JU Journal of Information Technology (JIT), Vol. 2, June 2013
17
Application of Graph theory and Error
Correcting Code in VANETs
Mostofa Kamal Nasir and Shamim Al Mamun
Abstract—Vehicular Ad-Hoc Networks (VANETs) are fetching
more and more importance for researchers trying to find
solutions to improve safety and comfort of passenger and drivers.
VANET applications demand some form of concentration and
dealings with the driver, raising a legitimate concern on how safe
is their use while driving. Finding the best route towards a
destination in the complex and complicated roads network of the
modern cities is a major challenge in the attempt to improve
traffic conditions. This paper presents an application of graph
theory in VANET that offers a solution to this problem, based on
the Bellman-Ford algorithm and Dijktra algorithm.
This
application aims at reducing the total travel time towards a
destination by providing the best route. This paper also represent
how to correct error while transmitting information in VANET.
Index Terms— ITS, VANET, Graph, Hamming Code, Ad-hoc
and Routing.
V
I. INTRODUCTION
ANET is an emerging new communication technology
between nodes that they are beyond of the reach of
transmission of the radio is made in multi hops through
the intermediate nodes
contribution[5]. Moreover, the
topology of the networks can move dynamics due to
inoperative. On the other hand, the media without wire, into
the absence of infrastructures and the multi hops routing
transforms these networks in potentially drop the
performance[6]. The characteristics of the VANET require a
solution that integrates the routing protocols of ad-hoc
networks. Over the past ten years, research on this technology
has accelerated sharply due to possible commercial
implications and the likely impact on road. It arises over the
years many development organizations in order to give a
boost to the imminent standardization of protocols and devices
on the VANET.
It is possible to employ the VANET scenario in a graph
structure G = (V, E) with V equal to the set of vehicles and E
the set of physical links between nodes. The following figure
1, can realize a scenario of this type of networks.
which has attracted a lot of research attention from
academic community and industry. VANET is based on Wi-Fi
technology aim to offer vehicles the possibility of exchange of
information of any kind, whose nodes are mainly the vehicles
and characterized by high mobility. VANET is a special type
of mobile ad-hoc networks (MANET), are free to move
randomly and organize themselves arbitrarily various rapidly
and unpredictably topology[1]. Such a network may operate
alone or be connected to the Internet. VANET differ from the
simple MANET to the high mobility of nodes which causes
frequent and radical topology changes[2]. You may also
notice how the set of candidate applications to be developed
for this technology as well as available resources and
limitations due to development scenario, make the VANET
distinct area of environment of wireless communications[3].
The main characteristic of the VANET is the infrastructure
absence[4], such as access point or base stations, existing in
the Wi-Fi, WiMax, GSM or UMTS. The communication
Fig:-1: Vehicular Ad-hoc Network
Manuscript received February 9, 2013.
Mostofa Kamal Nasir, was with Dept. Of CSE, Mawlana Bhashani Science
and Technology University Santosh, Tangail, Bangladesh; (e-mail:
kamal.mostofa@ gmail.com).
Shamim Al Mamun, was with Institute of Information Technology,
Jahangirnagar University, Savar, Dhaka-1342, Bangladesh (e-mail:
[email protected]).
II.
APPLICATION OF VANET
The use of radio communications for the interaction between
vehicles to vehicles and vehicle to infrastructure is strongly
aim at the establishment of an ITS. The use of these
JU Journal of Information Technology (JIT), Vol. 2, June 2013
18
technologies is intended that as well as get real-time news
about what is happening on the road that was running. There
are three types of application of VANET that are safety, nonsafety and infotainment[7]. Applications for VANETs include
safety, traffic management, commercial ad dissemination,
driver assistance, web surfing, voice, gaming and infotainment
applications. A vehicle may contain multiple application units
which are built-in or portable communication devices running
a variety of these applications. These applications have
different delay, reliability, security, and bandwidth
requirements. Due to the mere size that a VANET might grow
into, with the millions of vehicles in each country, and due to
the diversity of non-safety vehicular applications desired by
various users, researchers have identified the necessity for a
new mobility mechanism, defined as network mobility, to
match these needs. Some major application of VANET are
reduction of traffic congestion, reduction of the emission of
exhaust gas due to traffic, prevention of road accidents and
improvement of the social role of the automobile. The vehicleto-vehicle communications, namely those for the exchange of
information between vehicles only, however, played a
dominant role much of the research produce then are still valid
today.
sequence number); flag of validity of the route (whether the
route is valid or invalid or repair); distance in number of hops
(hop count), list of precursors for that route, time of validity
(lifetime). If the node want to transfer a packet, first know
who is connected to the network and also needs to know the
topology of the network so that with the Bellman-Ford
algorithm, the shortest path can be calculated and then
proceed with the routing. The routing based on distance vector
is simple from the computational point of view and does not
require large quantities of memory. However, the protocol
requires a longer time than other protocols to establish a
connection between two nodes of a network.
