a high-reliability relay algorithm based on network coding in multi-hop wireless...
TRANSCRIPT
A high-reliability relay algorithm based on network codingin multi-hop wireless networks
Xi Cheng1 • Qi Wang1 • Qingshan Wang1 • Di Wang1
Published online: 7 November 2017
� Springer Science+Business Media, LLC 2017
Abstract In multi-hop wireless networks, minimizing the
transmission time is very important. In this paper, a high-
reliability relay algorithm (HRRA) is proposed to decrease
the transmission time based on the network coding in
multi-rate environment. The HRRA includes the relay
selection algorithm (RSA) and the block transmission
algorithm (BTA). Based on the relay reliability of node,
RSA chooses the neighbor with the higher link rate as the
common relay node and creates more network coding
opportunities at the common relay node. Thus, the network
coding opportunities and the high-rate links associated with
common node could both be exploited in the transmissions
of BTA. Moreover, a comprehensive theoretical analysis of
the transmission time of HRRA in a block is presented.
Lastly, the simulation results show that HRRA can sig-
nificantly reduce the transmission time compared with the
shortest path algorithm and heuristic relay node selection
algorithm and COPE.
Keywords Relay reliability � Transmission time � Block �Multi-hop networks � Network coding
1 Introduction
Network coding (NC) [1–3] is increasingly attracting the
attention of researchers because it is a promising scheme to
reduce the transmission time and improve the network
throughput in wireless networks. In the traditional
transmission scheme, beyond the source node and the
destination node, the other nodes of the path are only
responsible for routing, not processing the packets. Instead,
in the network coding, when an intermediate node receives
some packets, it will try to encode the packets and transmit
them. COPE [4] proposes a general scheme for inter-ses-
sion wireless network coding to improve the network
throughput. Context-aware interflow network coding and
scheduling (CARE) [5] adaptively encodes some packets to
maximize the network Quality of Service (QoS) and
throughput. The CARE considers both channel conditions
and characteristics of traffic. Maheshwar [6] focuses on
combination network coding (CNC), and shows that net-
work coding can improve the throughput and reduce the
routing cost. A new analysis [7] of COPE under UDP
traffic and a modified COPE are proposed. GUESS–
MCMI–COPE [8] uses two lists to reduce the space of
reception reports and increase the throughput. The
improved upper and lower bounds on the probability of
decoding failure [9] are presented in a multi-source multi-
relay network. And other works focuses on maximizing the
energy efficiency [10], and minimizing transmission time
[11] by using network coding.
In recent years, the IEEE 802.11 protocols [12, 13]
support the multi-rate transmission. For example, IEEE
802.11b [12] supports four transmission rates from 1 to
11 Mbps, and IEEE 802.11g [13] supports eight transmis-
sion rates from 6 to 54 Mbps. The sender can choose the
higher-rate links to improve the network performance.
More and more research focus on link adaption or relay
selecting. Relay selecting [14] is a fundamental operation
for diffusing the messages to the whole wireless network.
The heuristic relay node selection algorithm (HRNSA) [15]
uses the two high-rate links instead of the low-rate link.
The feasible solution construction (FSC) [16] is put forth to
& Qi Wang
1 School of Mathematics, Hefei University of Technology,
Hefei 230009, China
123
Wireless Netw (2019) 25:1557–1566
DOI 10.1007/s11276-017-1611-1
optimize the relay node assignment, and achieves signifi-
cant rate gain in wireless networks. An optimal relay
assignment (ORA) algorithm [17] assigns the available
relay nodes to different source–destination pairs to maxi-
mize the minimum data rate among all pairs. Joint rate
allocation and relaying strategy adaption (JRRA) [18]
improves the network throughput performance according to
the current network state information.
