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Weight Pick: an efficient packet selection algorithm for networkcoding based multicast retransmission in mobile communicationnetworks
Qiang Hu • Jun Zheng
Published online: 23 June 2012
� Springer Science+Business Media, LLC 2012
Abstract This paper proposes an efficient packet selection
algorithm, called Weight Pick, for improving the efficiency
of a network coding based multicast retransmission pro-
tocol in mobile communication networks. Unlike existing
packet selection algorithms, Weight Pick introduces the
concept of a dynamic combination number in performing
network coding. Based on this concept, a base station
dynamically determines the number of packets combined
or encoded in a retransmission packet based on the current
packet receiving status of users and the combination
number for each retransmission packet can be different. In
packet selection, Weight Pick attempts to find an encoding
combination whose weight is not less than (C - 1) for
every user, where C is the combination number of that
retransmission packet. Simulation results show that Weight
Pick can significantly improve the retransmission perfor-
mance as compared with existing packet selection algo-
rithms in terms of both packet loss ratio and packet
transmission delay.
Keywords Multicast � Network coding � Retransmission �Dynamic combination � Mobile communication network
1 Introduction
Multicast is a data delivery service in mobile communi-
cation networks [1]. In multicast service, a base station
(BS) broadcasts its data to a group of mobile terminals or
users simultaneously through a common transmission
channel. Due to the non-ideal quality of the transmission
channel and the interference of other radio signals, how-
ever, a data packet may be corrupted and even lost during
its transmission. In this case, retransmission can be used as
an effective technique to ensure reliable data delivery.
A simple retransmission strategy is to allow the base sta-
tion to retransmit every packet that the mobile users request
for retransmission by employing a transmission protocol,
for example, the conventional stop-and-wait transmission
protocol [2]. However, this would introduce considerable
retransmission overhead and result in low retransmission
efficiency. To address this problem, it is desirable to
introduce new transmission or processing techniques into a
multicast retransmission protocol to reduce retransmission
overhead and increase retransmission efficiency.
Network coding is a new coding technique that has
demonstrated its potential to improve the throughput per-
formance of a wireless network [3–6]. The core concept of
network coding is to allow the data received from multiple
links to be mixed at intermediate network nodes for further
transmission so that the amount of data transmitted in the
network is reduced and the network performance in terms
of throughput is increased. This concept can also be
applied to the data received on a single link within a single
data stream. As a result, network coding has recently been
introduced in multicast retransmission to improve the
retransmission efficiency of a multicast retransmission
protocol [7, 8]. In a network coding based multicast
retransmission protocol, packet selection is an important
Q. Hu � J. Zheng (&)
National Mobile Communications Research Laboratory,
Southeast University, Nanjing 210096, Jiangsu, China
e-mail: [email protected]
Q. Hu
State Key Laboratory of Integrated Services Networks,
Xidian University, Xi’an 710071, Shaanxi, China
123
Wireless Netw (2013) 19:363–372
DOI 10.1007/s11276-012-0472-x
component and has a big impact on the performance of the
retransmission protocol. To improve retransmission per-
formance of the retransmission protocol, it is desirable to
have an efficient packet selection algorithm, which moti-
vated this work.
In this paper, we propose an efficient packet selection
algorithm, called Weight Pick, for improving the efficiency
of a network coding based multicast retransmission pro-
tocol for mobile communication networks. Unlike existing
packet selection algorithms, Weight Pick introduces the
concept of a dynamic combination number in performing
network coding. Based on this concept, a base station
dynamically determines the number of packets combined
or encoded in a retransmission packet based on the current
packet receiving status of mobile users and the number of
packets combined in each retransmission packet can be
different. In packet selection, Weight Pick attempts to find
an encoding combination whose weight is not less than
(C - 1) for every user, where C is the combination number
of that retransmission packet. Simulation results show that
Weight Pick can significantly improve the retransmission
performance as compared with existing Random Pick and
Hamming Pick in terms of both packet loss ratio and packet
transmission delay. To the best of our knowledge, this is
the first time that the concept of a dynamic combination
number is proposed for performing network coding in
multicast transmission.
The reminder of the paper is organized as follows.
