and a
sufficiently large number of relays. On the other hand, decoding relays, where
the relays decode the source message, re-encode, and forward it to the
destination, achieve the capacity when the number of relays is small. In
addition, we show that any coding scheme that requires decoding at any relay is
suboptimal in large parallel-relay networks, where forwarding relays achieve
strictly higher rates.