III.
APPLICATION OF GRAPH IN VANET
Practical applications of graph theory are route planning in
different types of network. The research question for this
work is how efficiently graph theory can be use in route
planning for VANET. It makes use of this theory because
trivially think of the network as a graph, formed by the
vehicles as nodes and wireless links as sides. In essence, the
level of the protocol stack, called the network layer, which is
responsible for routing data will essentially implement the
techniques based on the Bellman-Ford algorithm[8] and
Dijktra algorithm[9]. Due to the high dynamic nature of the
VANET, find and maintain paths for routing packets is a
difficult task. There are few proposals to solve the problem
that have arises in the implementation of VANET routing
protocols. VANET routing can be classify as topology based,
position-based, cluster-based, broadcast and geocast. These
groups include whole range of different protocols with each
covering specific needs. In this work we will describe how
graph theory deployed on VANET. This technique essentially
consists in the transmission, by all the nodes, from a table or
vector, containing the connections that nodes have. Ultimately
each node, check your connections, create a table with one
record for each connection and exchange with their
neighbours, so updating your table. This ends when all nodes
have received all the tables. In addition, the table should be
submitted periodically or when there is a change of network
topology. In essence each node with the exchange of the
tables tends to know the topology of the network for which,
given the circumstance, it is possible to use the Bellman-Ford
algorithm for the calculation of the minimum path. In the
routing table stored by every node have the information about
the IP addresses of the destination node (destination IP);
sequence number of the destination node (destination
IV.
SCENARIO
In this paper we will precede with a demonstration of a real
scenario in which it is necessary to communicate through this
kind of networks. The following figure presents an
intersection of four roads where vehicles form a network and
if one vehicle wants to data passes to another through the
theoretical considerations set out above.
The yellow lines in the figure show the links that exist
between the various wireless nodes (vehicle), the yellow car
on the left has three connections, one with the blue car and the
other two with other cars cut off from the figure, for
completeness will be considered in the graph that represents
the network. Now going to consider only the necessary parts
of this scenario we get the following picture:
Fig-3: S Scenario network alone VANET
Graph representation of the scenario is:
Fig:-4: Graph representing the scenario
JU Journal of Information Technology (JIT), Vol. 2, June 2013
19
STEP 1: Creating tables from all nodes (S = Source, D = Destination, W = Weight).
S
1
Node1
D
W
3
5
S
2
Node2
D
W
3
3
S
3
3
3
Node3
D
1
2
4
W
5
3
4
S
4
4
Node4
D
W
3
4
5
6
Node5
D
4
6
9
8
S
5
5
5
5
W
6
6
3
4
Node6
D
5
4
7
S
6
6
6
W
6
5
2
Node7
D
W
6
2
S
7
S
8
Node8
D
W
5
4
STEP 2: The nodes communicate with their neighboring tables built by deleting duplicate records
S
1
3
3
Node1
D W
3
5
2
3
4
4
S
2
3
3
Node2
D W
3
3
1
5
4
4
S
3
3
3
Node3
D W
1
5
2
3
4
4
3
3
5
5
S
4
4
4
1
2
6
9
Node4
D W
3
4
5
6
6
5
5
3
6
3
S
5
5
5
5
4
4
6
6
Node5
D W
4
6
6
6
9
3
8
4
3
4
6
5
4
5
7
2
We consider that the propose scenario is form by the shown
nodes, also here the weight of each link be arbitrarily assigned
while in reality is calculate from a series of factors such as
vehicle speed, weather conditions etc. Each node (vehicle) has
a protocol stack consisting of layers from which we find the
physical layer is formed by hardware that allows wireless
connection, then the latter is located between the application
layer formed by a number of utilities and between them there
is the network layer that implements the protocols. We use the
distance vector and in turn make use of the Bellman-Ford
algorithm for the resolution of paths. The above graph show in
order to define a shortest path between two nodes for
exchange data, it will be necessary to implement the technique
of distance vector.
