International Journal of Pure and Applied …COMMUNICATION IN VANET 1Senthamilselvan, 2Wahidabanu...

ANALYSIS OF SPAWN PROTOCOL AND EDFC ALGORITHM FOR SECURE

COMMUNICATION IN VANET

1Senthamilselvan, 2Wahidabanu

1Research Scholar, Bharath University, Chennai, Tamilnadu, India. 2Professor, Department of Electronics and Communication Engineering,

2Government College of Engineering, Thanjavur, Anna University, Chennai, Tamilnadu, India.

[email protected]

Abstract: In this paper wireless sensor networks

(WSN), are similar to wireless ad hoc networks in the

sense that they rely on wireless connectivity and

anomalous generation of networks so that sensor data

can be transported wirelessly. Here we propose a novel

decentralized implementation of fountain codes in

sensor networks, such that data can be encoded in a

completely distributed fashion. In our proposed

algorithms, a sensor disseminates its data to a random

subset of sensors in the network, while each sensor

only encodes data that it has received. As the collector

collects a sufficient number of encoded data blocks by

visiting more and more sensors, it is able to decode all

original data with an efficient decoding process

designed for fountain codes. The salient and original

contribution of this paper is a solution to disseminate

data from one sensor to others in an efficient and

scalable fashion with the help of Exact Decentralized

Fountain Codes (EDFC) along with the routing

SPAWN protocol. As has been well known,

conventional shortest-path routing algorithms require

each sensor to maintain a routing table with a size

proportional to the total number of sensors in the

network with their respective locations. Be that as it

may, we have observed that our decentralized

implementation of fountain codes does not require the

support of a generic layer of SPAWN routing protocol.

We propose SPAWN (Swarming Protocol for vehicular

Adhoc Wireless Networks), a simple cooperative

strategy for content delivery in future vehicular

networks. The issues involved in using a strategy from

the standpoint of Vehicular Adhoc networks. In this

paper, we propose a decentralized algorithm using

fountain codes to guarantee the persistence and

reliability of cached data on unreliable sensors. With

fountain codes, the collector is able to recover all data

as long as a sufficient number of sensors are alive. Our

theoretical analysis and simulation-based studies have

shown that, the EDFC algorithm maintains the level of

fault tolerances the original centralized fountain code,

while introducing lower overhead than naive random-

walk based implementation in the dissemination

process. Finally we bring that ad hoc relay wireless

networks, based on NS2 simulation technologies, have

potential for many prominent applications of this kind.

Keywords: Vehicular Networks (VANET), Content

Distribution, SPAWN Protocol, EDFC, Data

Dissemination, Broadcast, Adaptive Traffic Control

Scheme.

1. Introduction

Wireless sensor networks consist of unreliable and

energy-constrained sensors communicating with one

another wire-lessly. It has been a conventional

assumption that, in wireless sensor networks, measured

data in individual sensors are gathered (via data

aggregation) and processed en masse at powered

sinks with Internet connections [1]. There are, however,

at least two cases in which this assumption may not

realistically hold. First, if sensor networks consist of a

large number of sensors (in the order of tens of

thousands or higher), it may not be energy efficient to

gather measured data from sensors to sinks using data

aggregation. Second, if sensors are randomly deployed

in inaccessible geographical regions or environments, it

may not be feasible to deploy powered sinks as well.

Along with the industrial development and

technological progress, monitoring the environment

plays a very vital role. Many research works have been

built-up on monitoring systems that can replace

traditional systems in critical environments [2].

Wireless sensor networks (WSNs) are deployed to

an area of interest to sense phenomena. Wireless sensor

network is a type of ad-hoc networks that has the

ability of sensing and processing data collected from

the environment. These networks are comprised of

autonomous devices, called sensor nodes. Each sensor

has a buffer which can be divided into small slots.

Wireless Sensor Networks are recently applied in many

environmental applications such as measuring

temperature, humidity, salts or monitoring objects and

others.WSNs applications have common task, which is

environmental monitoring [3]. This task is realized by

using nodes to sense data from the environment and

International Journal of Pure and Applied MathematicsVolume 118 No. 20 2018, 1961-1973ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

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sends it to the base station. In all applications, we must

take into account to use an efficient data collection

approach. Wireless sensor networks have many

advantages but the main problem is the limitation of

node's resources. Due to that fact, any node may fail to

communicate with other nodes in the network or

disappear from the network due to accidental events in

harsh environments or due to battery depletion.

