  This paper proposes a relaying strategy for the multiple-relay network in
which each relay decodes a selection of transmitted messages by other
transmitting terminals, and forwards parities of the decoded codewords. This
protocol improves the previously known achievable rate of the
decode-and-forward (DF) strategy for multirelay networks by allowing relays to
decode only a selection of messages from relays with strong links to it. Hence,
each relay may have several choices as to which messages to decode, and for a
given network many different parity forwarding protocols may exist. A tree
structure is devised to characterize a class of parity forwarding protocols for
an arbitrary multirelay network. Based on this tree structure, closed-form
expressions for the achievable rates of these DF schemes are derived. It is
shown that parity forwarding is capacity achieving for new forms of degraded
relay networks.
