**International Journal of Emerging Technology and Advanced Engineering **

**Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 9, Issue 10, October 2019)**

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## Reducing Error in Packet Switched Wide Area Networks Using

## a Modified Method

### Ogbimi, Voke Francis

*Department of Information Technology, University of Debrecen, Debrecen, Hungary *

**Abstract-- Modelling of discrete systems such as ****communication networks have previously and even today **
**receive much attention from different scientific communities **
**in both academia and modern industries. Scientific, economic **
**and technical progress and the increasing complexity of these **
**systems raise more new challenges and new problems for **
**researchers. In addition, since imperfections in the simulation **
**process can be negative factors in time, cost and operational **
**efficiency in the development of a new or existing systems. It **
**is necessary to use effective and suitable methods that aid the **
**researcher in the simulation process when they allow the **
**evaluation of the performance of a new or existing system for **
**example, the evaluation new possible features in the system **
**that must achieve new goals. **

**A model was proposed and it solved the problem of error in **
**packet switched wide area networks by looking at the effect of **
**the number of erased channels on packet error probability of **
**the schemes. In this problem the effect on the number of **
**erasures on number of messages in relation to packet error **
**probability was investigated. Messages are always sent and **
**acknowledged. When messages are sent and there is no **
**acknowledgement, it means that error has occurred. **
**Equations were presented to show the effect of erasures and to **
**minimize the error despite the number of erasures in the **
**network. **

**Keywords: Error, Dynamic Erasure. Packet Switched, ****Modified Method. Wide Area Networks **

I. INTRODUCTION

The data communication industry created a framework that is capable of delivering cheap bandwidth in high volumes in the 1990s during the expansion of the internet. Bandwidth became surplus to the extent that even the effect of Meltcalfe’s law (the network growth is inversely proportional to the number of users square in a given area) were inadequate to consume the available bandwidth for years [1]. The result of bandwidth rapid expansion was bandwidth commercialization with decrease in prices and an environment that actively promoted the fantasy that high bandwidth can address almost any performance problem. However, application performance in networks is affected by many factors associated with both network and application logic that must be addressed in order to achieve satisfactory application performance.

At the network level, it is limited by congestion, packet loss, jitter and high latency (the effect of physical distance between networks) [2]. At the application level, performance is further limited by natural behaviour of application protocols especially with latency, packet loss and congestion at the network level.

II. WIDE AREA NETWORKS (WAN)

A Wide Area Network is an interconnection of computers and computer related devices to perform many given functions, typically using local and long range telecommunication or networked systems. Wide area Networks are typically used to send large data between endpoints and deliver to user electronic mail services, give access to database systems and Internet. Wide Area Networks also help with specialized operations in many fields such as manufacturing, medicine, navigation, education, entertainment and telecommunication. Because there are so many workstations (computer devices) in a wide area network and are spread over large distances, a mesh design is required to route and transfer data across the network.

All wide area networks are collection of two or more block types of equipment: a station and a node. A station is a device that a user communicates with interacts with to access networks and it contains the software applications that allow someone to use the network for a particular purpose.

*A*

*WAN Architecture*

**International Journal of Emerging Technology and Advanced Engineering **

**Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 9, Issue 10, October 2019)**

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The network cloud is the virtually physical interconnection of nodes and communications lines that transfer data from between locations. All these components work in concert to create the network. A user at a workstation and running a network application passes his or her data to the network through a station, which passes the data to the cloud. The network cloud gets the data to the designated node, which then delivers it to the appropriate designated station. Clearly, there would be no network without a network cloud, but it should not matter to the network what the inside of the network cloud looks like. The network cloud is the medium for getting the data from sender to destination.**Figure 1: Diagram showing WAN Architecture in form of a network **
**cloud**

*B. Past Error Control Methods used in Wired and Wireless *
*Networks *

Lots of past research works carried out using Automatic Repeat request Method. Among them are [3] which maximized throughput of SW ARQ with Network Coding through Forward Error Correction. The paper investigated whether adding data recovery technique improved the performance network that used network coding. A comparative analysis of throughput in a Stop and Wait Automatic Repeat Request (SW_ARQ) data transmission with Network Coding (NC) and Forward Error Correction (FEC) was analysed. Programming Language developed three discrete event simulations using Vandermonde matrix,: SW-ARQ without NC, SW-ARQ with NC and SW with NC and FEC.