There are some works combined the network coding and
relay selection. Opportunistic two-way relaying (O-TR)
[19] accomplishes the full diversity based on the modular
network coding method and the opportunistic relay selec-
tion in two-way relaying network. S–RS–NC and D-RS-
NC [20] joint RS and NC schemes to reduce the perfor-
mance loss in two-way relay networks. Space–time coding
and physical layer network coding (ST–PNC) [21] effi-
ciently combat channel fading and get the better system
performance according to dual relay selection (DRA).
However, the most existing RS–NC algorithms focus on
the two-way relaying network. In this paper, we investigate
the relay algorithm based on the network coding to
decrease the transmission time in multi-hop wireless net-
works. For example, in Fig. 1, we assume the packet length
is L. Each transmission rate, associated with the link, is
illustrated. In Fig. 1, node c1 wants to transmit a packet p1to node c3, and node c3 wants to send a packet p2 to node
c1. The shortest path algorithm (SPA) [22] chooses a path
with the minimum number of hops. For example, in SPA,
node c1 sends packet p1 to node c2, node c2 sends packet p1to node c3, node c3 sends packet p2 to node c2, and node c2sends packet p2 to node c1. The total transmission time of
SPA equals 2(L/2 ? L/2) = 2L. In contrast, the HRNSA
tries to replace a lower-rate link with two high-rate links. In
Fig. 1, HRNSA chooses node R1 and R2 as the relay nodes
of links c1c2��! and c2c3
��!, respectively. Thus, the transmission
time of HRNSA is 2(L/5.5 ? L/11 ? L/5.5 ? L/
5.5) = 14L/11. In this paper, each node is associated with a
common relay node. In Fig. 1, node R1 is chosen as the
common relay node of nodes c1, c2 and c3. Thus, the net-
work is divided into some blocks according to the common
relay nodes, and the common relay node can combine the
packets from its neighbor nodes to create more coding
opportunities than normal relay node. In Fig. 1, nodes R1,
c1, c2 and c3 comprise a block. Then, try to use the network
coding during transmitting the packets within a block. In
Fig. 1, node c1 sends packet p1 to node R1, node c3 sends
packet p2 to node R1, And node R1 broadcasts the coded
packet p1 � p2 to nodes c1 and c3 which can decode their
expected packet by XOR the coded packet with their held
packet. The transmission time of our scheme is L/5.5 ? L/
5.5 ? L/5.5 = 6L/11. It is clear that our scheme can reduce
the transmission times by 72 and 57% compared with SPA
and HRNSA, respectively. In this paper, we propose a
high-reliability relay algorithm (HRRA) based on network
coding in multi-hop wireless networks, which chooses a
common relay node for a block area based on the relay
reliability of node. Compared with the normal relay node,
the common relay node can not only be with high-rate links
but also has more coding opportunities. Thus, the network
coding opportunities and high-rate links could both be
exploited to decrease the transmission time.
The major contributions of the paper are summarized as
follows:
We define a metric of node’s relay reliability and then
design a relay selection algorithm to choose the common
relay nodes which can create more coding opportunity by
the metric.
• We propose a block transmission algorithm to deal with
common relay node’s transmission and non-common
relay node’s transmission by exploiting the network
coding opportunities and the high-rate links associated
with the common relay node.
• We analyze the gains of the proposed algorithm
compared with the shortest path algorithm and the
heuristic relay node selection algorithm in a block.
Moreover, we conduct simulations to show that our
algorithm significantly outperforms the existing
schemes in transmission time.
The remainder of this paper is organized as follows: The
network model and some definitions are presented in
Sect. 2. In Sect. 3, the high-reliability relay algorithm
(HRRA) is proposed. The transmission time gains of
HRRA over SPA and HRNSA are analyzed in Sect. 4.
Section 5 experimentally compares the performance of the
proposed algorithm against existing algorithms. We con-
clude our work in Sect. 6.