Finally we can find a routing table of each node with the
shortest path length like the following table:
From the above table it is clear that each node knows the
topology of the graph and by considering the case in which
one of them requires the transmission of a data to another
node will then process to the calculation of the shortest path
through the algorithm repeatedly invoke.
S
6
6
6
4
4
5
5
5
Node6
D W
5
6
4
5
7
2
3
4
5
6
4
6
9
3
8
4
S
7
6
6
Node7
D W
6
2
5
6
4
5
S
8
5
5
5
Node8
D W
5
4
4
6
6
6
9
3
S
9
Node9
D W
5
3
TABLE-1
SHORTEST PATH TABLE
All
nodes
S
D
W
1
3
5
2
3
3
3
4
4
4
5
6
4
6
5
5
6
6
5
8
4
5
9
3
6
7
2
Assume, the node 1 wants to transmit a packet to node 7, and
then it will display the table2 of minimum weights:
TABLE 2
MINIMUM WEIGHTS TABLE
Iter
N
N2
N3
N4
N5
N6
N7
N8
N9
h=
0
h=
1
h=
2
h=
3
h=
4
h=
5
0
∞
∞
∞
∞
∞
∞
∞
∞
0
∞
5 (1)
∞
∞
∞
∞
∞
∞
0
8 (3)
5 (1)
9 (3)
∞
∞
∞
∞
∞
0
8 (3)
5 (1)
9 (3)
15 (4)
14 (4)
∞
∞
∞
0
8 (3)
5 (1)
9 (3)
15 (4)
14 (4)
∞
19 (5)
18 (5)
0
8 (3)
5 (1)
9 (3)
15 (4)
14 (4)
16 (6)
19 (5)
18 (5)
JU Journal of Information Technology (JIT), Vol. 2, June 2013
TABLE 3:
HAMMING (7, 4) CODE
d1
d2
d3
d4
0
0
0
0
0
0
0
0
0
0
20
apparatuses available in this type of application does not have
large computational capacity in terms of processor and
memory, so it is a time consuming tasks of encoding and
decoding of a code and also make the communication between
devices on the network very slow. Hence the hamming code is
an option for the choice of error detection and correction[10].
Hamming code is linear, perfect, and capable of detecting and
correcting an error, for which it is possible to implement
directly into hardware encoding and decoding.
There are two methods to encode and decode by hamming,
first method with logical operations and second one is with
matrices G and H. For the Hamming code (7, 4), taking
advantage of the scheme in Table 2 is obtained the following
code words
p1
p2
d1
p3
d2
→
0
0
0
0
0
1
→
1
1
0
1
0
1
0
→
0
1
0
1
0
0
1
1
→
1
0
0
0
0
0
1
0
0
→
1
0
0
1
1
0
1
0
1
→
0
1
0
0
1
0
1
1
0
→
1
1
0
0
1
0
1
1
1
→
0
0
0
1
1
1
0
0
0
→
1
1
1
0
0
1
0
0
1
→
0
0
1
1
0
p3 = d 2 + d3 + d 4
1
0
1
0
→
1
0
1
1
0
1
0
1
1
→
0
1
1
0
0
The coverage of the parity bit can be defined by the following
diagram:
1
1
0
0
→
0
1
1
1
1
1
1
0
1
→
1
0
1
0
1
1
1
1
0
→
0
0
1
0
1
1
1
1
1
→
1
1
1
1
1
node from which it takes the weight calculation. From the
table and the graph we see that the node 1 wants to send a data
to node 7, it will know that the entire path weight is equal to
16 and the packet traverse through the node p= 1, 3,4,6,7.
From Table 1 shows that for Hamming (7, 4) is obtain as
follows.
p1 = d1 + d 2 + d3
p2 = d1 + d3 + d 4
Fig-5:- Coverage of parity bits
Asserting that the parity bit 1 (p1), the data bits d1, d2 and d4
means that it is able to correct an error of one of these bits.
The word p1, p2, p3, d1, d2, d3, d4 that must be coded to generate
other three bits k1, k2 and k3 defined as follows:
k1 = p1 + d1 + d 2 + d 4
k2 = p2 + d1 + d3 + d 4
k3 = p3 + d 2 + d3 + d 4
Fig-5: Graph of shortest paths for the scenario analyzed
I.
