  We consider the role of Wyner-Ziv binning in compress-forward for relay
channels. In the one-way relay channel, we analyze a compress-forward scheme
without Wyner- Ziv binning but with joint decoding of both the message and
compression index. It achieves the same rate as the original compress-forward
scheme with binning and successive decoding. Therefore, binning helps reduce
decoding complexity by allowing successive decoding, but has no impact on
achievable rate for the one-way relay channel. On the other hand, no binning
simplifies relay operation. By extending compress-forward without binning to
the two-way relay channel, we can achieve a larger rate region than the
original compress-forward scheme when the channel is asymmetric for the two
users. Binning and successive decoding limits the compression rate to match the
weaker of the channels from relay to two users, whereas without binning, this
restriction no longer applies. Compared with noisy network coding,
compress-forward without binning achieves the same rate region in certain
Gaussian channel configurations, and it has much less delay. This work is a
step toward understanding the role of Wyner-Ziv binning in compress-forward
relaying.
