Genetic-Based Randomized Network Coding forDynamic Satellite Multicast

Tao Zhang, Qiaoyu Li, and Hongyong AnSchool of Electronic and Information Engineering,

Beihang University, Beijing 100191, ChinaEmail: zhtao@buaa.edu.cn, {q.li, hongyong.an}@ee.buaa.edu.cn

Abstract—The multicast rate of satellite communication net-works (SCN) can be maximized by using randomized networkcoding (RNC). To optimize the RNC-based multicast for SCN,the number of coding links should be minimized to reduce thecomputational complexity on satellite, while the dynamic topologyneeds to be considered. To this end, in this paper, we proposean improved genetic algorithm (IGA) to minimize the numberof coding links and provide successful multicast for dynamicnetwork topology. In order to support dynamic multicast, theerasure protection (EP) is carried out with the IGA in fitness testprocess to select child generations with a better-fitness. It showsthat the IGA method provides good performance for RNC-basedmulticast in dynamic SCN scenarios, where the number of codinglinks is minimized to reduce the complexity. Through simulationresults, we can confirm that our proposed method outperformsthe existing ones, where dynamic multicast is not considered.

I. INTRODUCTION

As a developing wireless communications system, broad-

band satellite communication network (SCN) is able to provide

seamless communications for ground and air-based users.

Since the topology of SCN varies with time rapidly under low-

earth-orbit (LEO) or middle-earth-orbit (MEO) circumstances,

communications algorithms and protocols for SCN should be

designed to support dynamic topology. On the other hand,

considering the limited computing power on satellites, low

complexity methods are desired to reduce the complexity of

communications for SCN.

It has been well known that multicast plays a crucial role

in SCN [1]. Using network coding (NC), the rate of multicast

is able to reach the minimum-cut max-flow capacity [2].

Therefore, NC-based multicast for SCN framework becomes a

key means to support dynamic topology and be implemented

with low coding complexity. Two schemes, linear coding [3]

and nonlinear coding [4], can be used to perform the NC. In

this paper, as an effective method, only linear NC is consid-

ered out. On the other hand, with respect to the generation

manner of coding schemes, centralized coding [5], [6] and

distributed coding [7], [8] are carried out for NC. As the

overall topology is required at the central processing node, the

use of centralized NC becomes impractical. On the contrary,

distributed NC requires only the local topology information

and low encoding complexity [7], which is appropriate for

SCN multicast. Furthermore, NC can also be classified by

the generation manner of coding coefficients as randomized

coding and deterministic coding.

To support multicast with dynamic topology, another

method, namely the distributed randomized NC (RNC), is

proposed in [7], which is a combination of both distributed

and randmized coding schemes. As little overall topology

information is needed for RNC, the complexity in RNC mainly

depends on the number of coding links at intermediate nodes.

Since the optimal solution to minimize the number of coding

links is a non-deterministic polynomial-time hard (NP-hard)

problem [11], low complexity approaches are carried out

to provide the suboptimal solutions. In order to minimize

coding resource without reducing the multicast rate, a graph

decomposition technique is studied in [8], where the closed-

form results for multi-source networks are not provided. In

[12] and [13], optimization theory is carried out to minimize

the coding sources, yet high complexity is considered with

large scale networks. The genetic algorithm (GA) has been

considered in [14] to minimize the number of coding links

in static multicast NC, however, the static GA cannot provide

a proper solution with the maximized multicast rate when a

dynamic topology is employed.

To find NC solutions for dynamic multicast, erasure protec-

tion (EP) technique has been well studied. In this paper, the

GA approach in [14] is considered together with EP technique

in [9] to find NC solutions supporting dynamic multicast

in SCN with a low coding cost. This GA-based method is

regarded as the improved GA or IGA. By introducing EP

into the fitness test step of the IGA, the fitness of each

chromosome is considered for dynamic link failure tolerance,

while chormosomes of high fitness for EP test would be in

the child generation with a high probability. Comparing to

GA in [14], simulation results show that our proposed IGA

provides a better solution for dynamic network topology in

SCN multicast, while the number of coding links in IGA

remains the same level as that in the original GA.