APPLICATION OF HAMMING CODE IN VANET
For the error correction and security application the channel
coding plays a vital role because the transmission channel may
be easily affected by noise. So it is necessary to consider
another aspect which concerns the application context, the
The location of the error in accordance with the following
table: This type of coding is extremely fast and simple to
implement due to the fact that requires the use of only XOR
gates. Possible circuit diagram is as follows:
JU Journal of Information Technology (JIT), Vol. 2, June 2013
21
The code words are all linear combinations of rows of the
matrix G. The three equations of equality contained in the
block X of the matrix G are
This write as c • H = 0 where H is a matrix 7×3 are called
parity matrix:
⎡0
⎢1
⎢
⎢1
⎢
H = ⎢1
⎢1
⎢
⎢0
⎢0
⎣
1 1⎤
0 1⎥⎥
1 0⎥
⎥ ⎡X ⎤
1 1⎥ = ⎢ ⎥
⎣I 3 ⎦
0 0⎥
⎥
1 0⎥
0 1⎥⎦
TABLE 5:
CORRECTION TABLE USING MATRIX G AND H
Fig-6:- Circuit diagram to detects of parity bits
I1
I2
I3
I4
0
0
0
0
p1 = i2 + i3 + i4
p2 = i1 + i3 + i4
p3 = i2 + i3 + i4
0
0
0
0
0
0
which are arranged in to form the 16 words of the code:
In total 2k =16 and 2n = 128 configurations are use for 7 bits,
and the code words differ in at least three positions. Then d =
3 and the code can detect all single and double errors and is
TABLE -4:
OUTPUT OF THE ENCODER
Second method with matrices G and H
The three-digit parity are different combinations of the four
digits of information in the following scheme:
K1
K2
K3
Meaning
0
0
0
No Error
Output
Encoder
0000000
0
0
1
Error in receiving bit 1(bit p1)
1000000
0
1
0
Error in receiving bit 2(bit p2)
0100000
0
1
1
Error in receiving bit3(bit p3)
0010000
1
0
0
Error in receiving bit4(bit p4)
0001000
1
0
1
Error in receiving bit5(bit p5)
0000100
1
1
0
Error in receiving bit6(bit p6)
0000010
1
1
1
Error in receiving bit7(bit p7)
0000001
I1
I2
I3
I4
P1
P2
P3
→
0
0
0
0
0
0
0
1
→
0
0
0
1
1
1
1
1
0
→
0
0
1
0
1
1
0
0
1
1
→
0
0
1
1
0
0
1
0
1
0
0
→
0
1
0
0
1
0
1
0
1
0
1
→
0
1
0
1
0
1
0
0
1
1
0
→
0
1
1
0
0
1
1
0
1
1
1
→
0
1
1
1
1
0
0
1
0
0
0
→
1
0
0
0
0
1
1
1
0
0
1
→
1
0
0
1
1
0
0
1
0
1
0
→
1
0
1
0
1
0
1
1
0
1
1
→
1
0
1
1
0
1
0
1
1
0
0
→
1
1
0
0
1
1
0
1
1
0
1
→
1
1
0
1
0
0
1
1
1
1
0
→
1
1
1
0
0
0
0
1
1
1
1
→
1
1
1
1
1
1
1
able to correct all. For the correction simply search the word
that differs in only one bit from the one received.
It coding in the form c = i • G where c is the vector of 7
elements transfer (code word), i is the vector of 4 elements of
the digits of information, G is the matrix generating size 4x7:
⎡1
⎢0
G=⎢
⎢0
⎢
⎣0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1⎤
1⎥⎥
= [I 4 × X ]
0⎥
⎥
1⎦
we can calculate the Syndrome y = c + e where e is the error
vector,
s = y.H = c.H + e.H = e.H
The Syndrome[11] is a vector of n - k = 3 components, which
says if the three rules are equal or less satisfied. The syndrome
may occur in 23 = 8 ways, while the possible configurations of
error (including the lack of errors) are 27 = 128. Easily occurs
that the same syndrome corresponds to 128/8 = 16 different
configurations of error. If the calculation of the Syndrome s
JU Journal of Information Technology (JIT), Vol. 2, June 2013
produces a null vector means that the received word is correct,
otherwise adding the coset leader, corresponding to the
obtained syndrome, the word received will be possible to
correct the error.
In this, the Standard Decoding Array (SDA) will be composed
as coset leaders syndrome[12] as follows: u u • H
For example, if the received word is w = 1110000 then
w • H = 000 which is the syndrome 0000000. From that
v = W + u = 1,110,000 + 0,000,000 = 1,110,000.