Section 2 reviews related work on network coding based
multicast retransmission protocols and packet selection
algorithms. Section 3 presents the proposed Weight Pick
algorithm. Section 4 evaluates the performance of Weight
Pick through simulation results. Section 5 concludes this
paper.
2 Related work
Network coding has recently been studied for improving
the performance of multicast retransmission in mobile
communication networks. Several network coding based
multicast retransmission protocols have already been pro-
posed in the literature [7–10] and different packet selection
algorithms are employed in these retransmission protocols,
including Random Pick [7], MostLeast [9], and Hamming
Pick [10]. In Random Pick, the base station randomly
selects two packets from all packets that need to be
retransmitted and performs a XOR operation on the selected
packets to generate an encoded packet for retransmission.
Although this algorithm is simple to implement, it cannot
achieve high retransmission efficiency [9].
To improve retransmission efficiency, Wu and Zheng
recently proposed a couple of packet selection algorithms:
MostLeast and Hamming Pick. In MostLeast, the base
station selects the two packets with the most retransmission
requests and the least retransmission requests in generating
an encoded packet for retransmission. In Hamming Pick,
the base station selects the two packets with the largest
Hamming distance in a packet status table it maintains for
encoding. The simulation results show that both MostLeast
and Hamming Pick can achieve better performance than
Random Pick in terms of packet loss ratio and the number
of transmitted packets.
For all the three algorithms mentioned above, however,
the number of packets combined or encoded in a retrans-
mission packet is predetermined and fixed throughout the
system operation. According to the simulation results in
[10], this number has a big impact on the performance of a
network coding based retransmission protocol. This moti-
vated us to consider using a dynamic combination number
in generating an encoded packet for retransmission in order
to improve the performance of a retransmission protocol.
3 Weight Pick: an efficient packet selection algorithm
In this section, we present the proposed packet selection
algorithm, Weight Pick, including its basic rationales and
major procedures.
3.1 Network model
We consider a network model with a BS and a multicast
group of n mobile users, as shown in Fig. 1. In this net-
work, the base station broadcasts data packets to the users
in the group through the transmission channel between the
base station and each user. Due to the non-ideal channel
quality and the interference of other radio signals, not all
users can correctly receive the packets sent by the base
station. If a user does not receive a packet correctly, it will
send a request to the base station for retransmitting the
BSU1
U3
Un
U2
Fig. 1 Network model
364 Wireless Netw (2013) 19:363–372
123
packet. When the base station receives a retransmission
request, it will employ a retransmission protocol to
retransmit the packet.
3.2 Benefit of network coding
Consider the network model shown in Fig. 1. Assume that
there are a group of three users (U1, U2, U3) in the net-
work and the base station has broadcasted six packets
(P1, P2, …, P6) to the users. The receiving status of each
packet by each user is shown in Table 1, which is
maintained by the base station. In the table, the value ‘‘1’’
represents that the corresponding packet is correctly
received by the corresponding user while the value ‘‘0’’
represents that the corresponding packet fails to be
received by the corresponding user and thus retransmis-
sion is expected for the packet. Using a conventional
retransmission protocol, the base station will separately
retransmit each of the three failed packets (i.e., P2, P3, P5),
which needs three transmission timeslots. If network coding
is introduced, however, the base station can combine P2, P3
and P5 into Pr1 through an XOR operation on the three
packets, i.e., Pr1 = P2 � P3 � P5, and then broadcast Pr1.
Since U1 has already received P2 and P5 correctly, it can
decode P3 through an XOR operation, i.e.,
P3 = Pr1 � P2 � P5, as long as Pr1 is correctly received.
Similarly, U2 and U3 can obtain P5 and P2, respectively. As a
result, only one transmission timeslot is needed for the
retransmission of the three failed packets, and two timeslots
can be saved compared with using the conventional
retransmission protocol. Obviously, network coding can
reduce the number of retransmission timeslots used and the
number of data packets transmitted in the network, and
therefore improve the retransmission efficiency and network
throughput.
3.3 Assumptions
We make the following few assumptions for Weight Pick:
1. There are m slots in each transmission cycle, which
can be used for transmitting either original packets or
old packets. Here an old packet is one that has been
transmitted by the base station but needs to be
retransmitted.