The rest of the paper is organized as follows. In Section

II, the problem is formulated. The IGA-based RNC approach

for SCN multicast is developed in Section III, where trade-off

between overhead and performance is also studied. Section IV

presents simulation results. Finally, this paper is concluded in

Section V.

II. PROBLEM FORMULATION

In this paper, we consider the single source multicast

scenario, where a single source s ∈ V attempts to transmit

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data at rate h to a set of multiple sinks T ⊂ V . Here, Vdenotes the set of nodes participating in multicast and |T | = d.

Consider a multicast sub-graph and denote by G = (V,E) a

directed multi-graph, where E is the set of links and each link

contains unit capacity. Links with larger capacity are modeled

as multiple parallel unit-capacity links. Note that rate h is

considered to be achievable if all of d sinks are able to decode

the information sent by the source node. Moreover, only linear

NC is considered as the coding scheme in this paper.

In order to support dynamic topology for SCN, RNC is car-

ried out to perform encoding at source and intermediate nodes.

For RNC-based multicast, the h symbols {X1, X2, ..., Xh}transmitted by source are elements from infinite field Fq ,

where q = 2u, and each symbol is an element of u bits in Fq .

At the source node, for each out-coming link, a randomized

linear combination of the transmit symbols are generated and

then sent. Denote by d(l) and o(l) the destination and the

origin of link l, respectively, and by Yl the symbol transmitted

on link l. Then, we have

Yj =∑

d(l)=o(j)

ξl,jYl. (1)

In (1), coefficients ξl,j are randomly selected from Fq at each

node, and the operations of addition and multiplication are

also over Fq . For a certain sink node β, the symbol received

from a certain in-coming link, i.e., Zβ , is a randomized linear

combination of the symbols sent by the source. Let αj be the

randomized coding coefficients vector on the jth input link of

sink β, which is combined from h elements of Fq . Therefore,

as sink β has received the symbols and coding vectors from

all the input links, the coefficient matrix is given by

Σ = [α1 α2 ... αdvin]T, (2)

where dvin ≥ 1 denotes the in-degree of intermediate merging

node v.

Let a node with multiple incoming links be defined as a

merging node. As an output link of a merging node v, the

link l, is referred to as a coding link, if symbol transmitted on

l is the linear combination of information from the input links

of v. On the other hand, link l is referred to as a non-coding

link, if symbol transmitted on l is only the information form

one of the input links of v. Considering the limited computing

power of satellite, the RNC for SCN should also be optimized

according to the coding resource. The basic optimization goal

of RNC in SCN is to minimize the number of coding links in a

multicast network. Since the optimal solution to minimize the

number of coding links or coding nodes leads to an NP-hard

problem [11], other optimizations can be used as suboptimal

method. In [14], the efficient GA is carried out to minimize

coding links.

Besides minimizing the number of coding links, dynamic

topology is another important issue to be considered for RNC

in SCN. Note that the graphic representation of dynamic

topology is referred to as link failures in this paper. To

overcome the influence from link failures, EP is carried out

to protect the RNC frameworks from unsuccessful multicast.

Let the last k symbols of the h symbols sent by source be 0at source node beforehand, which is also notified by the sink

nodes. For sink β, the RNC for SCN is successful under the

condition that

rank(Σ) ≥ h− k (3)

holds, which becomes a preliminary thesis of applying EP in

NC-based multicast. A more sophisticated version of EP has

been used in [9]. For the sake of simplicity, in this paper, only

the preliminary version of EP is considered.

III. GENETIC RNC FOR DYNAMIC MULTICAST

In [14], a distributed genetic framework is studied by M.

Kim to minimize coding links. A main assumption of M.