The results showed that Network coding with FEC was highly profitable and that its throughput improved after adding FEC to the system and has a higher throughput than SW with FEC but fell sharply with increased error rate. It was also found out that SW-NC-FEC rose more sharply when packet generation rate increased. The paper also found out that SW-NC-FEC produced more throughput as vandermonde matrix was enlarged, while SW-NC degraded.

The paper [4] adopted ARQ and BCH Codes in developing an adaptive Error Control in Sensor Networks Using Coverage Area Information. The proposed adaptive error control strategy was informational value. To evaluate the informational value that uses coverage area information, a novel approach was proposed. Packets from sensor nodes in regions with low spatial density had higher informational value. The adaptive schemes using ARQ and BCH codes increased the reliability of packets with high informational value when compared to static error control, without a great increase in the energy consumption. In future work they hope to analyse Different FEC and hybrid FEC/ARQ strategies. The proposed strategies could be used and adapted to several applications of sensor networks to increase the reliability of messages considered more important in the network.

The paper[5] analysed the Feedback Error in Automatic Repeat request. They proposed a new method of acknowledging packet delivery for unreliable feedback channel conditions. The proposed method, dubbed BCF-SAW, relied on backwards composite acknowledgement and provided the retransmission protocols with configurable ultra-reliability. It further provided the scheduler of the wireless system with new degrees of freedom to configure the communication link in order to meet the desirable reliability requirement even in highly-unstable feedback channel conditions. The presented numerical analysis showed orders of magnitude increase in reliability of the retransmission protocols over the practical range of target block error rate only at the expense of a negligible increase in experienced average packet delay.

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The methods lead to a performance utilization of the real-time communication by providing retransmissions and a better quality of service. Basically a lower message error rate were provided by adding one retransmission packet per message while the promises of real-time deadlines are kept. Calculating the delay bounds of the messages, a retransmission packet was scheduled in the channel. This way, a notable reduction of message error rate is achievable with the cost of a reasonable overhead. The possibility and schedulability of the presented methods have been evaluated and some simulations were done to verify the strength of the methods in accepting real-time channels. The evaluation shows the performance of the methods in accepting real-time channels in reality, and at last a comparison was been made between the two methods.The paper [7] increased the information throughput efficiency over a stop and wait protocol by developing an adaptive ARQ Strategy for Packet Switching Data Communications Networks. This improvement from the simulation results was particularly evident for a communication system operating in an environment with high channel Pb. The adaptive features to an existing Software protocol was added and also designed only to be modified with no hardware requirements. Several different adaptive arq strategies were presented, and all adapted to the packet length as the channel Pb increased or decreased. The noise or interference analysis or empirical data of the specific system which reflected the condition required to determine how many levels to use in an adaptive structure for a system. The different strategies were presented to provide a system designer with the ability to optimize a specific system for the particular noise or fading conditions experienced.

The adaptive software protocol model simulation program used could possibly be modified to simulate other ARQ protocols and also compare with other protocols in attempt to optimize the system further.

*C Past Research works in Forward Error Correction *

Lots of research works using Forward Error control have been performed. Among them are [8] which combined Path Diversity with Forward Error Correction (PDF) systems for Packet Switched Networks. In this research work, packet loss rate was reduced by sending packets on appropriate rates on disjoint paths from single sender to receivers. This work was extended to applications that were sensitive to delay over packet switched networks for which single sender to receiver connection were established using collection of relay nodes.

The paper proposed a scalable heuristic scheme for selecting a redundant path and classified the resulting redundant path length and disjointness according to their characteristics for various internet like topologies. The simulation showed that for various topologies of the Internet, only 10% of the participating nodes were needed for the proposed path redundant selection scheme to effectively find redundant path sharing few links which reduced packet loss by 66 percent.