2. If an acknowledgement for a transmitted packet (or a
retransmission request) is not received by the base
station at the end of a transmission cycle, the packet is
considered not being received correctly.
3. The maximum number of transmission cycles for a
packet is Dmax cycles, i.e., if a packet has been
retransmitted for Dmax transmission cycles and is not
received correctly, it will be discarded.
4. The combination number for an encoded retransmis-
sion packet is C. For Random Pick and Hamming Pick,
C is typically fixed and predetermined. The maximum
dynamic combination number for each encoded
retransmission packet used in Weight Pick is Cmax.
5. The encoding and decoding operations in performing
network coding are bitwise XOR.
3.4 Retransmission information table
To support Weight Pick, the base station maintains a
retransmission information table, in which each row cor-
responds to a user and each column corresponds to an old
packet that needs to be retransmitted. In the table, the first
row stores the ID of each old packet and the second row
stores the number of transmission cycles that an old packet
has been transmitted (i.e., No. of transmission cycles). An
element in the table indicates the receiving status of the
corresponding old packet by the corresponding user. If a
packet is received correctly, the corresponding receiving
status is set to 1; otherwise, it is set to 0. Table 2 gives a
simple example of the retransmission information table
with 10 users (U1 to U10). The table is periodically refre-
shed at the beginning of every transmission cycle. If all
Table 1 An example of the packet receiving status table
P1 P2 P3 P4 P5 P6
U1 1 1 0 1 1 1
U2 1 1 1 1 0 1
U3 1 0 1 1 1 1
Table 2 Retransmission information table (n = 10)
Packet ID P1 P2 P3 P4 P5 P6
No. of transmission
cycles
1 1 1 1 1 1
U1 1 0 1 1 1 1
U2 1 1 0 0 1 1
U3 0 1 1 1 1 1
U4 1 1 1 0 1 0
U5 1 1 1 0 0 0
U6 0 0 1 1 1 1
U7 1 1 1 1 1 1
U8 1 1 1 1 1 1
U9 1 1 1 1 1 1
U10 1 1 0 0 1 1
Wireless Netw (2013) 19:363–372 365
123
elements in a column become 1 or an old packet has
already stayed in this table for more than Dmax transmission
cycles, the corresponding column will be deleted from the
table. A new column will be added if a corresponding
original packet was not correctly received by all users in its
first transmission.
3.5 Rationales
To understand Weight Pick, let us observe Table 2. This
table contains 6 old packets (P1 to P6) that need to be
retransmitted. According to the packet receiving status
shown in the table, we can find the following three ratio-
nales, which can be exploited to design an efficient packet
selection algorithm.
Rationale 1 To increase retransmission efficiency, an
encoded retransmission packet should be decodable by as
many users as possible, preferably by all users.
Since both the encoding and decoding operations are
XOR, an encoded retransmission packet can have at most
one old packet that is unknown to a user in order for the
retransmission packet to be decoded by the user. Other-
wise, the retransmission packet cannot be decoded by the
user and the retransmission is ineffective for the user. For
example, P = (P1 � P2) � P3 can be decoded by U1, but
cannot be decoded by U6 in Table 2.
We define a set of old packets combined in an encoded
retransmission packet as an encoding combination, e.g.,
{P1, P3, P6}. For this encoding combination, to ensure
that an encoded retransmission packet can be decoded by
all users, the corresponding elements in each row can
have at most one ‘‘0’’. If the corresponding elements in a
row have more than one ‘‘0’’, it means that the corre-
sponding encoded retransmission packet has more than
one old packet unknown to the corresponding user. As a
result, this retransmission packet could not be decoded by
the user. In this case, all the old packets in this retrans-
mission packet need to be retransmitted again, which
would reduce the retransmission efficiency and thus
undesirable. Therefore, if we define the weight of an
encoding combination for a user as the sum of the ele-
ment values corresponding to the old packers contained in
the encoding combination, an efficient packet selection
algorithm should attempt to find an encoding combination
whose weight is not less than (C - 1) for every user,
where C is the combination number of that encoding
combination.