Figure 1. (a) WSN is randomly Distributed in a field.

A node S is Source node and Flood its data to its

neighboring nodes D and D unicast of its Data

to one of its neighbors and so on

In this paper, we propose a best Shortest Path

algorithm which is called a Exact Decentralized

Fountain Codes (EDFC) along with SPAWN protocol

depends on unicasting instead of multicasting to

provide controlled-redundancy of data through the

network [4]. A consequence of these modifications, the

number of created messages and the energy

consumption are reduced. Also, taking into account the

buffer status whether it is empty or not. If it is full, it

will cancel the operation to reduce processing load on

the nodes. The proposed model is applied in large-scale

wireless sensor network where these nodes are

randomly distributed in the serviced environment.

2. Preliminaries

2.1 The Spawn Protocol

SPAWN has the same generic structure of any

swarming protocol. Peers downloading a file form a

mesh and exchange pieces of the file amongst

themselves. However the wireless setting of SPAWN,

characterized by limited capacity, intermittent

connectivity and high degree of churn in nodes requires

it to adapt in specific ways. As we shall see, this

particular scenario provides a compelling incentive for

individual nodes to cooperate while accessing the

Internet. Figure I.a describes the basic operation of the

SPAWN protocol.

Figure 1. (a) Evolution of a file in a node using SPAWN Protocol

(1) A car arrives in the range of a gateway, (2)

initiates a download (3) download a piece of the file.

(4) After getting out of range, (5) starts to gossip with

its neighbours about content availability and (6)

exchanges pieces of the file, thereby getting a larger

portion of the file as opposed to waiting for the next

gateway to resume the download

International Journal of Pure and Applied Mathematics Special Issue

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2.2 Peer Discovery

There are several components to the operation of the

SPAWN protocol, but for brevity we just focus on Peer

Discovery. We propose a decentralized mechanism for

peer discovery. We utilize the broadcast medium of the

wireless channel to gossip information about the

content availability at neighbours. In a mobile

environment, gossiping provides a way to incorporate

location awareness into the peer discovery scheme [3].

Since TCP over multiple-hops suffers quite

Figure 1. (b) Gossip Message format, here ni denotes

the address the address of the ith node in the path that

the gossip message traversed

Dramatically in the ad-hoc wireless scenario [4], a

node is better off using unicast TCP connections with

near-by peers. Gossiping helps here in constructing

overlapping meshes of physically close peers for

exchanging pieces of the file. Figure shows the

structure of a Gossip message in SPAWN.

2.3 Coded Cooperative Data Transmission

A. Spurring Example

In this work, a basic bidirectional transmission

convention utilizing system coding is proposed and

computerized Fountain codes; Network Simulator

(NS2) is a very adaptable, quickest simulator for large

heterogeneous system that supports the wired and

wireless network protocol. In the proposed protocols,

the XOR operation is utilized for the first information.

Furthermore, we likewise consider the bidirectional

transmission plot with multi-transfer. Versatile

methodologies focus on recreating established systems

by mitigating detachment, data transfer capacity decline

and constrained correspondence extend utilizing nature

of administration and steering components. System

coding is less inclined to a solitary purpose of

disappointment. A functional utilization of system

coding has been exhibited in [3] for large scale content

partaking in the wired Internet. In the wake of getting

adequate number of pieces related with directly

autonomous coefficients, an accepting hub can interpret

the squares.

B. Cooperative Downloading

Cooperative downloading is a reasonable and

successful contrasting option to reflect servers and

substance conveyance systems. Bit Torrent is a

standout amongst the most mainstream helpful

conveyed downloading conventions being used today.

It depends on the rule of swarming, wherein the

coveted document is downloaded in parallel from

various participating associates. The parallel download

approach utilized by Bit Torrent empowers it to

accomplish enhanced execution when contrasted with

other shared frameworks, with the current advances in

remote correspondence innovations and the expansive

development in the quantity of versatile clients, content

appropriation in portable remote situations is picking

up significance. A few directing methodologies

appropriate for distributed record sharing over MANET

have been examined in [4].