[9] combined Forward Error Correction and Network Coding in Bufferless Networks using Optical Packet Switching as a case study. A combined forward Error Correction and Network coding scheme was used to address performance issues arising in a bufferless network. A case study for reducing packet loss in optical packet switched networks was presented. The Analysis showed that combining coding scheme has indeed increased successful decoding probability and reduced packet loss rate with orders of magnitude, if the underlying FEC demonstrated sufficient redundancy. Factoring in realistic contention probabilities in OPS networks, high rate, low over head Reed Solomon Codes were used to reduce packet loss and meet both buffering and decoding delay requirements simultaneously.

The Paper [10] improved the efficiency of Forward Error Correction coding in reducing packet loss in Internet Protocol networks. A method was explored for measuring the performance of FEC coding thereby the coding method combining with interleaving in reducing the packet loss in IP networks. The performance of FEC data transferred from the source to destination was evaluated using FEC decoder which also voluntarily created the packet loss, and recovered lost packets at the destination. The FEC coding performance was measured using an analytical method stated in the paper. Single multiplexer network model was used for transmission of the data from multiple sources to destinations. In the paper, the unified method provided an integrated framework for exploring the compromises between the various key parameters i.e. channel coding rates, interleaving depths, block lengths. It provided the selection of various optimal coding strategies with various QOS requirements and system constraints.

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An erasure decoder was developed by combining two erasure decoding techniques. The performances of various erasure decoders were compared. These techniques were also deployed in optical networks to reduce the effect of packet loss arising from contention errors and Redundant Array of Inexpensive Disks systems.III. ERASURE CODING IN PACKET SWICHED NETWORKS Erasure codes are FEC code classes which does not require retransmission when they are employed. An erasure is an error at which its location in the message is known to the decoder but has an unknown value. An erasure code is designed to recover the erasures, as a substitute for correcting errors from the packets correctly received or encoded bits. In a packet based network, an (n, k) erasure consists of k information packets and n-k parity packets over a finite field GF(q) (q is a power of a prime).

It is assumed that packet-loss in an erasure channel is an independent event introduced by [12], with a fixed constant probability, . Packets are either presented as erasures or correctly received as erasures to the decoder in this channel model. The Erasure channel Shannon capacity is (1- and transmission at any rate R< (1( with a random linear code can be achieved [12]. The number of erasures an erasure code can correct, is bounded by d – 1 where d is the minimum distance of the code. Clearly, this same code doubles the number of errors that can be corrected when it is used solely for error correction. The construction of erasure codes can be classified into two categories using a simple taxonomy: the maximum-distance separable (MDS) code approach and sparse graph-code approach. The construction methods and performance features are some of the summarised useful erasure codes as follows

*A Reed Solomon codes *

Reed Solomon codes are q-uary BCH codes special subclass and form the most important class of the MDS codes. They have been widely used for error control in digital communications and storage systems because of their powerful correcting capacity of burst error. RS codes can also be applied effective erasure codes to recover errors of multiple erasures of size q. In general (n,k) RS code can be formulated using the generator polynomial.

g(x) = (x – αb)(x – αb+1)………….( for
some 2 and some a 1, where GF(q) for any i
and αn_{ = 1 but α}s _{ 1 for any positive s} _{ n. The codes }
produced have in length n = q – 1 symbols (or packet) with
each packet containing q bits.

RS code as an MDS code, meets the conditions d = n – k + 1 or alternatively d – 1 = n – k, which means that it can correct any combination up to n – t erasures according to equation above when it is used as the erasure code for reliable end to end communication in packet switched network. In this scenario, the source node transport layer produces n transport packets using the RS encoder for every k information packets made known from the application layer. At the destination node transport layer, the RS decoder is able to recover the original information as long as it can receive any k out of the n packets transmitted correctly. For this reason, the MDS erasure codes are also called the k-out-of-n codes.