Rationale 2 To increase the retransmission efficiency, an
encoded retransmission packet should combine as many
old packets as possible provided that it can be decoded by
the users.
This is obvious because the larger the combination
number, the fewer the retransmission slots needed.
Rationale 3 To increase the retransmission efficiency, an
old packet can be retransmitted more than once in one
transmission cycle provided that it does not use additional
retransmission slots.
If an old packet is allowed to be retransmitted more
than once in one transmission cycle without using
additional retransmission slots, it could increase the
retransmission efficiency provided an encoded retrans-
mission packet contains at least one old packet that was
never transmitted earlier in this transmission cycle. For
example, if slot 1 transmits Pr1 = P1 � P5, transmitting
Pr20 = (P2 � P3) � P5 in slot 2 would be more efficient
than simply transmitting Pr2 = P2 � P3. This is because
both Pr20 and Pr2 could be decoded in all users, but Pr2
0
gives old packet P5 a second retransmission in this
cycle, which makes P5 more likely to be correctly
received.
Based on the above rationales, we propose the concept
of a dynamic combination number and introduce it into
Weight Pick. Based on this concept, Weight Pick uses a
dynamic combination number for an encoded retransmis-
sion packet instead of a fixed one, which is dynamically
determined by the base station based on the current packet
receiving status of users. Moreover, the combination
number for each encoded retransmission packet can be
different.
Fig. 2 Illustration of m-parallel stop-and-wait protocol (m = 6)
366 Wireless Netw (2013) 19:363–372
123
3.6 Transmission protocol
To support Weight Pick, an m-parallel stop-and-wait pro-
tocol is employed as the transmission protocol, which is
based on the basic stop-and-wait protocol [2]. In the
m-parallel stop-and-wait protocol, m is the protocol window
size, and a transmission cycle consists of m transmission
timeslots. When a sender has data to send, it first sends
m packets to the receiver continuously. Meanwhile, it keeps
receiving the acknowledgments of these packets sent back by
the receiver. Compared with the basic stop-and-wait protocol,
the m-parallel stop-and-wait protocol allows the sender to
send packets and receive acknowledgements simultaneously,
and thus can effectively increase transmission efficiency and
save network resources. After a transmission cycle, the sender
performs retransmission based on the retransmission request
information contained in the acknowledgements. If a packet is
not received correctly, the sender will receive a retransmis-
sion request from the receiver. In this case, the sender will
retransmit the packet in the next transmission cycle, as
illustrated in Fig. 2, where a NACK message serves as a
retransmission request.
3.7 Signaling overhead
To support Weight Pick, additional bits need to be intro-
duced into the header of a packet in order for an encoded
retransmission packet to be decoded by corresponding
users.
Figure 3 shows the additional bits introduced in the
packet header used in Weight Pick. We define two types of
packets: original packet and retransmission packet, and use
Bit-1 to indicate the type of a packet. If Bit-1 = 0, it
indicates that the packet is an original packet, and there is
no need to contain the other bits in the header. If Bit-1 = 1,
it indicates that the packet is a retransmission packet. In
this case, the subsequent k bits are used to indicate the
number of old packets combined in the retransmission
packet. The number k depends on the maximum number of
old packets (i.e., Cmax) allowed to be encoded in a
retransmission packet, and it can be calculated as
k = dlog2Cmaxe. Moreover, to make a retransmission
packet decodable at each user, the IDs of the old packets
contained in the retransmission packet should be inserted
into the header of the retransmission packet. Therefore, the
subsequent C bytes are used to indicate the IDs of the old
packets, and C is the combination number of an encoded
retransmission packet.
3.8 Major procedures
The major packet selection procedures of the Weight Pick
algorithm are described as follow:
Step 0: Refresh the retransmission information table based
on the receiving status of each transmitted packet.
Step 1: Search the first row of the retransmission
information table. If the number of old packets Num_OP
is smaller than 3, combine all old packets into one packet
for retransmission; Otherwise, go to Step 2.
Step 2: Search for encoding combinations with the
combination number i (i starts with Cmax) based on
Rationale 1 in the retransmission information table. If at
most one packet in all I old packets is unknown to each
user, this encoding combination is selected. If the search
result is null and i [ 2, the combination number is
decremented (i.e., i = i - 1). In this case, go back to
Step 2; otherwise, go to Step 3.
