Full Text - Journal of Theoretical and Applied Information Technology

Journal of Theoretical and Applied Information Technology
10 th June 2013. Vol. 52 No.1
© 2005 - 2013 JATIT & LLS. All rights reserved .
ISSN: 1992-8645 www.jatit.org E-ISSN: 1817-3195
was divided into M blocks zi(1), zi(2),..., z
i( M ) ,
The encoding function of the source (or relay) node
was X ( ζ (1)) , X ( ζ (2)) ,…, X ( ζ ( M))
.
Si
i
Si
i
In the model of received signals above, the relay
node R ( w≠ j)
decoded the Code Book
X
Si
w
( ζ ( l))
of l block.. When
i
ù g , the biggest
2
i
< log(1 + |
ij
| ⋅PS (
i
))
misunderstanding code probability would be so
small. After obtaining the signal of Decode Block,
the relay node sent the signal series
0, X ( ζ (1)) , X ( ζ (2)) ,…, X ( ζ ( M))
which
Rw
i
Rw
i
was decoded in the next Block Slot. The transport
method of block code signal was called Decode
Relay. To the model architecture of System in this
paper, the target (or relay) nodes used parallel
decoding technology12.
Supposed the destination (or relay) node had
received the signal z ( k)
of k block, and
i
Meanwhile, the Code Book XS i
( ζ
i
( k−
2)) was
decoded by the small misunderstanding code
probability, then the form of parallel decoding
signal based on the model of received signals in the
target (or relay) nodes was
⎡
⎣
X ( ( ))
S
ζ
i i
k +
∑
w= 12 , ...m, w≠
j
Rw
G (cosθ + isin θ ) X ( ζ ( k− 1)) + C ,
X
i
Si
jw jw Rw
i j
( ζ ( k − 1)) + C
- ⎦
(7)
⎤
Si
i j 1
If the source (or relay) node Si
( i = 1,2,..., m)
sent a code word that described the information
received by the destination (or relay) node. Based
on the discussion mentioned above, the relay node
R ( w≠ j)
would decode the information before
R
w
j
. So when the information was decoded
successfully, every receiver node began to use
another scheduled code word and sent the same
information in the average power conditions.
Supposed that the decoding time of the node R in
a code block cycle was represented in the time slot
t
j
. Then, t
j
means a period of a fading code block
cycle when the node R j
decoded and realied the
information to the node Rw
( w≠
j)
. According to
the condition of right decoding, there was
2
ù log(1 + | g | ⋅ PS ( )) < 1 .
i ij i
i
j
Based on the actual physical channel and
decoding conditions, we supposed that the node R
would neither decode nor send information when
t ≥ 1.
j
Let p
j
to represent the probability which the
node R
j
was decoded successfully. In addition, the
mutual information related to node S
i
,
R
j
was
j
2 2
j
= ∑( l
−
l −1)log(1 + | gij | ⋅ (
i
) + G ( −1))
l = 1
I t t PS l
(8)
In which t 0
= 0 , by solving a equation I
j
= ù
i
, j = 1,2,..., n, we have:
ù
t =
log(1 + | | ⋅PS
( ))
i
1 2
gi
1
2 2
i2
i
ù
i
+ t1 log
2
1 + | gi2
| ⋅PS
(
i)
2
=
2 2
log(1 + | gi2
| ⋅ PS (
i) + G )
t
t
n
=
i
1 + | g | ⋅ PS ( ) + G
1 + | g | ⋅ PS ( ) + G
ù
i
+ t
+
log(1 + | | ⋅ ( ) + ( −1) )
2 2
i2
i
1
log
2
1 + | gi2
| ⋅PS
(
i)
2 2
gin
PSi
n G
2 2
i3
i
2 2 2
+ gi3
⋅ PSi
+ G
2 2
+ gin
⋅ PSi
+ n−
G
,…,
1 + | g | ⋅ PS ( ) + 2G
t log 1 | | ( )
+ + ...
log(1 | | ( ) ( 1) )
t
+
1 + | g | ⋅ PS ( ) + ( n−1)
G
2 2
in
i
n−1 log 1 | |
2 ( ) ( 2)
2
+ gin
⋅ PSi
+ n−
G
2 2
log(1 + | gin
| ⋅ PS (
i
) + ( n−1) G )
j
,
(9)
( i = 1,2,..., m)
Naturally, when t
j
< 1 and t
j + 1
≥ 1 , then p
j
> 0 ,
p +
= , ( j = 1,2,..., m)
, and vice versa. So
j 1
0
pj
= Pr{ tj
< 1}
(10)
Through the analysis (node decoding,
cooperation and relay) mentioned above and the
literature[15], in the sense of probability
expectations, the throughput of mulit-hop relay
sensor network based on cooperative diversity was
expressed as
6