Kim’s algorithm is that only fixed multicast rate is considered

for static network topology. Thus, it could only be used in

static multicast. However, a dynamic topology and link failures

are always considered in practical NC-based multicast, where

the original GA may not provide a proper RNC solution.

To protect NC solutions from unsuccessful multicast, EP

is carried out to deal with link failures. The basic concept

of EP has been introduced in Section II, while details of EP

technique can be found in [9]. To overcome the link failures,

in this section, we combine EP testing for genetic fitness

evaluation with GA, where an IGA architecture is proposed

for RNC in SCN.

A. Genetic RNC with EP

In this subsection, we introduce our proposed IGA in details.

The flow chart of the IGA is summarized in Table I. For the

sake of convenience, the original GA approach is referred to

as “GA” in the following contents. The proposed IGA method

is summarized as follows.

[S1] Preliminary Processing: At the source node, an “opti-

mizing initialization” signal is transmitted as the one in GA,

which includes target multicast rate h, initialized population

number N , size of infinite field q, crossover rate, and mutation

rate. Moreover, for the transmitted signal of IGA, the number

of packets used for EP (NEP) and the number of the maximum

tolerable failure times during the evaluations for multicast with

link failures (NmaxEP) are also included.

[S2] Population Initialization: At the merging node, a

Coding Vector in a distributed and randomized manner is gen-

eralized after the “optimizing initialization” signal is received.

Note that the generalization employed in IGA follows the same

principle as the one used in GA. For each of dvout outgoing

links at intermediate node v, a binary vector of length dvinis managed to indicate the states for a single chromosome.

Specifically, components 1 and 0 corresponding to input link

i and output j represent that symbols transmitted on output

link j with and without the information provided by input

link i, respectively. As a result, at each intermediate node,

Ndvindvout binary numbers are generated, where it is necessary

to set an “all 1” vector for the first chromosome. Note that in

GA, as the elements are all 0, low linear independence from

mathematical perspective is considered, which is regarded as

nothing is transmitted on that link from physical perspective.

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TABLE IFLOW OF IMPROVED GENETIC ALGORITHM

[S1] preliminary processing (sources)[S2] initialize population (merging node)[S3] improved forward evaluation (all nodes)[S4] improved backward evaluation (all nodes)[S5] improved fitness calculation (source)[S6] improved selection (sources)[S7] circulation ending judgment (sources) {

[S8] coordinate vector calculation (sources)[S9] genetic operation, crossover and mutation (merging nodes)[S10] improved forward evaluation (all nodes)[S11] improved backward evaluation (all nodes)[S12] improved fitness calculation (sources)[S13] improved selection (sources)

}[S14] final solution calculation (sources)

In IGA, we can avoid such a situation (i.e., “all 0”) in coding

vector generalization.

[S3][S10] Improved Forward Evaluation: Distributed RNC

is combined with EP to evaluate one chromosome as follows.

(1) Let the minimum-cut maximum-flow rate calculated by

Ford-Fulkerson algorithm be h, and the number of symbols

protected by EP be NEP. Then, for each chromosome, at the

intermediate node, a coding vector with h elements from the

infinite field Fq is transmitted. Assuming that the size of the

infinite field is 28, which is large enough to provide successful

multicast by RNC [14], the overhead cost of transmitting

coding coefficients in each packet is Nh Bytes.

(2) It is assumed that link failures within one multicast

session are able to be predicted, or at least the set of links

with higher failing possibility could be predicted. The above

assumption could be appropriate for SCN as ephemeris is

usually available at each node. Denote by Lfail the number

of failed links in one multicast session. At each intermediate

node, a coding vector with h elements for each links of the

Lfail links is additionally transmitted, during an improved

forward evaluation. For link j of the Lfail possible failure links,

we assume that the failure test information is available at both

head and tail nodes. In other words, as one of the Lfail links

is failed, the multicast fitness evaluations are carried out for

each chromosome with EP. Thus, the test operation requires

some coordination among different nodes.