VANET (Vehicular Adhoc Networks) is an

uncommon sort of MANET (Metro Politian Adhoc

Networks) where the way, direction and speeds of the

hubs are very deterministic. Also, the VANET hubs

frequently cross stationary passages from which they

can exchange information. Likewise the rapid of the

hubs in VANET (Vehicular Adhoc Network) causes a

few disengagements and consequent course breakages,

which impede the operation of shared conventions that

depend on steering for finding the associates. For

VANETs, where the hubs move at a fast and topology

changes quickly, vehicles can just download

incomplete information from the passages before

disengagement. In this manner it is in a perfect world

suited possibility for agreeable substance sharing

frameworks. Notwithstanding, most existing shared

swarming conventions are intended for settled topology

based systems. Because of the changing topology and

high versatility, executing these plans in VANETs is

exceptionally testing [5]. Specifically, conceiving

associate and substance choice procedures for sharing

is very intricate. The SPAWN convention utilizes a talk

system to promote the piece list every hub has and

considers while choosing substance among peers.

Besides, utilizing the communicate idea of remote

media empowers SPAWN to lessen excess

transmissions.

C. Unequal Packet Importance

This fact lies at the heart of multimedia streaming: the

unequal importance of packets is used to guide

prioritized transmission over a network. Depending on

the transmission scenario, available differentiation

mechanisms are used to ensure that the most important

packets of a particular stream are given priority, thus

providing a graceful degradation in the presence of

adverse network conditions [6]. One challenge that

arises from this fundamental property of multimedia,

with respect to network coding, is that network coding,

so far, has been agnostic to the content of the packets

that are coded together.

In inter-session network coding, the goal is to mix

together several packets from different flows, thus


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increasing the information per packet and eventually

the throughput. However, for media streaming it is not

only the quantity of delivered packets that matters but

also their quality.

Using an analogy to Redundant Array of

Independent Disks (RAID) in computer systems [5], we

explain a number of alternatives that motivate the credo

of this paper.

2.4 Why Fountain Codes?

Similar to RAID 1 disk arrays (mirrored disks), the first

alternative is to utilize other sensors to “mirror” or

“replicate” data from a particular sensor. After such

mirroring, when a sensor fails, the data it has gathered

before its failure can be retrieved from other “backup”

sensors, improving data persistence and fault tolerance.

As an example of existing work, Hass et al. [6] have

addressed the fault tolerance of distributed location

databases by using replication. It is easy to see that a

large number of replicas are required to maintain a

certain degree of fault tolerance, when the failure rate

of sensors increases. Analogous to RAID 6 disk arrays

(in which Reed-Solomon codes are used), error-

correcting codes may be used to alleviate the

disadvantages of mirroring data. It has also been

proposed that Reed-Solomon and LDPC codes may be

used towards building reliable and distributed data

storage systems over wide-area networks [7], [8]. There

is one catch, however, in that the encoding and

decoding processes of conventional error-correcting

codes have to be implemented in a centralized fashion.

To make good use of them in sensor networks, all data

have to be delivered to a centralized sensor node, which

encodes them and re-distributes the encoded data

within the network. This is obviously not realistic, in

that a single sensor is not assumed to have sufficient

energy or computational power to encode all the data

received, it suffers from a single point of failure and the

communication cost of forwarding all data to a central

node for encoding is prohibitive.

In wireless sensor networks, where data are

generated from different sensors in a distributed way, it

has been proposed in existing work that random linear

codes may be used to improve the degree of fault

tolerance [9], [10], [11] by decentralized encoding.

Random linear codes are also investigated in distributed

networked storage [12]. Unfortunately, similar to Reed-

Solomon codes, the decoding process of random linear

codes is computationally expensive, with a decoding

complexity of O (K3), where K is the number of data

blocks1 to be encoded. We believe that the superior

decoding complexity of fountain codes — O (K lnK)

— may come to our rescue, even though the encoding

process of fountain codes is also centralized in coding

literature.

We briefly introduce LT codes [4], the first

fountain codes proposed in the coding literature. We

use LT codes in our subsequent discussions and

performance evaluation. Fountain codes are rateless in

the sense that the numbers of encoded data blocks that

can be generated from the original data blocks are

potentially unlimited, and the encoded blocks can be

computed on the fly. Therefore, fountain codes are

especially suitable for erasure channels where the

erasure probabilities are unknown. Fountain codes also

enjoy excellent computational efficiency for both

encoding and decoding processes. In LT codes, it has

been shown that K source blocks can be decoded from

any subset of K + O (√K ln2(K/_)) encoded blocks with

probability 1−_. The encoding and the decoding

complexity are both K ln (K/_). The number of source

blocks that are used to generate an encoded block is

referred to as the degree of the encoded block. The

degree distribution of encoded blocks in LT codes

follows the Robust Soliton.