Step 3: Search for non-overlapped combinations among
the results of Step 2. For example, {P1, P2, P3} and
{P4, P5, P6} are a couple of non-overlapped combina-
tions.
If a selected encoding combination contains any old
packet that was already transmitted in this cycle earlier, it
will be discarded; otherwise, it will be retransmitted.
If the search result is null, an encoding combination with
only old packets that have never been transmitted earlier in
this cycle will be selected for retransmission.
If there still exist empty slots in this cycle and i C 2, go
back to Step 2; otherwise, go to Step 4.
Step 4: If there still exist old packets that need to be
retransmitted, re-search the retransmission information
table for encoding combinations that contain these old
packets based on Rationale 1. A selected encoding
combination can contain old packets that were already
retransmitted in this cycle earlier based on Rationale 3.
If the search result is null, randomly combine these old
packets pairwise. Then transmit the combined packets
and go to Step 5.
Step 5: Transmit original packets in the remaining
slots.
Fig. 3 Additional bits
introduced in the packet header
Wireless Netw (2013) 19:363–372 367
123
4 Performance evaluation
In this section, we evaluate the performance of Weight
Pick through simulation results. For this purpose, we
conducted a Monte Carlo simulation to compare Weight
Pick with Random Pick and Hamming Pick in terms of
packet loss ratio and packet transmission delay, where
the packet loss ratio is defined as the number of packets
discarded over the number of packets transmitted during
a certain number of transmission cycles observed and the
packet transmission delay is defined as the average
number of transmission cycles experienced by an original
packet before it is correctly received by all users. As we
indicated earlier, a packet is discarded if it is not
received correctly by all users within Dmax transmission
cycles.
4.1 Retransmission performance
In this simulation, we assume m = 6, n = 30, Dmax = 4,
Cmax = 5 and C = 2, and the number of transmission
cycles observed is 1,000.
Figure 4 shows the packet loss ratio with Random Pick,
Hamming Pick, and Weight Pick, respectively. It is seen
that Weight Pick can significantly improve the packet loss
ratio compared with Random Pick and Hamming Pick.
With the channel packet error probability increasing, the
packet loss ratio is increasing as well. In particular, when
the channel error probability is small, the performance of
Weight Pick is 10 times better than that of Hamming Pick
and 20 times better than that of Random Pick.
Figure 5 shows the end-to-end packet transmission
delay with Random Pick, Hamming Pick, and Weight Pick,
368 Wireless Netw (2013) 19:363–372
123
respectively. It is seen that the packet transmission delay
with Weight Pick is smaller than that with Hamming Pick
or Random Pick. With the channel packet error probability
increasing, the packet transmission delay increases as well.
4.2 Impact of the combination number
In this simulation, we assume m = 6, n = 30, Dmax = 4,
Cmax = 5 and the number of transmission cycles observed
is 1,000.
Figure 6 shows the impact of the combination number
C on the performance with Random Pick, Hamming Pick
and Weight Pick in term of packet loss ratio, respectively.
It is seen that with C increasing, the packet loss ratio with
Random Pick or Hamming Pick decreases remarkably.
However, C does not have any impact on Weight Pick
because Weight Pick uses a dynamic combination number
in generating an encoded retransmission packet. Therefore,
for Random Pick or Hamming Pick, it is preferred to set 2
as the combination number while for Weight Pick it is
unnecessary to set a fixed combination number.
