  We consider "virtual" full-duplex relaying by means of half-duplex relays. In
this configuration, each relay stage in a multi-hop relaying network is formed
by at least two relays, used alternatively in transmit and receive modes, such
that while one relay transmits its signal to the next stage, the other relay
receives a signal from the previous stage. With such a pipelined scheme, the
source is active and sends a new information message in each time slot. We
consider the achievable rates for different coding schemes and compare them
with a cut-set upper bound, which is tight in certain conditions. In
particular, we show that both lattice-based Compute and Forward (CoF) and
Quantize reMap and Forward (QMF) yield attractive performance and can be easily
implemented. In particular, QMF in this context does not require "long"
messages and joint (non-unique) decoding, if the quantization mean-square
distortion at the relays is chosen appropriately. Also, in the multi-hop case
the gap of QMF from the cut-set upper bound grows logarithmically with the
number of stages, and not linearly as in the case of "noise level"
quantization. Furthermore, we show that CoF is particularly attractive in the
case of multi-hop relaying, when the channel gains have fluctuations not larger
than 3dB, yielding a rate that does not depend on the number of relaying
stages. In particular, we argue that such architecture may be useful for a
wireless backhaul with line-of-sight propagation between the relays.
