  Quantize-Map-and-Forward (QMF) relaying has been shown to achieve the optimal
diversity-multiplexing trade-off (DMT) for arbitrary slow fading full-duplex
networks as well as for the single-relay half-duplex network. A key reason for
this is that quantizing at the noise level suffices to achieve the cut-set
bound approximately to within an additive gap, without any requirement of
instantaneous channel state information (CSI). However, DMT only captures the
high SNR performance and potentially, limited CSI at the relay can improve
performance at moderate SNRs. In this work we propose an optimization framework
for QMF relaying over slow fading channels. Focusing on vector Gaussian
quantizers, we optimize the outage probability for the full-duplex and
half-duplex single relay by finding the best quantization level and relay
schedule according to the available CSI at the relays. For the N-relay diamond
network, we derive an universal quantizer that sharpens the additive
approximation gap of QMF from the conventional \Theta(N) bits/s/Hz to
\Theta(log(N)) bits/s/Hz using only network topology information. Analytical
solutions to channel-aware optimal quantizers for two-relay and symmetric
N-relay diamond networks are also derived. In addition, we prove that suitable
hybridizations of our optimized QMF schemes with Decode-Forward (DF) or Dynamic
DF protocols provide significant finite SNR gains over the individual schemes.