Figure 7 shows the impact of the combination number
C on the performance with Random Pick, Hamming Pick
and Weight Pick in term of packet transmission delay,
respectively. It is seen that since the upper bound of packet
transmission delay Dmax is four transmission cycles, the
packet transmission delay with all the three algorithms is
always smaller than four. When the channel packet error
probability is relatively small, the packet transmission
delay increases with the increase of the channel packet
error probability and a larger value of C results in a larger
packet transmission delay for both Random Pick and
Hamming Pick. Moreover, it is interesting to find that in
Random Pick and Hamming Pick the packet transmission
delay drops when the channel packet error probability is
beyond 0.35. This is because in this case some encoded
packets could be successfully received by all users and it
takes Dmax or Dmax - 1 cycles to successfully receive most
of these packets. For example, suppose that five packets are
successfully received when p = 0.35 with one of them
having a delay of 3 cycles and the others a delay of 4
cycles. When p = 0.4, three packets are successfully
received with one of them having a delay of 3 cycles and
the others a delay of 4 cycles. In this case, the average
packet transmission delay for p = 0.35 is 3.8 cycles, which
is larger than the average delay of 3.73 cycles for p = 0.4.
In contrast, C has no impact on the packet transmission
delay with Weight Pick, which is also because to the use of
a dynamic combination number.
4.3 Impact of the maximum number of transmission
cycles
In this simulation, we assume m = 6, n = 30, C = 2, and
Cmax = 5, and the number of transmission cycles observed
is 1,000.
Figure 8 shows the impact of the maximum number of
transmission cycles Dmax on the packet loss performance
with Random Pick, Hamming Pick, and Weight Pick,
respectively. It is seen that for all the three algorithms the
packet loss ratio decreases with Dmax increasing, and
Weight Pick always has the best performance among the
three.
Figure 9 shows the impact of the maximum number of
transmission cycles Dmax on the packet transmission delay
performance with Random Pick, Hamming Pick, and
Weight Pick, respectively. It is seen that for all the three
algorithms the packet transmission delay increases with
Dmax increasing, and Weight Pick always has the smallest
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Channel Packet Error Probability
Pac
ket L
oss
Rat
io
Random
Hamming
Weight
Fig. 4 Packet loss ratio
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.41
1.5
2
2.5
3
3.5
4
Channel Packet Error Probability
End
-to-
end
Pac
ket T
rans
mis
sion
Del
ay
Random
Hamming
Weight
Fig. 5 Packet transmission delay
Wireless Netw (2013) 19:363–372 369
123
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Channel Packet Error Probability
Pac
ket L
oss
Rat
io
C = 2
C = 3
C = 4
(a) Random Pick
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Channel Packet Error Probability
Pac
ket L
oss
Rat
io
C = 2
C = 3
C = 4
(b) Hamming Pick
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1C = 2
C = 3
C = 4
(c) Weight Pick
Fig. 6 Impact of C on packet loss ratio. a Random Pick, b HammingPick, c Weight Pick
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.41
1.5
2
2.5
3
3.5
4
Channel Packet Error Probability
End
-to-
end
Pac
ket T
rans
mis
sion
Del
ay
C = 2
C = 3
C = 4
(a) Random Pick
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.41
1.5
2
2.5
3
3.5
4
Channel Packet Error Probability
End
-to-
end
Pac
ket T
rans
mis
sion
Del
ay
C = 2
C = 3
C = 4
(b) Hamming Pick
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.41
1.5
2
2.5
3
3.5
4
Channel Packet Error Probability
End
-to-
end
Pac
ket T
rans
mis
sion
Del
ay
C = 2
C = 3
C = 4
(c) Weight Pick
Fig. 7 Impact of C on packet transmission delay. a Random Pick,
b Hamming Pick, c Weight Pick
370 Wireless Netw (2013) 19:363–372
123
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Channel Packet Error Probability
Pac
ket L
oss
Rat
io
Dmax = 3
Dmax = 4
Dmax = 5
Dmax = 6
(a) Random Pick
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Channel Packet Error Probability
Pac
ket L
oss
Rat
io
Dmax = 3
Dmax = 4
Dmax = 5
Dmax = 6
(b) Hamming Pick
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Channel Packet Error Probability
Pac
ket L
oss
Rat
io
Dmax = 3
Dmax = 4
Dmax = 5
Dmax = 6
(c) Weight Pick
Fig. 8 Impact of Dmax on packet loss ratio. a Random Pick,
b Hamming Pick, c Weight Pick
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.41
1.5
2
2.5
3
3.5
4
4.5
5
Channel Packet Error Probability
End
-to-
end
Pac
ket T
rans
mis
sion
Del
ay
Dmax = 3
Dmax = 4
Dmax = 5
Dmax = 6
(a) Random Pick
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.41
1.5
2
2.5
3
3.5
4
4.5
5
Channel Packet Error Probability
End
-to-
end
Pac
ket T
rans
mis
sion
Del
ay
Dmax = 3
Dmax = 4Dmax = 5
Dmax = 6
(b) Hamming Pick
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.41
1.5
2
2.5
3
3.5
4
4.5
5
Channel Packet Error Probability
End
-to-
end
Pac
ket T
rans
mis
sion
Del
ay
Dmax = 3
Dmax = 4
Dmax = 5
Dmax = 6
(c) Weight Pick
Fig. 9 Impact of Dmax on packet transmission delay. a Random Pick,
b Hamming Pick, c Weight Pick
Wireless Netw (2013) 19:363–372 371
123
delay among the three. Moreover, for a particular value of
Dmax, the average packet transmission delay is always
smaller than this delay upper bound.