(3) Consider one of the output links i at an intermediate

node v. Denote by αi, ξi,j , and ξi = [ξi,1, ξi,2, ..., ξi,dvin]T,

the coding vector transmitted on link i, the local coding

coefficient corresponding to v’s input link j, and the local

coding coefficient vector, respectively. Then, the expression

of RNC at a merging node is given by

αi =

dvin∑

j=1

αi,jξi,jαj , (4)

where the additions are operated among corresponding ele-

ments, and all the operations are over infinite field Fq . It

is noteworthy that the forward evaluation information for

chromosomes in one generation is transmitted using a single

packet with a coded multicast.

[S4][S11] Improved Backward Evaluation: In backward e-

valuation, the information of multicast fitness with and without

link failures and the corresponding number of coding links are

obtained at different terminals according to the order of

sinks ⇒ intermediate nodes ⇒ source node.

For each sink, fitness test is operated to calculate the rank

of N chromosomes’ global coding coefficient matrices. If the

rank is larger than (h−NEP), the corresponding chromosome

is considered with successful multicast.

When the feedback of information is carried out, at each

node, a fitness vector A combined of N binary components

and a fitness vector B combined of NLfail binary compo-

nents in the opposite direction of the forward evaluation are

transmitted. Each element in fitness vector A represents the

number of coding links for one chromosome, while each

element in fitness vector B represents if one chromosome can

successfully multicast in the corresponding scenario of link

failure. It is defined that if any sink cannot perform successful

decoding, the chromosome fails in the corresponding scenario.

Otherwise, the chromosome is referred to as success in the

corresponding scenario. Memory request for each component

in fitness vector A is the same as the one in GA, while the

memory request in fitness vector B is 1 bit per component.

Feedback framework is summarized as follows.

(1) For fitness vector A, at each sink, the components

corresponding to successful multicast are set to be “0”, while

the components corresponding to failed multicast are set to be

“infinite”. Fitness vector A is transmitted to every neighbor

of each sink.

(2) For fitness vector B, at each sink, the components

corresponding to successful multicast are set to be “1”, while

the components corresponding to failed multicast are set to be

“0”. Fitness vector B is transmitted to every neighbor of each

sink.

(3) For each non-merging node, the fitness vector A is the

sum of all the fitness vectors received. For each merging node,

the ith component of the fitness vector A is the sum of all

the fitness vectors received and the number of coding links.

At each intermediate node, the fitness vector A is transmitted

to a neighbor, while 0 vectors are transmitted to the other

neighbors in the opposite direction of the forward evaluation.

(4) The calculation of fitness vector B for each component

at intermediate nodes is based on the following method. In

the received fitness vector B, if there is one component that

equals to “0”, then the corresponding component at such

intermediate node is set to be “0”. Otherwise, in fitness

vector B, if all the components received are “1”, then the

corresponding component at such intermediate node is set to

be “1”. The operation in above is actually the binary “AND”

operation. At each intermediate node, the fitness vector B is

transmitted to all the neighbors in the opposite direction of

the forward evaluation. It is noteworthy that the network is

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assumed to be acyclic, which guarantees that each coding link

of a chromosome is only calculated once.

[S5][S12] Improved Fitness Calculation: For fitness calcu-

lation at source node, algebra addition is carried out over the

entire received fitness vector A. The calculation of fitness vec-

tor B at the source shares the same mechanism at intermediate

nodes. In fitness vector A, an infinite component indicates a

failed network coding based multicast, while a finite compo-

nent represents the corresponding number of coding links. In

fitness vector B, the “0” and “1” components denote a failed

or a successful NC multicast with corresponding link failure

scenarios, respectively.

