Cooperative Diversity: Capacity Bounds and Code Designs - Adaptive Signal Processing in Wireless Communications - page 344

Wyner-Ziv coding Dirty-paper coding



Encoder Decoder X

m X Y m

X 

Encoder Decoder

Z~N (0 , σ 2 )

S

S

FIgure 12.4 Coding with side information. WZC refers to lossy source coding of X with
decoder side information S , whereas DPC considers channel encoding of message m with encoder
side information S over an AWGN channel.

minimum rate for compressing X was derived. In general, WZC incurs a rate loss when
compared to the case with S , also available at the encoder. However, if the correlation
between X and S is modeled as X = S + Z , with Z being an i.i.d., memoryless Gaussian
random variable, independent of S , then there is no rate loss with WZC under the mean-
squared error (MSE) distortion measure.
The information-theoretical dual [17] of WZC is channel coding with side infor-
mation at the encoder, or Gelfand-Pinsker coding [18], where the encoder has perfect
(noncausal) knowledge of the side information or CSI. The limits on the rate at which
messages can be transmitted to a receiver are given in [18]. In general, there is a rate loss
compared to the case when the receiver also knows noncausally the CSI, i.e., the encoder
side information. However, when the channel is additive white Gaussian noise (AWGN),
Gelfand-Pinsker coding does not suffer any rate loss. In this case we have the celebrated
dirty-paper coding (DPC) problem [14], shown in Figure 12.4 (right), where the decoder
can completely cancel out the effect of the interference caused by the side information.
Practical WZC and DPC both involve source-channel coding. WZC can be imple-
mented by first quantizing the source X , followed by Slepian-Wolf coding of the quan-
tized X with side information S at the decoder [19]. Using syndrome-based channel
coding for compression, Slepian-Wolf coding here plays the role of conditional entropy
coding. For DPC, source coding is needed to quantize the side information to satisfy the
power constraint. In the meantime, the quantizer induces a constrained channel, for
which practical channel codes can be designed to approach its capacity. Indeed, limit-
approaching code designs [20-22] have appeared for both WZC and DPC recently.

12.3.2 The Relay Channel
Since cooperative diversity is largely based on relaying messages, its information-
theoretical foundation is built upon the landmark 1979 paper of Cover and El Gamal
[23] on capacity bounds for relay channels. We thus start with the relay channel, give
the theoretical bounds on its capacity, and describe proposed coding strategies in the
Gaussian and Rayleigh flat-fading environments. Then we proceed with extensions to
two-transmitter two-receiver cooperative channels.
The relay channel, introduced by van der Meulen in [5], is a three-node channel where
the source communicates to the destination with the help of an intermediate relay node.
It is shown in Figure 12.5 . The source broadcasts encoded messages to the relay and
destination. The relay processes the received information and forwards the resulting
signal to the destination. The destination collects signals from both the source and relay