If the received word is w = 1110001 then w • H = 001 which
is the syndrome of 0,000,001.
From that
v = w + u =1110001 + 0000001 = 1110000.
The word received was correct.
II. CONCLUSION
The application of graph theory in routing of different
network is very common. In this research work we try to
adopt some graph theory for VANET. We consider VANET
as a dynamic graph where vehicle is a node of graph and link
among the vehicle think as an edge. The aim is to transmitting
and receiving the data among the vehicle by constructing a
network. Transmission and reception is occurring at network
layer and the techniques used for this based on Bellman-Ford
algorithm and Dijktra algorithm. Recent research confirms
that further technical and innovative protocols that enable data
transmission vehicle to vehicles with fewer problems, eg. data
loss, poor safety, etc. Regarding the channel coding, in real
application contexts using other types of codes such as
convolution codes or turbo codes can correct more than one
error and with high performance in terms of time required for
the encoding or decoding.
22
REFERENCES
[1]
D. R. Girinath and S. Selvan, "Vehicular adhoc network routing
protocols in realistic situations," in International Conference on Control,
Automation, Communication and Energy Conservation, INCACEC
2009, pp. 1-6.
[2] H. Menouar, et al., "Movement Prediction-Based Routing (MOPR)
Concept for Position-Based Routing in Vehicular Networks," in IEEE
66th Vehicular Technology Conference, VTC-2007, pp. 2101-2105.
[3] T. Hua-Wen, et al., "An on-demand routing protocol with backtracking
for mobile ad hoc networks," in IEEE Wireless Communications and
Networking Conference, WCNC 2004, pp. 1557-1562 Vol.3.
[4] J. e. o. H¨arri, et al., "Mobility Models for Vehicular Ad Hoc Networks:
A Survey and Taxonomy," EURECOM Sophia-Antipolis, 2006.
[5] C. Jingwen, et al., "A novel trusted routing scheme using attribute
similarity for VANET," in 3rd International Conference on Advanced
Computer Control (ICACC), 2011, pp. 427-430.
[6] L. Fan and W. Yu, "Routing in vehicular ad hoc networks: A survey,"
IEEE Vehicular Technology Magazine, vol. 2, pp. 12-22, 2007.
[7] Y. Toor, et al., "Vehicle Ad Hoc networks: applications and related
technical issues," IEEE Communications Surveys & Tutorials, vol. 10,
pp. 74-88, 2008.
[8] M. Ekpanyapong, et al., "Statistical Bellman-Ford algorithm with an
application to retiming," presented at the Proceedings of the 2006 Asia
and South Pacific Design Automation Conference, Yokohama, Japan,
2006.
[9] D. B. Johnson, "A Note on Dijkstra's Shortest Path Algorithm," J. ACM,
vol. 20, pp. 385-388, 1973.
[10] R. ma and S. Cheng, "Hamming coding for Multiple Sources," in IEEE
International Symposium on Information Theory Proceedings (ISIT),
2010, pp. 171-175.
[11] W. Fanglei and W. Jijie, "Syndrome testable design software package,
instrument and Syndrome testing system for sequential circuits," in Test
Symposium, 1992. (ATS '92), Proceedings., First Asian (Cat.
No.TH0458-0), 1992, pp. 218-222.
[12] T. Crimmins and H. Horwitz, "Mean-square-error optimum coset
leaders for group codes," IEEE Transactions on Information Theory,
vol. 16, pp. 429-432, 1970.
TABLE 6
SDA FOR THE HAMMING CODE(7,4)
Coset leaders u
Mostofa Kamal Nasir has been serving as an Assistant
Professor and
chairman
of the Department of
Computer Science and Engineering, Mawlana Bhashani
Science
and
Technology
University
(www.mbstu.ac.bd), Santosh, Tangail-1902, Field of
Interest is Vehicular Adhoc Network , Cloud
Computing, and Mobile Wireless Network
E-mail: [email protected]
Sindrome u H
0000000
000
1000000
011
0100000
101
0010000
110
0001000
111
0000100
100
0000010
010
0000001
001
Shamim Al Mamun has been serving as an Assistant
Professor in the Institute of Information Technology
(IIT), Jahangirnagar University (www.juniv.edu), Savar,
Dhaka. His research interest includes optical wireless
communications.
He is the member of IEEE Computer Society.
.