RS codes for different application requirements can provide a large number of MDS codes. Extended RS codes are also maximum distance separable [13] and [14] by adding one or two overall parity check(s). These attributes have made RS codes an attractive candidate in this field.

The decoding complexity of RS codes is achieved using the fast Fourier transform technique at the scale of O (n log2 n), [15]. RS codes have been considered for different applications in the network environment [16], [17], and [18], [19] and [20]. For example, employing the RS code in association with the ARQ technique can largely improve the performance of reliable multicast in the IP network [18], which is important for ensuring QoS in multimedia (video and audio) distribution across the network.

*B Bose- Chaudhuri Hocquenghem Code (BCH) Code *

They discovered a code called BCH. It could be used to detect and correct multiple errors code. BCH code is a generalized form of Hamming code. For any positive integer possibility codes for m (m >3) and t (t < a binary BCH code exists with the following parameters: Block length n =

Number of Parity Check digits = n – k mt Minimum distance d 2t + 1

Generating polynomial g(x) is generally created as follows:

Lowest Common Multiple (L.C.M) of {m1(x), m2(x), ………….m2t-1(x)}

The message m(x) is divided by g(x) and remainder will be represented as check bits r(x). Now whole encoded message is represented as:

E(x) = m(x) + r(x) (1)

*BCH Decoding *

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Error location polynomial is generated from set ofequations and derived from the syndrome.

Error location polynomial is used to identify and correct the errant bits.

*C Combined Coding Scheme *

The data link layer adds authenticity to the physical layer by adding mechanism to detect and retransmit damages or lost packets. It also used a mechanism to recognize duplicate packets. Error control is normally achieved adding a trailer to the end of the packet. In this coding scheme was designed in detail.

Link

Link

Link

End System

Intermediate System

Intermediate System Intermediate

System

[image:5.612.53.280.279.481.2]End System

**Figure 2: Hop to Hop Delivery For Error Control **

The combined coding scheme is as follows. First we calculate the number of packets and find the parity symbol bit transmitted. The erased channel or servers is k using RS and BCH codes. Parity digits is added at the end of the packet. Remember that there will still be symbols, so after RS and BCH coding, there will be RS packets and BCH packets with the proposed packets. Both RS and BCH packets will be decoded with the decoder and parity checking for the symbols will be obtained. If there is erasure in the parity checking, then the bits are discarded. The remaining packets symbols are erasure free and will be used as a decoding process. When all the source symbols are decoded successfully, then the receiver feeds back an acknowledgement to the sender. The Sender continues to transmit the information until it receives the acknowledgement.

*D. Simulating the proposed Coding with both RS codes and *
*BCH Codes *

We analyze the packet loss rate of the coding schemes with RS codes and BCH codes. For the simplicity of the analysis, RS (n, k) code and BCH codes (n, k) are used. Both codes correct up to m erroneous messages. The messages we are talking about now is with respect to RS and BCH codes are in digits. The packet error ratio (PER) is the ratio of altered received packets of data to the total number of the received packets. A packet is declared incorrect if at least one bit is erroneous. The expectation value of the PER is called packet error probability, Pp for which data packet length of N digits can be expressed as

= 1 – (1- )N (2)

Where N is the number of packets in the network and in queue, assuming that the bit errors are independent of each other.

Using Dynamic Erasure with both RS and BCH codes, up to, m errors can be corrected.

Number of packets in a source data block denote the transmission of the block of source data, the number of erasures as a throughput. The packet error probability produced in blocks of data is given by

Dynamic Erasure + RS Code (3)

Dynamic Erasure + BCH Code (4)

IV. RESULTS AND DISCUSSION

This section shows the table and graphs of Packet error Probability produced from number of erasures generated from the proposed method compared with the combination of the proposed method and two other methods.