[S6][S13] Improved Selection: For improved selection, the

un-fit populations are eliminated at source node according to

the calculated fitness vectors A and B. First of all, if an

“infinite” element appears in a chromosome’s fitness vector A,

the corresponding chromosome is deleted, which is the basic

operation in GA that leads to a smaller number of coding links

with the growth of generation. After that, the total number of

failed NC multicast of all link failure scenarios is assumed

to be Nfail, while the upper bound of acceptable number of

such failure is NmaxEP. Note that the chromosome is removed

from the population if Nfail > NmaxEP. As a new mechanism

in IGA, chromosomes are obtained with the better fitness of

link failures. Combining the original selection mechanism,

the chromosomes with lower number of coding links are

considered at the same time. The status of chromosomes

(remaining or removing) is transmitted with the next forward

evaluation to all intermediate nodes.

[S7] Circulation Ending Judgment: According to the pre-

determined rules, the termination of circulation is decided

at the source node (e.g., generation number reaching G, or

population number decreasing to P ).

[S8] Coordinate Vector Calculation: The chromosomes that

cross over in pairs are chosen at the source node, based on

the fitness of remaining chromosomes. Specifically, assuming

that the population number is T , T/2 random selections are

considered from the entire population, where 2 chromosomes

are generated as the child generation for each selection. The

information of child generation is referred to as coordinate

vector, which is transmitted in the next forward evaluation

to all coding nodes. The chromosomes with lower fitness are

selected to the child generation with a higher probability. Here,

it is assumed that the number of chromosome n’s coding

links is NLink(n), while the full number of coding links is

NMaxLink. Then, the probability of the child generation is

given by

Prs =NMaxLink −NLink(n) + δ

NMaxLink, (5)

where δ is a considerably small. Note that without δ, the

probability of a chromosome that has full number of coding

links becomes 0.

[S9] Genetic Operation, Crossover, and Mutation: The

crossover and mutation are performed at each intermediate

node according to the coordinate vector received. Here, either

block wise representation and operation or bit wise presenta-

tion and operation introduced in [14] can be employed. How-

ever, certain benefits are considered with the block operation,

which will be illustrated through simulations.

[S14] Final Solution Calculation: The best chromosome

based on two fitness vectors is selected at the source node,

when IGA reaches the circulation ending condition. Note that

a small chance is considered as all the chromosomes fail to

perform the successful multicast in any of the link failure

scenarios when the circulation ends, since IGA is randomized.

To solve this problem, it is worthy to storing the best-fitting

chromosome in each generation and transmit information of

this chromosome in the next forward evaluation.

B. Overhead and Performance Trade-off

Both IGA and GA require to transmit information during

forward evaluation. Let N, h, 28, and Lfail be the population

number, the target multicast rate, the size of infinite field

for the codebook of RNC, and the number of failure links

to be considered, respectively. The size of the transmitting

information overhead is given by

Nh(1 + Lfail) (Bytes), (6)

where the information for the scenario without link failures is

also considered. Note that the size of coordinate vector is not

included in (6) as it is relatively marginal.

There is a trade-off between the number of failure links (that

the final solution is able to overcome) and the communication

quality during the GA process, as evaluation information are

transmitted with effective multicast packet together.

Note that in this paper, two mechanisms are considered to

perform genetic operations, where a fixed population number

of each generation (T ) is used for the first one, while the

population is not enlarged with the growth of generation for

the second one. Specifically, for the second mechanism, circu-

lation may end when generation does not reach G. Although

the second mechanism may suffer from the performance degra-

dation of the final solution, the corresponding GA process

may cost less time compared to the first mechanism due to

packet overhead for the evaluation information decreases with

the growth of generation.

Then, in this paper, the proposed IGA with the first genetic

mechanism (fixed population number) is referred to as IGA-F,

while the one with the second genetic mechanism (decreasing

population number) is referred to as IGA-D. Analogously,

denote by GA-F and GA-D the original GA approach in [14]

with the first and second genetic mechanisms, respectively.

IV. SIMULATION RESULTS

In this section, we compare the performance of the proposed

IGA with the original GA in [14], using numerical results.