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The encoder of LT codes generates each encoded

block independently by first randomly choosing the

degree d of an encoded block from the Robust Soliton

distribution, and then chooses d distinct blocks from K

source blocks uniformly at random[13]. The encoded

block is the bitwise exclusive-or (XOR) of the d source

blocks. The decoding process utilizes the Belief

Propagation (BP) algorithm, which intuitively is more

computationally efficient than the general matrix

inversion process, since degree-one encoded blocks are

used to activate a cascading backward cancellation

process, producing more degree-one encoded blocks.

2.5 Data Access Through decentralized Fountain

Codes

We propose to use decentralized fountain codes to

efficiently maintain data persistence in large-scale

sensor networks. In this section, we first show how

fountain codes can be used to access sensed data in a

decentralized fashion, then present two data

dissemination algorithms based on “one-way” random

walks.

A. Decentralized Fountain Codes

We model a sensor network as a graph G = (V, E),

where V represents the set of sensors and E represents

the set of links. Let N denote the total number of nodes

in V .We assume that a subset of K nodes, called

sensing nodes, monitor the environment and generate

sensed data to be disseminated. The sensing nodes are

able to cache their data on all other nodes (referred to

as caching nodes), such that their data are available

even when they fail or otherwise become unavailable

[14],[15]. In fountain codes, each encoded block is the

XOR combination of a number of source blocks,

randomly selected based on a special distribution, such

as the Robust Soliton distribution in LT codes.

To take advantage of fountain codes in sensor

networks, one way to design a straightforward

implementation is based on “two-way” random walks

as follows. A node first generates the code-degree d

from the Robust Soliton distribution, where the code-

degree of a node refers to the degree of the encoded

block cached on the node. This node may then request

the source blocks from d distinct sensing nodes,

uniformly distributed in the K sensing nodes, using

random walks to deliver these requests. All d random-

walk paths to the d sensing nodes are recorded in the

network. Upon receiving the requests, the d sensing

nodes disseminate their source blocks through the

previous recorded d random-walk paths to the node.

Finally, this node encodes the d received source blocks

for later retrieval.

However, we believe that such “two-way”

random-walk paths are rigid, not realistic and

undesirable. First, sending data along the recorded

random-walk paths makes the more demanding

assumptions of bi-directional wireless links, which is

sometimes not the case in reality. Second, to record

random walk paths in the network, sensors have to

maintain forwarding tables with the size proportional to

the number of random walks in the network. Third,

sensor networks are inherently unreliable, and random-

walk paths may be broken or lost if any of the sensors

on these paths fails during the transmission. Finally,

excessive overhead of transmitting control messages is

unavoidable when selecting random sensing nodes and

additional random walks have to be activated if the

selected node is not a sensing node, or a duplicate of

previous selections. In this paper, we seek to construct

decentralized fountain codes with only one traversal of

random walks, from sensing nodes to the caching nodes

that encode and store the source blocks. Though

nontrivial to design, such “one-way” random walks are

much more scalable, completely stateless, and have

avoided all the overhead and drawbacks of the

aforementioned “two-way” walks. Our algorithms are

intuitively justified based on the following rationale. If

the steady-state probabilities of two nodes are different

in the random-walk Markov chain, e.g., _i > _j, random


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walks guarantee that each source block has a higher

probability to stop on node i than on node j. Therefore,

node i will receive more distinct source blocks than

node j, which results in node i obtaining a higher code-

degree than node j[16].

Henceforth, we propose two heuristic algorithms

to guarantee the Robust Soliton distribution of LT

codes, in a completely decentralized fashion, and using

“one-way” random walks. These two algorithms are

called Exact Decentralized Fountain Codes (EDFC)

and Approximate Decentralized Fountain Codes

(ADFC), since EDFC achieves the same coding

performance of the original centralized LT codes,

whereas ADFC offers degraded performance with the

tradeoff of lower dissemination cost. For both

algorithms, we assume that, before execution, every

node has been pre-programmed with the number of

sensing nodes K, the total number of nodes N, and the

Robust Soliton distribution. All these information can

be broadcast to every node when the sensor network is

initialized. However, K and N may decrease with time

when some sensors die. In Section V, we will show that

EDFC and ADFC do not require each node to know the

precise value of K and N.