2 Network model and definition
In this section, the network model and some definitions are
provided. Let R ¼ fR1;R2; . . .;RKg, where R1 �R2 � � � ��RK be the set of K transmission rates [12, 13] associated
11Mbps 5.5Mbps
2Mbps 2Mbps
5.5Mbps
1R
1c 2c 3c
2R
5.5Mbps 5.5Mbps
Fig. 1 An example
1558 Wireless Netw (2019) 25:1557–1566
123
with a specific network card. The wireless network is
modeled as an undirected graph G ¼ ðV ;EÞ, where V ¼fv1; v2; . . .; vng and E ¼ ðvi; vjÞ
� �
are the sets of nodes and
edges, respectively. For two nodes vi and vj, there is an
edge ðvi; vjÞ if di;j �D, where di;j is the distance between
node vi and vj, and D is the transmit range of the lowest
transmission rate. Edge ðvi; vjÞ has a corresponding highest
transmission rate ri;j 2 R. Let Ni be the neighbor set of
node vi.
To illustrate our algorithm, we give the following
definitions:
Definition 1 Let hi be the average link rate of node vi,
and be given by
hi ¼jNij
P
vj2N 0i
1ri;j
; ð1Þ
where N0
i is the subset of neighbors of node vi. Initially
N0i ¼ Ni.
Definition 2 Suppose node vi wants send a packet to node
vj and the transmission path is denoted vivj�!. let cij be the
average link rate of path vivj�!,
cij ¼vivj�!�
�
�
�
P
ðvm;vnÞ2vivj�! 1
rm;n
; ð2Þ
where vivj�!�
�
�
� is the hop count of the path from vi to vj. The
average link rate cij is a harmonic average. Thus, the
average transmission time of the path is easily calculated as
follows
tij ¼L
rij¼
P
vm;vnð Þ2vivj�! L
rm;n
vivj�!�
�
�
�
: ð3Þ
where L is the packet length.
In Fig. 2, node v2 wants to send a packet to node v5, and
the path is denoted v2v5��! with the intermediate nodes v6 and
v7. We can obtain the average link rate of path v2v5��!,
c25 ¼ 6619, and the average transmission time of the path,
t25 ¼ 1966L.
Definition 3 We define the relay reliability vi of node vias vi ¼ x1di þ x2hi, where di is the degree of node vi, hi is
the average link rate of node vi, and x1,x2 are constant
satisfied with x1 þ x2 ¼ 1.
di reflects the coding opportunity of node vi, higher himeans higher transmission rate of the link associated with
node vi. In Fig. 2, the degree d1, of node v1 is 4, the
average link rate of node v1 is h1 ¼ 41=11þ1=11þ1=11þ1=5:5¼ 44
5.
Thus, the relay reliability of node v1,
v1 ¼ x1 � 4þ x2 � 445¼7:36, where x1 ¼ 0:3, x2 ¼ 0:7
in this paper.
3 A high-reliability relay algorithm
In this section, we propose a high-reliability relay algo-
rithm (HRRA) based on network coding to reduce the
transmission time in multi-hop wireless networks. The
HRRA includes two sub-algorithms: relay selection algo-
rithm (RSA) and block transmission algorithm (BTA). The
main idea of RSA is to construct blocks which include
some nodes with the same common relay node. In each
block, the common relay node is a center node, and can
encode the packets from its neighbor nodes. Thus, it has
more coding opportunities compared with normal relay
node. Then, we execute BTA to complete the transmission
scheme. In HRRA, we use some notations to help us
understand it as shown in Table 1.
