  In this work, a new static relaying protocol is introduced for half duplex
single-relay networks, and its performance is studied in the context of
communications over slow fading wireless channels. The proposed protocol is
based on a Decode or Quantize and Forward (DoQF) approach. In slow fading
scenarios, two performance metrics are relevant and complementary, namely the
outage probability gain and the Diversity-Multiplexing Tradeoff (DMT).
  First, we analyze the behavior of the outage probability P_o associated with
the proposed protocol as the SNR tends to infinity. In this case, we prove that
SNR^2 P_o converges to a constant. We refer to this constant as the outage gain
and we derive its closed-form expression for a general class of wireless
channels that includes the Rayleigh and the Rice channels as particular cases.
We furthermore prove that the DoQF protocol has the best achievable outage gain
in the wide class of half-duplex static relaying protocols. A method for
minimizing the outage gain with respect to the power distribution between the
source and the relay, and with respect to the durations of the slots is also
provided.
  Next, we focus on Rayleigh distributed fading channels to derive the DMT
associated with the proposed DoQF protocol. Our results show that the DMT of
DoQF achieves the 2 by 1 MISO upper-bound for multiplexing gains r < 0.25.
