Digital Signal Processing Reference
In-Depth Information
(node 2) wants to communicate to node 3 (node 4). We consider only the full-duplex case,
i.e., nodes 3 and 4 can simultaneously transmit and receive. Since the cooperative chan-
nel can be viewed as a combination of the interference channel and the relay channel,
its best achievable rate regions are obtained by combining DF or CF coding techniques
for the relay channel with coding for the interference channel [9]. In receiver coopera-
tion, a receiver node processes the received information and forwards the result to the
other receiver node to help decoding. Because the distance between the two receivers
is expected to be much smaller than that between a transmitter and a receiver, CF with
WZC provides the highest achievable rates. Indeed, from (12.2), the received signals in
nodes 3 and 4 at time instants
i
and
i
+ 1 are
yi xi cxicxi zi
[]
=+ +
[]
[]
[]
+
[],
3
1
32
2
344
3
yi
[
+==++
1
]
xi
[
1
]
cxi
[
+ +
1
]
c xi
[
+ ++
1
]
zi
[
1
],
(12.12)
3
1
322
34
4
3
y
[
i
]
=
cxi xi cxi
[ ]
+ +
[ ]
[ ]
+
zi
[ ],
4
41
1
2
43
3
4
yi
[
+=
1
]
c
xi
[
++ ++ ++ +
1
]
xi
[
1
]
cxi
[
1
]
z i
[
1
].
4
41
1
2
43
3
4
In CF [36], the receiver in node 3 (or node 4) employs WZC to compress the signal
y
3
[
i
] (or
y
4
[
i
]) it has received, while assuming
y
4
[
i
] (or
y
3
[
i
]) as the decoder side informa-
tion, before passing the resulting codeword
x
3
[
i
+ 1] (or
x
4
[
i
+ 1]) to the collaborating
receiver in node 4 (or node 3). Node 3 starts by decoding
x
4
[
i
+ 1] from
y
3
[
i
+ 1] while
treating
x
1
[
i
+ 1] +
c
32
x
2
[
i
+ 1] as part of the Gaussian noise. In
forward decoding
,
x
4
[
i
],
recovered in the previous time instant, is Wyner-Ziv decoded using
y
3
[
i
] as the decoder
side information, resulting in an estimate of
y
4
[
i
]. Next, the joint or individual decoding
technique [9] proposed for the interference channel is employed to reconstruct
x
1
[
i
] (and
x
2
[
i
]) from the obtained estimates
yi c
x
i
[]
−
ˆ []
= +
xicxi zi
[]
[]
+
[]
3
34
4
1
322
3
and
y
i
ˆ []
−
cxi cxi
[]
=
[]
++.
xi
[]
zi
[]
43
3
411
2
4
4
A similar procedure can be performed at node 4. Besides forward decoding, it is also
feasible to employ
backward decoding
, where the decoder starts by decoding the previ-
ously received block of symbols and proceeding backwards. In [36], forward decoding is
combined with either joint or individual decoding [9], and backward decoding is used
with joint decoding, giving three different decoding choices. Since nodes 3 and 4 can
use three different decoding methods each, there are nine possibilities, each providing a
different rate bound. To obtain the best achievable CF rate bound, the maximum of all
nine rate bounds should be taken.
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