3.1 Relay selection algorithm
As mentioned before, we first use the RSA to choose some
common relay nodes (as shown in Algorithm 1). These
common relay nodes are expected to create more coding
opportunity. Firstly, all nodes compute their own relay
reliability and broadcast it to their neighbors, as shown in
lines 1–2. Secondly, as shown in lines 5–6, if a node has
not chosen its common relay node, it will search for a
common relay for a common relay or itself
with maximum relay reliability. Third, as shown in lines
7–14, if one node has been chosen as the common relay
node, it will broadcast this to its neighbors, and its neighbor
checks whether the node meets the qualifications for being
its common relay node. If the common relay node candi-
date or the existing common relay node is not qualified to
be the common relay node, as shown in line 15, it will
2 5.5 5.5
5.5111111
5.5
5.55.5 2
5.5
1v
2v 6v 7v 5v
4v3v
Fig. 2 A multi-hop wireless network model with link rate (Mbps)
Wireless Netw (2019) 25:1557–1566 1559
123
receive the notification. If a node receives the information
about not be chosen as the common relay node, it will
update its own relay reliability and broadcast it to its
neighbors as shown in line 19. If a node is notified that its
common relay node has changed the relay reliability, it will
reselect its common relay node as shown in line 22. The
algorithm continues to run until each node has its own
common relay node.
Definition 4 Block H is a sub-graph of G, where the
nodes have the same common relay node.
Thus, the network is divided into some blocks corre-
sponding with the common relay node-centered areas.
Table 1 Summary of notationsSymbol Description
vi The relay reliability of node vi
1i The common relay node of node vi
Ni The set of neighbors of node vi
N0i The subset of neighbors of node vi, N
0i � Ni, used to compute the relay reliability of node vi
vivj�!�
�
�
� The hop count of path from node vi to node vj
ri;j The highest transmission rate of edge vi; vj� �
1560 Wireless Netw (2019) 25:1557–1566
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For example, in Fig. 2, the relay reliabilities of nodes
from v1 to v7 are 26.75, 16.3, 12.45, 10, 12.45, 19.7, and
13.85, respectively. Then, each node finds the node with
the maximum relay reliability from its neighbors. Thus,
node v1 is acted as the common relay node for its neighbor
nodes because of its higher relay reliability among nodes
v1, v2, v5, v6 and v7. By analogy, node v3 is acted as the
common relay nodes. Apparently, each block common
relay node is corresponding with one block. In Fig. 3, there
are two blocks.
3.2 Block transmission algorithm
After processing with RSA, we obtain a group of blocks
with the corresponding common relay node. Now, we use
the BTA, as shown in Algorithms 3 and 4, to transmit the
packets in these blocks. BTA includes two parts: common
relay node’s transmission scheme (in Algorithm 3) and
non-common relay node’s transmission scheme (in Algo-
rithm 4). The common relay node tries to use the network
coding opportunity to transmit the packets, and the non-
common relay nodes will compare the total link rates of
different paths and then decide whether or not use its
common relay node chosen in RSA. In Algorithm 3, as
shown in Lines 2–4, the common relay node vi tries to
encode two packets in a transmission by exploiting the
network coding opportunity. In algorithm 4, as shown in
lines 3–5, if the total transmission time from nodes vj to vkthrough their common relay node vi is less than that of the
direct transmission from nodes vj to vk, then node vj sends
packet to node vk through the common relay node vi.
Otherwise, as shown in lines 7, 10, node vj sends packet to
node vk by HRNSA.
4 Analysis of HRRA
In this section, we compare the total transmission time of
our HRRA with those of SPA and HRNSA. Before the
analysis, we present a definition.
Definition 5 If a node wants to send m packets
p1; p2. . .pm to its neighbor nodes, and the number of
transmissions is n, then mn
is said to be its encoding
opportunity.
block 1 block 2
1v
2v 6v 7v 5v 4v 3v
Fig. 3 The blocks after RSA
Wireless Netw (2019) 25:1557–1566 1561
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The HRRA uses the HRNSA to transmit the packet
when the sender and receiver are located in two adjacent
blocks. Therefore, for simplicity, we only analyze the
transmission times of all algorithms in one block. Assume
that node vi is a common relay node and vijð1� j� N0
i
�
�
�
�Þ isits neighbors in the block. We assume that there are some
transmission requests f1; f2; . . .; fk in one block and that the
average hop count of these transmission requests in this
block is s. In SPA, for the transmission request fi, suppose
that the transmission path of fið1� i� kÞ is vij vijþs���!, the
average link rate of path vijvijþs���! is c, and the approximate
transmission time of one transmission request fi is sLc .
