Weight Pick: an efficient packet selection algorithm for network coding based multicast...

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: junzheng@seu.edu.cn

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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