**Table I **

**Packet Error Probability Of The Schemes At Bit Error Probability **
**Of 0.1. **

**Erased **

**Channels ** **Dynamic **

**Dynamic with **
**Reed solomon **

**Dynamic with **
**BCH Code **

2 1 1 0.999983

4 0.96955 1 1

6 1 1 1

8 1 0.89288 1

10 1 1 1

12 0.996993 1 1

14 0.87368 1 1

16 1 1 1

18 1 0.9978 1

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**Figure 3: Figure showing Packet Error probability of the Schemes at**

**Bit Error probability of 0.1 **

The graph shows the packet error probability for each of the scheme at bit error probability of 0.1. The blue graph shows the Dynamic Erasure Coding Method. The wine colored graph shows the Dynamic Erasure coding with Reed Solomon Method while the Lemon green coloured graph shows the Dynamic Erasure coding with BCH Coding method. Dynamic erasure coding graph reduced from 1 to 0.96955 and rose back to one, became uniform and then reduced to 0.87368, rose to 1, became uniform and sloped down to 0.999115. Dynamic Erasure coding with Reed Solomon was uniform at 1 the fell to 0.89288 and rose back to 1, remained uniform, fell to 0.9978 and finally rose to 1. Dynamic with BCH code rose from 0.999983 to 1 and remained uniform for the remaining number of erasures. This graph shows that Dynamic Erasure coding produced a lower packet error probability at points 2, 6,8,10, 16 and 18. Dynamic Erasure with Reed Solomon produced a lower packet error probability from 2, 4,6, 10, 12, 14, 16 and 20. Dynamic Erasure with BCH coding was uniform apart from point 4, 6, 8 10, 11, 12, 14, 16, 18, 20. Dynamic with BCH have a better retention of packet error probability more than the Dynamic Erasure with Reed Solomon code and Dynamic Erasure coding. This is because of the deep production of steeper slope from both graphs (Dynamic Erasure Coding and Dynamic Erasure coding with Reed Solomon coding.)

**Table II **

**Packet Error Probability Of The Schemes At Bit Error Probability Of **
**0.3 **

**Erased **

**Channels ** **Dynamic **

**Dynamic **
**with Reed **
**solomon **

**Dynamic **
**with BCH **
**Code **

2 1 1 1

4 1 1 1

6 1 1 1

8 0.413 1 1

10 1 0.999999 1

12 0.999846 1 1

14 0.16897 1 1

16 1 0.988549 1

18 1 0.903109 1

20 1 1 1

**Figure 4: Graph showing Packet Error probability of the Schemes at **
**Bit Error probability of 0.3 **

The graph shows the packet error probability for each of the scheme at bit error probability of 0.3. The blue graph shows the Dynamic Erasure Coding Method. The wine colored graph shows the Dynamic Erasure coding with Reed Solomon Method while the Lemon green coloured graph shows the Dynamic Erasure coding with BCH Coding method.

0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.02

0 10 20 30

**P**

**ack**

**e**

**t **

**Er**

**ror **

**P**

**robabi**

**lit**

**y **

**Number of Erased Channels **

**Graph showing Packet Error probability at Bit Error **
**probability of 0.1 **

Dynamic

Dynamic with Reed solomon

Dynamic with BCH Code

0.00 0.20 0.40 0.60 0.80 1.00 1.20

0 10 20 30

**P**

**ack**

**e**

**t **

**Er**

**ror **

**P**

**robabi**

**lit**

**y **

**Number of Erased Channels **

**Graph showing Packet Error probability of the Schemes **
**at Bit Error probability of 0.3 **

Dynamic

Dynamic with Reed solomon

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Dynamic erasure coding graph reduced from 1 to 0.413 and rose back to 1, fell and pass through two points and then, rose back to 1, became uniform till the end. Dynamic Erasure coding with Reed Solomon was uniform at 1 and sloped down to 0.999999 and rose back to 1, remained uniform, fell to 0.903109 and finally rose to 1. Dynamic with BCH code remained uniform at 1 for althrough the number of erasures. This graph shows that Dynamic Erasure coding produced a lower packet error probability at points 2, 4, 6, 8, 10, 16, 18 and 20. Dynamic Erasure with Reed Solomon produced a lower packet error probability from 2, 4, 6, 8, 12, 14, and 20. Dynamic Erasure with BCH coding was uniform although the point. Dynamic with BCH have a better retention of packet error probability more than the Dynamic Erasure with Reed Solomon code and Dynamic Erasure coding. This is because of the deep production of steeper slope from both graphs (Dynamic Erasure Coding and Dynamic Erasure with Reed Solomon coding).**Table III **