Therefore, the transmission time of SPA within this block
is obtained
T1 ¼ ksLc; ð4Þ
HRNSA is an enhancement algorithm based on SPA.
HRNSA will compute the transmission rate for each hop to
decide whether to use a relay node. For a single hop that is
using a relay node, we assume that the transmission time of
SPA is q times that of HRNSA, and the probability of using
a relay node in the sender is g. The transmission time of
HRNSA is given by
T2 ¼ 1� gð ÞT1 þ g1
qT1
¼ ð1þ gð1q� 1ÞÞk sL
c
ð5Þ
For convenience in calculating the total transmission time
of the proposed algorithm within this block, we assume: (1)
The common relay node vi is not a sender; and (2) the
neighbor nodes vijð1� j� N0
i
�
�
�
�Þ only transmit packets to
their common relay node vi, and do not use HRNSA to
transmit a packet to its next hop.Based on the assumptions,
the HRRA includes two steps. To begin with, the neighbor
nodes transmit all packets to the common relay node vi,
then vi transmits the packets by trying to use the network
coding. We assume that hi is the average link rate of the
common relay node vi(Def .1), p is the encoding opportu-
nity of relay node vi, as defined in Def. 5, and the trans-
mission time of HRRA is
T3 ¼ kL
hiþ kL
phi¼ pþ 1ð ÞkL
phi; ð6Þ
where k Lhiis the transmission time of step 1, and kL
phiis the
transmission time of step 2. Hence, the transmission time
gains of HRRA over SPA and HRNSA, respectively, are
T1 � T3
T1¼
k sLc � ðpþ1ÞkL
phi
k sLc
¼ 1� ðpþ 1Þcphis
¼ 1� pþ 1ð Þps
ð7Þ
¼ 1� pþ 1ð Þps
ð8Þ
and
T2 � T3
T2¼
ð1þ gð1q� 1ÞÞk sL
c � ðpþ1ÞkLphi
ð1þ gð1q� 1ÞÞk sL
c
¼ 1� cðpþ 1Þphisð1þ gð1
q� 1ÞÞ
� 1� hiðpþ 1Þphisð1þ gð1
q� 1ÞÞ
ð9Þ
¼ 1� pþ 1
spð1þ gð1q� 1ÞÞ
ð10Þ
The reasoning in the derivations of Eqs. (7), (9) is that
node vi is the common relay node and it has a high relay
reliability, the average link rate of node vi is higher than the
average link rate of path vij vijþs���!, in other words, c� hi.
Thus, Eqs. (7) and (9) are lower bounds of gain.
Now, we conduct a simulation to verify our algorithm
performance in X topology [8]. As shown in Fig. 4, the
topology has 5 nodes. And in our simulation, the packet
generate rate is 20 packets/min. The link transmission rate
and the corresponding transmission range of IEEE 802.11b
are shown in Table 2, and the simulation parameters are
shown in Table 3. We generate 120 X topologies which
choose node S as the common relay node, thus all the nodes
form a block. We compare the transmission time of the
proposed algorithm with the existing algorithms, SPA [22]
and HRNSA [15] in different flow numbers.
In this simulation, we count the average values of p, s, qand g which is 2, 2.26, 2.25 and 0.22, respectively. Thus,
according to Eqs. (8) and (10), we obtain the gain of
s
1c
4c
3c
2c
Fig. 4 X Topology
1562 Wireless Netw (2019) 25:1557–1566
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HRRA over SPA and HRNSA is 33.7 and 24%. Moreover,
Fig. 5 shows a comparison of the transmission time of
three algorithms according to simulation and analytical
results. The simulation results shows that the HRRA
algorithm can save the transmission time 44 and 28% on
average than that of SPA and HRNSA, respectively. The
gain of analysis is lower than that of corresponding simu-
lation. This is reasonable because the analysis result is a
lower bound value as mentioned below Eq. (10). Further-
more, Fig. 5 shows that the transmission time of analysis is
in agreement with that of simulation.