5 Conclusions
In this paper, we proposed an efficient packet selection
algorithm, called Weight Pick, for improving the efficiency
of a network coding based multicast retransmission pro-
tocol in mobile communication network. Weight Pick
introduces the concept of a dynamic combination number
in performing network coding, which allows a base station
to dynamically determine the number of packets combined
or encoded in a retransmission packet based on the current
packet receiving status of users and the number of packets
combined in each retransmission packet can be different.
The simulation results show that Weight Pick can signifi-
cantly improve the retransmission performance in terms of
both packet loss ratio and packet transmission delay as
compared with Random Pick and Hamming Pick.
Acknowledgments This work was supported by the National
Natural Science Foundation of China under Grant No. 61071115, the
Research Fund for the Doctoral Program of Higher Education of
China under Grant No. 20110092110007, the Research Fund of The
State Key Laboratory of Integrated Services Networks, Xidian
University, China, under Grant No. ISN11-02, and the Research Fund
of National Mobile Communications Research Laboratory, Southeast
University, China, under Grant No. 2012A02.
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Author Biographies
Qiang Hu received the B.S.
degree in electrical engineering
from the School of Information
Science and Engineering, South-
east University, China, in 2011.
He is currently a graduate student
with the National Mobile Com-
munications Research Lab
(NCRL), Southeast University.
His research interests include
network coding and wireless
communication networks.
Jun Zheng received the Ph.D.
degree in electrical and elec-
tronic engineering from The
University of Hong Kong, Hong
Kong, China, in 2000. He is
currently a Full Professor with
the National Mobile Communi-
cations Research Laboratory,
Southeast University (SEU),
Nanjing, China. Before joining
SEU, he was with the School of
Information Technology and
Engineering, University of
Ottawa, Ottawa, Canada. He has
coauthored (first author) the
book Wireless Sensor Networks: A Networking Perspective (New
York: Wiley-IEEE Press, 2009), and has published nearly 100 tech-
nical papers in refereed journals and magazines, and peer-reviewed
conference proceedings. His research interests include mobile com-
munication networks, wireless sensor networks, and mobile ad hoc
networks, focused on network architectures and protocols. Dr. Zheng
serves as a Technical Editor of IEEE Communications Magazine and
an editorial board member of several other refereed journals,
including Elsevier Ad Hoc Networks Journal, Springer WirelessNetworks, and Wiley Wireless Communications and Mobile Com-puting. He was an Editor of IEEE Communications Surveys &Tutorials between 2006 and 2011, and an Associate Editor of IEEE/OSA Journal of Optical Communications and Networking between
2009 and 2011. As Lead Guest Editor, he has co-edited more than ten
special issues for different refereed journals and magazines, including
a feature issue of IEEE Communications Magazine, two special issues
of IEEE Network, and two special issues of IEEE Journal on SelectedAreas in Communications. He has served as the founding General
Chair of AdHocNets’09, General Chair of AccessNets’07, and TPC or
Symposium Co-Chair for several international conferences and
symposia, including IEEE GLOBECOM’08, ICC’09, GLOBE-COM’10, ICC’11, and GLOBECOM’12. He has also served as a TPC
member for a number of international conferences and symposiums.
He is a senior member of the IEEE.
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