**Packet Error Probability Of The Schemes At Bit Error Probability Of **
**0.5 **

**Erased **

**Channels ** **Dynamic **

**Dynamic **
**with Reed **
**solomon **

**Dynamic **
**with BCH **
**Code **

2 0.972044 0.984449 0.983857

4 1 1 1

6 1 0.999988 1

8 1 1 1

10 1 1 1

12 0.993305 0.996276 0.995857

14 0.999999 0.999999 0.999999

16 1 1 1

18 1 1 1

[image:7.612.58.277.386.578.2]20 1 1 1

**Figure 5: Graph showing Packet Error probability of the Schemes at **
**Bit Error probability of 0.5 **

The graph shows the packet error probability for each of the scheme at bit error probability of 0.3. The blue graph shows the Dynamic Erasure Coding Method. The wine colored graph shows the Dynamic Erasure coding with Reed Solomon Method while the Lemon green coloured graph shows the Dynamic Erasure coding with BCH Coding method. Dynamic erasure coding graph rose from 0.983857 and remained uniform from points 4 to 10 and fell to 0.993305 and rose back to 1, became uniform till the last point. Dynamic Erasure coding with Reed Solomon graph rose from 0.984449 to 1, and sloped down to 0.996276, and rose back to 1, remained uniform, passing through 0.999999 and rose back to 1, remained uniform until the last point. Dynamic with BCH code graph rose from 0.983857 to 1 and remained uniform from points 4 to 10, fell to 0.995857, rose back to 1 passing through point 0.999999 and remained uniform till the end of the points for number of erasures. This graph shows that Dynamic Erasure coding produced a lower packet error probability at points 4, 6, 8, 10, 16, 18 and 20. Dynamic Erasure with Reed Solomon produced a lower packet error probability from 4, 8, 10, 16, 18, and 20.

0.97 0.98 0.98 0.99 0.99 1.00 1.00 1.01

0 10 20 30

**P**

**ack**

**e**

**t **

**Er**

**ror **

**P**

**robabi**

**lit**

**y **

**Number of Erased Channel **

**Graph showing Packet Error probability at Bit Error **
**probability of 0.5 **

Dynamic

Dynamic with Reed solomon

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Dynamic Erasure with BCH coding graph produced a lower packet error probability at points 4, 6, 8, 10, 16, 18, 20. Both Dynamic Erasure Coding and Dynamic Coding with BCH have a better retention of packet error probability more than the Dynamic Erasure with Reed Solomon coding. This is because of the deep production of steeper slope from Dynamic Erasure with Reed Solomon coding.**Table IV **