B. Exact Decentralized Fountain Codes (EDFC)

Because of the randomization introduced by random

walks the number of distinct source blocks received by

a node is uncertain and usually does not equal the code-

degree of this node. EDFC attempts to overcome such

challenge and guarantee the Robust Soliton degree

distribution. It is based on the observation that we may

disseminate more than d source blocks on each node,

but encode only d of them, where d is the code-degree

of a node. Assume each node receives xd ・ d source

blocks on average, where xd is called the redundancy

coefficient. By choosing a sufficiently large xd, the

probability that such number of source blocks comprise

less than d distinct source blocks can be made

arbitrarily small. Therefore, the distribution of the

number of source blocks used in encoding can be

arbitrarily close to the Robust Soliton degree

distribution. Note that, through the arguments of

symmetry, xd should depend only on d.

Algorithm Description: EDFC proceeds as follows.

Initially, each node generates its code-degree from the

Robust Soliton distribution. Next, each sensing node

sends out its source block by random walks. As long as

a source block stops at a node at the end of the random

walk, this node will store this source block. After all

source blocks are disseminated, each node generates its

encoded block from a subset of received source blocks

with cardinality equal to its code degree. Although the

algorithm is simple, two critical elements need to be

computed and are derived in details in the following:

the number of random walks launched from each

sensing node and the probabilistic forwarding tables for

random walks.

The number of random walks: It is clear that the

expected number of nodes with code-degree d in the

network is Nµ(d), where µ(d), the fraction of code-

degree d nodes, is defined in (1). Each code-degree d

node receives xdd source blocks. Therefore, the total

number of source blocks received in the network is

∑kd=1Nµ(d)xd d which also equals bK, the number of

source blocks disseminated from the K sensing nodes,

where b denotes the number of random walks from

each sensing node. Hence, we have

Figure 2. (a) Chosen Degree Distribution (b) Actual Degree Distribution

The actual degree distribution has a shape similar

to the Robust Soliton distribution as shown in Fig. 1,

though not exactly the same. Because of this

inaccuracy, we expect that the collector needs to collect

more encoded blocks than in EDFC to successfully

decode. However, further numerical computation


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reveals that the overhead ratio g2 is only 0.2326. This

suggests that far less transmission cost is required to

disseminate source blocks than EDFC or the ideal

algorithm.

3. Gossiping Schemes & Communication

Overhead In Spawn Protocol

Gossiping Schemes

We evaluate various gossiping schemes which we

describe in this section.

Probabilistic Spawn

Spawners not interested in the particular file listen to

gossip messages of that file and forward them with a

low probability. Interested Spawners listen to those

gossip messages and forward them with a higher

probability after stamping the route-list of the packet

with their own id. An Interested spawner who is

currently downloading a file will generate Gossip

messages on completion of downloading a new piece

Rate-Limited Spawn

Each Spawner maintains two caches, a Non-Interested

cache of gossip messages about files that it is not

interested in, and an interested cache. Periodically,

gossip messages are picked up from one of the caches

and re-broadcasted (without updating the origination

time-stamp). Interested cache messages are selected at

a higher frequency. The decision about which message

to select from a particular cache can be made in

different ways.

� Rate-Limited-Recent Spawn: The gossip

message with the most recent origination time-stamp is

forwarded.

� Rate-Limited-Random Spawn: The gossip

message is selected at random from the relevant table.

Figure 3. Local-file piece Evolution

Communication Overhead

We examine three metrics under different network

sizes: Message Cost, Energy Cost, and Termination

Time. In Figure.3, we compare the total message cost

of our ECPC algorithm with EDFC and RCDS. In

general, the total message cost of ECPC is much lower

than other two approaches. And the message cost

difference increases faster as the network size scales

up. This is because that the dissemination in EDFC and

RCDS rely on the random walks, which is at least O(n2

_ polylogn), while the dissemination of ECPC only

consumes O(1) message per node. In particular, the

message cost of ECPC stays under 1; 000 under the

network size of 500. RCDS requires 2; 000; 000

messages in total to achieve the expected code degree

distribution across the network. Approximately 1; 200;

000 messages are consumed in EDFC.


