Cooperative Diversity: Capacity Bounds and Code Designs - Adaptive Signal Processing in Wireless Communications - page 347

schemes can be classified into decode-forward and observe-forward [23], although hybrid
schemes are also possible [23].
The main operation of decode-forward (DF) is full decoding at the relay node. Upon
receiving y r , the relay node first decodes m 1 and then re-encodes it before forwarding the
resulting codeword x r ( m 1 ) to the destination during the relay-transmit period. It should
be emphasized that the relay might use a different codebook than the source. In any
case, the source can completely predict what the relay will transmit, and full coherency
is therefore possible. The destination attempts to reconstruct message m by combin-
ing the signals received during the relay-receive and relay-transmit periods using either
successive list decoding [8, 23], backward decoding [31], or decoding based on parallel
Gaussian channel arguments [28], which all result in the same achievable rate region.
Although DF can be very efficient in some scenarios [24, 25], since the relay must per-
fectly decode the source message, the achievable rates are bounded by the capacity of the
channel between the source and the relay. That is, the capacity of the DF relay channel
cannot be higher than that of the source-relay channel; hence, if the channel between the
source and relay is poor, the relay is useless, and direct transmission from the source to
the destination is a better option.
To alleviate this problem of DF, a class of observe-forward schemes has been pro-
posed, where the relay does not attempt to decode the signal from the source; it merely
forwards a processed version of its received signal to the destination.
The simplest observe-forward scheme is amplify-forward (AF) [32], in which the relay,
sticking to its rudimentary role, just amplifies the received signal before forwarding.
A more sophisticated scheme is compress-forward (CF), which is rooted in the original
work of Cover and El Gamal [23], where the relay compresses the signal it has received
from the source within certain distortion. Since y r (received by the relay node) and y d 1
(received by the destination node) are independently corrupted versions of the same
encoded message x s 1 ( m 1 ), they are correlated. Thus, the relay node can employ WZC [13]
when compressing y r by treating y d 1 as the decoder side information. The Wyner-Ziv
compressed signal is then channel encoded to x r ( m 1 ) before being forwarded to the des-
tination, which recovers m 2 and m 1 using successive cancellation decoding that involves
several steps. First, ˆ r ( m 1 ) is reconstructed by assuming x s 2 ( m 2 ) as the noise, and then it
is subtracted from y d 2 before m 2 is decoded. Second, to reconstruct m 1 , y r is estimated
from ˆ r ( m 1 ) using Wyner-Ziv decoding with y d 1 as the decoder side information; maxi-
mum ratio combining on y d 1 and the obtained estimate ˆ r is then invoked to recover m 1 .
CF based on WZC has higher computational complexity than DF, but it gives many rate
points that are not achievable with any other coding strategies. It provides the best solu-
tion [23-25] when the relay is close to the destination node.
12.3.3 Capacity Bounds of the Gaussian Half-Duplex
Relay Channel
In the flat-fading environment, channel coefficients vary in time. The upper and lower
bounds on capacity can be computed by averaging over all channel realizations (with
optimally allocated power). This average capacity is called ergodic capacity . he bounds
on ergodic capacity for the full-duplex and half-duplex flat-fading relay channel are