The network topology of Iridium system is considered in

simulations, which consists of 6 LEO polar orbits and each

orbit has 11 satellites. Within the same orbit, links between

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neighbor satellites remains stable, while links between neigh-

bor satellites in different orbits will be shut down before they

move over the polar area.Throughout the section, Roman numerals I to VI are used

to define as follows.I) Initializing population number;II) Maximum packet overhead (Bytes);III) Average population transmitted;IV) Average number of coding links in final solution;V) Average number of Nfail;VI) Average generation number when circulation ends.

A. Performance Comparison between GA-D and IGA-DWe first compare the performance between IGA-D and GA-

D. In simulation of IGA-D, we select an area covered by

a satellite randomly, and assume that the source is in that

area. Then, 3 other satellites are randomly selected under the

assumption that the sinks are among those 3 areas. There are

4 unit upward and downward links between each sink (source)

and the corresponding satellite. The Ford-Fulkerson algorithm

is considered for pre-processing to calculate target multicast

rate, where the routing algorithm in [15] is carried out to get

the multicast subgraph. After that, the Dijkstra algorithm is

carried out to delete all the circles, and meanwhile the target

rate by Ford-Fulkerson algorithm is generated. The target rate

in our case is defined as 3 units. The basic EP is used, where

NEP=1, and the number of links that may fail in this session

is 5. The full number of coding links is 24 in our case.To simulate GA-D, the steps in [14] are considered. The

exact multicast rate in GA-D is 3 units, while the exact

multicast rate in IGA-D is actually 2 units, as one unit is used

by EP. Let the mutation rate and crossover rate be 0.1 and 0.5,

respectively. The initializing population number is generated

from 10 to 100 by 10, where each scenario is calculated

30 times randomly. In IGA-D, chromosomes with successful

multicast in all the 5 link failure scenarios are selected as the

child generation, where the best-fitting chromosome searching

is operated for each generation. The circulation ends as the

population number is less then 2 or the maximum generation

number achieves 50. In Tables II and III, simulation results

of GA-D and IGA-D based on block operation are presented,

respectively.It is observed from Tables II and III that IGA-D outperforms

GA-D, in terms of the number of coding links and the fitness

of link failure. Specifically, IGA-D offers an average number

of 0 for Nfail to provide successful multicast in case of the

predetermined 5 link failure scenarios, while GA-D has an

average number of 5 for Nfail. It is noteworthy that although

IGA-D outperforms GA-D with respect to the number of

coding links, the actual multicast rate of IGA-D is one unit

less than that of GA-D, which implies that the performance

of minimizing the number of coding links are similar for both

of IGA-D and GA-D.

B. Performance Comparison between GA-F and IGA-FIn this subsection, we study the performance comparison

between GA-F and IGA-F. The same network topology and

TABLE IISIMULATION RESULTS OF GA-D BASED ON BLOCK OPERATION

I II III IV V VI

10 30 10.53 20.73 5.00 0.1720 60 24.30 18.07 4.93 1.1030 90 35.03 18.33 5.00 1.1040 120 48.70 16.83 4.90 1.7750 150 59.83 16.30 4.97 1.8360 180 75.00 14.93 4.87 2.5770 210 85.73 15.07 4.93 2.5380 240 97.77 14.63 4.90 2.4390 270 109.43 15.27 4.93 2.57100 300 122.07 14.70 4.97 2.80

TABLE IIISIMULATION RESULTS OF IGA-D BASED ON BLOCK OPERATION

I II III IV V VI

10 180 22.77 14.54 0 2.0720 360 24.30 11.90 0 3.5030 540 35.03 10.90 0 4.4740 720 48.70 10.63 0 4.9050 900 59.83 9.80 0 5.3360 1080 75.00 9.57 0 5.7770 1260 85.73 9.60 0 5.7380 1440 97.77 9.30 0 6.0090 1620 109.43 8.73 0 6.57100 1800 122.07 8.73 0 6.33

systems parameters in Section IV-A are employed to perform

the simulations. A tournament population number of 80%of initializing population number is considered, while the

maximum generation number is set to be 20. Performance of

GA-F and IGA-F based on block operation is shown in Tables

IV and V, respectively.