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Figure 4. Communication Overhead: Total Message Cost

Since the packet transmission power is

dynamically adjusted in ECPC, energy costs for every

message broadcasting indeed vary dramatically. Thus,

reduction of message cost does not guarantee better

energy efficiency. We consider the total energy

consumption required for protocol, avoiding the

arguable concerns about the energy efficiency of

proposed ECPC. In Figure 6, the measurement of total

energy ratio between RCDS and ECPC, EDFC and

ECPC are presented respectively. For RCDS, the

energy ratio to ECPC could rise from about 20 (N =

100) to 100 (N = 500). Compared with RCDS, EDFC

decreases the number of random walks for each raw

data by reducing the exact condition to approximated

conditions. Hence, the maximum energy ratio between

EDFC and ECPC is about 60 under network size

500[16],[17]. The reason behind this significant energy

saving is that ECPC only adopts single-hop packet

broadcasting to ensure the final degree distribution is

satisfied among encoded and stored packets. Though

transmission power may be increased to cover more

neighbors in one broadcasting attempt, the expected Tx

power value throughout multi-round encoding process

is closer to P’. In terms of time for data dissemination,

ECPC method terminates at a short time period, e.g.

less than 10 time units under varying network sizes,

shown in Figure.3 in EDFC and RCDS, each source

node can initiate its own random walk at the same time,

as far as there is no media access conflict.

Figure 5. Total Energy consumption distributed data storage Schemes

Their termination of encoding did cost a

considerable time, with 200 time units for EDFC and

400 time units for RCDS respectively under the

network size of 500.


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Figure 6. Communication Overhead: Total Termination Time

Data Recovery Ratio

We study the decoding performance in terms of data

recovery ratio. Data recovery ratio denotes the

percentage of original data recovered after decoding.

The node has a failure probability of 10%. First, we

observe that the recovery ratio of ECPC has 40% at the

network size 50, but, increase to over 90% as network

size increases beyond the 400. In experiment, ECPC

select ß 0.07 from range (0, 0.1) to maintain the

randomness properties. The decoding performance of

EDFC and RCDS also experience an increasing trend

as network size grows. The reason for their poor

performance is that nodes can fail when the random

walk is still going. It may result in a stop condition for

the random walk on that failure node. Thus, the

resultant degree distribution is not the best match of

expected code degree distribution. In particular, the

data recovery ratio is only 67% and 62% for EDFC and

RCDS respectively.

Figure 7. The decoding performance under varying network sizes: MAX data

recovery ratio for different network sizes

We examine the data recovery ratio for 500 nodes

along the axis of experiment time elapsed in Figure 6.

We keep node failure probability as 10%. Since we

repeat the experiments 50 times with node failure occur

randomly each time, the overall failure occurrence time

is also uniformly distributed. Since EDFC and RCDS

need 300 to 400 time units to 117 perform the random

walk based data dissemination, the recovery ratio is 0

during the early time period of data dissemination for

both EDFC and RCDS. On the other hand, ECPC

terminates in a short time period, making data recovery

possible even in a early stage, like at the time of 100

time units. The peak recovery ratio of EDFC can only

reach 67% is due to the node failure occur during the


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data dissemination. As the time elapses, the recovery

ratios of three approaches decrease. It is because that

more nodes fail as time elapses. However, the decoding

performance of ECPC degrades much less than other

two approaches.

4. Performance Evaluation

To evaluate the effectiveness and performance of the

proposed algorithms, we have implemented both the

original centralized and the decentralized

implementations of fountain codes. The centralized

implementation of fountain codes (LT codes in this

case) consists of about 1000 lines of C++ code, with

fully optimized implementation of the encoding and

decoding algorithms. The decentralized implementation

of fountain codes with random walks in wireless sensor

networks is also simulated with C++. We use the two-

dimensional Geometric Random Graph, G2(N, r), as

the topological model, where N sensors are uniformly

distributed on a unit disc. Besides the total number of

sensors N and the radio range r of each node, an

additional parameter special to our algorithms is the

total number of sensing nodes K. The K sensing nodes

are uniformly distributed among the N sensors. We set

K = 10000, N = 20000, and r = 0.033 in most

experiments with exceptions explicitly stated. The

average number of neighbors for each node is 21 in

such a setting. To mitigate randomness, we show, for

each data point in all figures, the average and the 95%

confidence interval from 10 independent experiments.

