  Compress-forward (CF) schemes are studied in general networks. The CF rate
for the one-relay channel defines outerbounds on both the CF rate for general
networks and the compression rate-vector region supporting this rate. We show
the outerbound is achievable using regular decoding with constant encoding
delays, avoiding the exponential delays and restrictions on bidirectional
communication in noisy network coding and backward decoding. The concept of
layering is introduced to harmonize regular CF schemes with the framework of
flow decomposition in the decode-forward setting. Layerings correspond to
regular decoding schemes. Any desired compression rate-vector in the outerbound
is achievable by some layering, which is found using the same "shift" operation
in flow decomposition. In separate work, we show that "shifting" minimizes the
operations needed to find layerings and thus minimizes the complexity of the
compression rate-vector region.