**Packet Error Probability Of The Schemes At Bit Error Probability **
**Of 0.7 **

**Erased **

**Channels ** **Dynamic **

**Dynamic **
**with Reed **
**solomon **

**Dynamic **
**with BCH **
**Code **

2 1 1 1

4 1 1 1

6 1 1 0.999995

8 0.999999 0.999997 0.999959

10 1 1 1

12 0.999827 1 1

14 1 1 1

16 1 1 1

18 0.999755 1 1

[image:8.612.331.554.516.701.2]20 1 1 1

**Figure 6: Graph showing Packet Error probability of the Schemes at **
**Bit Error probability of 0.7. **

The graph shows the packet error probability for each of the scheme at bit error probability of 0.7. The blue graph shows the Dynamic Erasure Coding Method. The wine colored graph shows the Dynamic Erasure coding with Reed Solomon Method while the Lemon green coloured graph shows the Dynamic Erasure coding with BCH Coding method. Dynamic erasure coding graph was initially uniform from points 2 to 6, sloped down to 0.999999, rose to 1 and fell to 0.999827, rose to 1, remained uniform at points 14 and 16, sloped down to 0.999755, and finally rose to 1 and remained uniform until the last point of number of erasures. Dynamic Erasure coding with Reed Solomon graph was initially uniform at 1, from point 4 and sloped down to 0.999997, rose back to 1, remained uniform until the last point. Dynamic with BCH code graph was initially uniform at 1 from points 2 to 4, sloped down to 0.999995, rose to 1 passing through 0.999959 and remained uniform until the end of points. This graph shows that Dynamic Erasure coding produced a lower packet error probability at points 2, 4, 6, 10, 14, 16 and 20. Dynamic Erasure with Reed Solomon produced a lower packet error probability at points 2, 4, 6, 10, 12, 14, 16, 18 and 20. Dynamic Erasure with BCH coding produced a lower packet error probability at points 2, 4, 6, 10, 12, 14, 16, 18, 20. Dynamic with Reed Solomon have a better retention of packet error probability more than the Dynamic Erasure with BCH code and Dynamic Erasure coding. This is because of the deep production of steeper slope from both graphs (Dynamic Erasure Coding and Dynamic Erasure with BCH).

**Table V **

**Packet Error Probability Of The Schemes At Bit Error Probability Of **
**0.9 **

**Erased **

**Channels ** **Dynamic **

**Dynamic **
**with Reed **
**solomon **

**Dynamic **
**with BCH **
**Code **

2 1 1 1

4 1 1 1

6 1 1 0.9

8 1 1 1

10 1 1 1

12 1 1 0.9999

14 1 1 1

16 1 1 1

18 1 1 0.99

20 1 1 1

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0 10 20 30

**P**

**ack**

**e**

**t **

**Er**

**ror **

**P**

**robabi**

**lit**

**y **

**Number of Erased Channels **

**Graph showing Packet Error probability at Bit Error **
**probability of 0.7 **

Dynamic

Dynamic with Reed solomon

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**Figure 7: Graph showing Packet Error Probability of the schemes at**

**bit Error Probability of 0.9 **

The graph shows the packet error probability for each of the scheme at bit error probability of 0.9. The blue graph shows the Dynamic Erasure Coding Method. The wine colored graph shows the Dynamic Erasure coding with Reed Solomon Method while the Lemon green coloured graph shows the Dynamic Erasure coding with BCH Coding method. Dynamic erasure coding graph, remained uniform at 1 althrough until the last point of number of erasures. Dynamic Erasure coding with Reed Solomon graph remained uniform although at 1 until the last point. Dynamic with BCH code graph was initially uniform at 1 from points 2 to 4, sloped down to 0.9, rose to 1, a remained uniformed at points 8 and 10, sloped down to 0.9999, rose to 1, remained uniform for points 14 and 16, sloped down to 0.99 and finally rose to 1. This graph shows that Dynamic Erasure coding produced a lower packet error probability at points 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20. Dynamic Erasure with Reed Solomon produced a lower packet error probability at points 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20. Dynamic Erasure with BCH coding produced a lower packet error probability at points 2, 4, 8, 10, 14, 16, 20. Both Dynamic Erasure coding and Dynamic Erasure Coding with Reed Solomon have a better retention of packet error probability more than the Dynamic Erasure with BCH code a. This is because of the deep production of steeper slope from both graphs (Dynamic Erasure with BCH).

V. CONCLUSION

In this paper, A method was proposed using Dynamic Erasure Coding Method based on the number of erased channels and good channels. Via simulation, It was shown that the method reduced Packet Error Probability. With increase in the number of erasures, the network error reduced to a very minimal level and combining Dynamic Erasure with Reed Solomon and Bose Chaudhurin Hoqchequeim Coding the Packet Error Probability reduced with also increase the number of messages transmitted and acknowledged.

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Dynamic

Dynamic with Reed solomon

**International Journal of Emerging Technology and Advanced Engineering **

### 286

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