5 Simulation
In this section, we develop a simulator using C?? to
compare the performance of the proposed HRRA with SPA
[22], HRNSA [15] and COPE [4]. The performance metric
is the transmission time and average delay. The nodes are
randomly distributed in a 2000 m 9 2000 m square area,
we use the Free space propagation model [23]. The other
simulation parameters are same as Sect. 4.
5.1 Impact of number of flows
Figure 6 shows the simulation results in different number
of flows. In this simulation, we set 70 nodes, and the packet
generate rate is 15 packets/min. Figure 6(a) shows that the
proposed algorithm can achieve transmission time decrease
of 55, 25 and 15% over SPA, HRNSA and COPE on
average, respectively. The reason may be that HRRA is
Table 2 The transmission rate and corresponding transmission range
Transmission rate (Mbps) Transmission range (m)
11 400
5.5 540
2 670
1 800
Table 3 Simulation parameters
Simulation parameters Value
Network area 1500 m 9 1500 m
Time-to-live (TTL) 40 s
L 0.5 Mb
x1 0.3
x2 0.7
10 12 14 16 18 20
Number of Flows
0
0.05
0.1
0.15
0.2
0.25
0.3
Tran
smis
sion
Tim
e(s)
HRRA(Simulation)HRRA(Analysis)SPA(Simulation)SPA(Analysis)HRNSA(Simulation)HRNSA(Analysis)
Fig. 5 Performance comparison under different number of flows in X
topology
10 15 20 25 30 35 40
Number of Flows
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5(a)
(b)
Tran
smis
sion
Tim
e(s)
HRRASPAHRNSACOPE
10 15 20 25 30 35 40
Number of Flows
26
28
30
32
34
36
38
40
42
Aver
age
Del
ay(s
)
HRRASPAHRNSACOPE
Fig. 6 Performance comparison under different number of flows.
a Transmission time, b Average delay
Wireless Netw (2019) 25:1557–1566 1563
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based on network coding and choose the common relay
nodes to increase the coding opportunity to reduce the
transmission time, and the common relay nodes may have
more coding opportunities with the increase of number of
flows. In Fig. 6(b), although the average delay of HRRA is
a bit higher than those of HRNSA, SPA and COPE about
11, 8, 5%, respectively, this is acceptable compared with
the gain of transmission time of HRRA.
5.2 Impact of number of nodes
In order to investigate the impact of the variation of the
number of nodes on our algorithm, we vary the number of
nodes from 50 to 100. In this simulation, we set 20 flows,
and the packet generate rate is 20 packets/min. The simu-
lation results are plotted in Fig. 7. As shown in Fig. 7(a), it
is obvious that HRRA decreases the transmission time
about 52, 33 and 10% on average, respectively, compared
with SPA, HRNSA and COPE. From Fig. 7(b), the
results show that the proposed algorithm increases average
delay to some extent. Moreover, the average delay declines
for values of node number greater than 70. It may cause by
the network load decreased with the number of node
increased.
5.3 Impact of packet generation rate
Figure 8 shows the simulation results in different packet
generation rate in the source node. In this simulation, we
set 60 nodes, and the number of flow is 20. The simulation
results are shown in Fig. 8(a), in contrast with HRNSA and
COPE, the HRRA can save 35 and 30% transmission time,
respectively. Moreover, the transmission time decreases
with the packet generation rate per node increasing except
SPA. The reason may be that the COPE, HRNSA, and
HRRA could encode more packets in each transmission. In
70 7560 65 90 95 100
Number of Nodes
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5(a)
(b)
Tran
smis
sion
Tim
e(s)
HRRASPAHRNSACOPE
70 75
80 85
80 8560 65 90 95 100
Number of Nodes
27
28
29
30
31
32
33
34
35
36
37
38
Aver
age
Del
ay(s
)
HRRASPAHRNSACOPE
Fig. 7 Performance comparison under different number of nodes.
