  We propose two coding schemes combining decode-forward (DF) and noisy network
coding (NNC) with different flavors. The first is a combined DF-NNC scheme for
the one-way relay channel which includes both DF and NNC as special cases by
performing rate splitting, partial block Markov encoding and NNC. The second
combines two different DF strategies and layered NNC for the two-way relay
channel. One DF strategy performs coherent block Markov encoding at the source
at the cost of power splitting at the relay, the other performs independent
source and relay encoding but with full relay power, and layered NNC allows a
different compression rate for each destination. Analysis and simulation show
that both proposed schemes supersede each individual scheme and take full
advantage of both DF and NNC.