It is observed from Tables IV and V that IGA-F outperforms

GA-F with respect to the number of coding links and the

fitness of link failure. However, as shown in Section IV-A, they

exhibit the similar behavior to minimize the number of coding

links. On the other hand, it shows that IGA-F outperforms GA-

F in terms of the fitness of link failures. Specifically, IGA-F

has an average number of 0 for Nfail to provide successful

multicast, while GA-D has an average number of 4 to 5 for

Nfail. Moreover, IGA-F offers less number of coding links

than GA-F, as the exact multicast rate of IGA-F is two third

of that in GA-F.

C. Performance Comparison between Block and Bit BasedOperations

Block-wise and bit-wise genetic operations have been dis-

cussed in [14]. In this subsection, we compare the performance

between these two operations for the proposed approach

through simulations. The performance of block-based oper-

ation for IGA-D is shown in Tabel III, while the performance

of bit-based operation is shown in Table VI.

It is observed that performance of bit-based and block-based

operations are similar on the fitness of link failures. However,

block-based operation outperforms bit-based one at average

coding link number of the final solutions, which indicates that

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block-based operation is more appropriate for the proposed

IGA.

TABLE IVSIMULATION RESULTS OF GA-F BASED ON BLOCK OPERATION

I II III IV V VI

10 30 47.07 17.67 4.97 4.6320 60 273.87 9.47 4.97 15.8730 90 493.20 7.13 4.97 19.3040 120 680.00 6.33 5.00 20.0050 150 850.00 5.67 4.07 20.0060 180 1020.00 5.43 4.03 20.0070 210 1190.00 5.90 4.10 20.0080 240 1360.00 5.47 4.10 20.0090 270 1530.00 5.33 4.10 20.00100 300 1700.00 5.70 4.03 20.00

TABLE VSIMULATION RESULTS OF IGA-F BASED ON BLOCK OPERATION

I II III IV V VI

10 180 111.60 8.43 0 12.7020 360 272.80 6.50 0 15.8030 540 434.00 5.33 0 16.8340 720 639.47 4.10 0 18.7350 900 698.00 5.47 0 16.2060 1080 959.20 3.73 0 18.7370 1260 1119.07 3.90 0 18.7380 1440 1319.47 3.30 0 19.3790 1620 1347.60 4.63 0 17.47100 1800 1548.00 4.43 0 18.10

TABLE VISIMULATION RESULTS OF IGA-D BASED ON BIT OPERATION

I II IV V

10 180 15.30 020 360 13.67 030 540 12.23 040 720 12.33 050 900 12.07 060 1080 11.93 070 1260 11.27 080 1440 11.13 090 1620 10.73 0100 1800 11.17 0

D. Performance Comparison between IGA-F and IGA-D

Now, we compare the performance between IGA-F in Table

III and IGA-D in Table V. It is noteworthy that for both

IGA-F and IGA-D, as circulation ends, the average numbers

of generation cannot reach the maximum generation number,

where the convergence time is considered for two approaches.

It is observed that the average convergence time of IGA-D

is much less than that of IGA-F. Nevertheless, IGA-F offers

a smaller number of coding links, as more generations are

required to obtain the final solutions.

V. CONCLUDING REMARKS

In this paper, an improved distributed GA or IGA has

been proposed to minimize the number of coding links in

RNC-based multicast for dynamic SCN. To support dynamic

topology in multicast, EP has been carried out in the genetic

operations to select child generations with better fitness to

link failures. Simulation results showed that the proposed IGA

outperforms the original GA approach in [14] with respect

to the minimizing coding resource and supporting dynamic

network topology. In conclusion, our proposed IGA provides

good performance for RNC-based multicast in dynamic SCN,

where the number of coding links is minimized to reduce the

processing complexity on satellites.

ACKNOWLEDGEMENT

The authors acknowledge the financial support from the

National Natural Science Foundation of China under Grant

No. 61171069 and 60933012.

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