Figure 8. Decoding Ratio of Centralized

Fountain Codes

Communication Cost and Decoding Ratio

We examine two main performance metrics, the

communication cost and the decoding ratio. The

communication cost, governed by the length of random

walks and the number of random walks from a sensing

node, represents the system efficiency. The decoding

ratio denotes the number of nodes that need to be

visited by a collector for decoding, normalized by the

number of sensing nodes. It reflects the degree of fault

tolerance of the network, since the fewer nodes are

required for a collector to visit in order to decode all

data, a higher percentage of nodes are allowed to fail.

We compare the performance of EDFC and ADFC with

the two-way algorithm as described in Section III-A.

First, the impact of random-walk lengths on the

decoding ratio is studied. Fig. 3 plots the decoding ratio

vs. the length of random walks for the three algorithms.

In general, the decoding ratio decreases when the

length of random walks increases, and stay stationary

on a certain value if the length exceeds a threshold for

all three algorithms. This is because the random walks

approach the steady-state distribution when their

lengths increase. In particular, for EDFC, Fig. 3 shows

that when the Random-walk length is larger than 500,

the decoding ratio stays stationary around 1.05, which

implies that EDFC achieves the same decoding

performance of the original centralized fountain codes.

For ADFC, Fig. 3 shows that when the random-

walk length is larger than 50, the decoding ratio stays

around 1.6, higher than what is achievable by EDFC.

This is because the actual degree distribution of ADFC

is slightly different from the Robust Soliton

distribution. However, ADFC requires much lower cost

in data dissemination as we will show later. For the

two-way algorithm, the length of random walks shown

in Fig. 3 is the one-way length. The decoding ratio of

the two-way algorithm is less than EDFC and ADFC

when the random-walk length is smaller than 500. This

is because the uniform steady-state distribution in the

two-way algorithm is easier to be achieved than the

biased steady-state distribution of EDFC and ADFC

[13],[16]. Yet, this does not imply that the two-way

algorithm has lower transmission cost than EDFC and

ADFC for a given decoding ratio, since its additional

random walk overhead due to selecting a node that is

not a sensing node, or a duplicate of previous

selections, is not reflected in the length of random

walks shown in the figure.

Next, we compare the communication costs of

these three algorithms. For EDFC and the two-way

algorithm, we record their minimal transmission costs

when their decoding ratios are similar to centralized

fountain codes. For ADFC, we record its minimal

transmission cost when its decoding ratio is stabilized

on some value (e.g., 1.6 in Fig. 3). In addition, for the

two way algorithm, the transmission cost of control

messages in selecting random nodes is considered the

same as the cost in data transmission. Fig. 4 shows that

the dissemination cost of ADFC is much lower than

EDFC and the two-way algorithm [16].

This is due to two reasons. First, the required

length of random walks of ADFC is shorter than both

EDFC and the two-way algorithm as shown in Fig. 3.

Second, for ADFC, the number of random walks from


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each sensing node is significantly smaller than that of

EDFC and the two-way algorithm. For example, in the

simulation setting of Fig. 3, we observe this number is

6 and 50 for ADFC and EDFC, respectively.

Figure 9. The ratio of dissemination cost of EDFC

and ADFC to that of two-way algorithm

Furthermore, Fig. 8 shows that the cost ratio of

EDFC to the two-way algorithm starts from 0.2 and

increases slowly to 0.8, as the number of source blocks

increases from 1000 to 20000. This cost ratio increases

sub-linearly with the number of source blocks, since as

shown in Theorem 1, the redundancy coefficient for

EDFC grows sub-linearly with the number of source

blocks. However, Fig. 4 shows that EDFC significantly

outperforms the two-way algorithm for practical sensor

networks with less than 20000 nodes. Furthermore, we

emphasize that, as explained in Section III-A, EDFC is

easier to implement and avoids the many disadvantages

of the two way algorithm. Furthermore, both figures

suggest that EDFC is more robust than ADFC with

overestimation of N or K.

5. Conclusion

Wireless ad-hoc networks may need to operate in the

absence of sinks in remote geographical zone. In this

paper, we seek to improve the fault tolerance and

persistence of data in sensor networks by proposing a

decentralized implementation of fountain codes, which

efficiently disseminates original data throughout the

network with SPAWN. We are attracted by the superior

decoding performance and low decoding complexity of

fountain codes as the number of nodes in the sensor

network scales up, especially when compared to

alternative coding techniques such as random linear

codes and ADFC. We have shown that simulation

result, as well as in actual experiments, the EDFC

algorithm is able to provide near-optimal fault tolerance

with minimal demand on local storage.

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