a Transmission time. b Average delay
10 12 14 16 18 20
Packet Generation Rate Per Node(packets/min)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35(a)
(b)
Tran
smis
sion
Tim
e(s)
HRRASPAHRNSACOPE
10 12 14 16 18 20
Packet Generation Rate Per Node(packets/min)
20
22
24
26
28
30
32
34
36
38
40
Aver
age
Del
ay(s
)
HRRASPAHRNSACOPE
Fig. 8 Performance comparison under different packet generation
rates. a Transmission time. b Average delay
1564 Wireless Netw (2019) 25:1557–1566
123
the meantime, as show in Fig. 8(b) illustrated, compared
with the average delays of SPA and HRNSA, the average
delay of HRRA has an acceptable increase, and less than
that of COPE. Figure 8(b) apparently shows that the
overall trends of delays of SPA, HRNSA and HRRA are on
the increase with the increase of the packet generation rate.
It may be caused by the network load increased with more
packet generated.
5.4 Impact of x1
In this subsection, we study the effect of x1 value on the
transmission time and average delay. As shown in Fig. 9,
the transmission time drops considerably first, while
x1 ¼ 0:4, the transmission time reaches the lowest value.
The minimum transmission time decreases 11% compared
with the maximum value. Thus it shows that x1 has
important impact on the transmission time. Similarly, the
tendency of average delay has similar property. Thus, we
can choose the different x1 values to accommodate the
variety of requirements.
6 Conclusion and future work
In this paper, we have studied the common relay node
selection with network coding to minimize the transmis-
sion time. We first define the node’s relay reliability to
choose the common relay node. Moreover, a high-relia-
bility relay algorithm (HRRA) based on network coding is
presented. Then, we analyze the gains of transmission time
of HRRA compared with SPA and HRNSA in a block.
Last, we conduct simulations to show that our algorithm
significantly outperforms existing schemes in transmission
time. Simulation results shows that the HRRA algorithm
can reduce transmission time at least 52, 25 and 10%
compared with SPA, HRNSA and COPE, respectively. In
our work, we focus on reducing the transmission time.
However, the energy consumption should also be consid-
ered. In future work, our plan is to minimize the energy
consumption using network coding in multi-rate wireless
networks.
Acknowledgements This work is partly supported by Natural Sci-
ence Foundation of China [61401144, 61571179].
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Fig. 9 The impact of different x1 values
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Xi Cheng received the B.S.
degree in Information and
Computing Science form
Chaohu College in 2015. Now
he is studying in the Department
of Mathematics at Hefei
University of Technology for
M.D. His research interests
include network coding and
delay tolerant networks.
Qi Wang received the Ph.D.
degree in Computer Science,
from Hefei University of Tech-
nology, Hefei of China in 2010.
She was a visiting scholar at
Temple University between
2014 and 2015. She is an asso-
ciate professor in the Depart-
ment of Mathematics at Hefei
University of Technology. Her
research interests include delay
tolerant networks, scheduling
algorithm, and network coding.
Qingshan Wang received his
Ph.D. degree in Computer Sci-
ence from University of Science
and Technology of China
(USTC) in 2007. He was a vis-
iting scholar at Cornell Univer-
sity between 2009 and 2010. He
is an associate professor in the
Department of Mathematics at
Hefei University of Technology.
His research interests include
delay tolerant networks and ad
hoc networks protocol design,
and network coding.
Di Wang received the B.S.
degree in Mathematics and
Applied Mathematics from
Hefei Normal University in
2012. Now he is studying in the
Department of Mathematics at
Hefei University of Technology
for M.D. His research interests
include network coding and
delay tolerant networks.
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123