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  • 1. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 3, March (2014), pp. 54-63 © IAEME 54 PERFORMANCE OF COMBINED FOUNTAIN CODE WITH NETWORK CODING OVER WIRELESS CHANNELS Zainab A. Abduljabbar¹&Dr.Abdulkareem A. Kadhim² 1 College of Information Eng. /Al-Nahrain University, Iraq. 2 College of Information Eng. /Al-Nahrain University, Iraq. ABSTRACT Recent advances in sparse graph codes have led to the proposal of fountain coding (FC). It becomes as an error correction coding scheme of choice for many multicasting and broadcasting systems. Network coding (NC) is used in modern wireless communication networks in order to gain throughput and some other advantages. In this paper, NC is used in conjunction with FC in order to obtain advantages of both techniques. A simple packet based network coding for butterfly network topology with FC is modelled and simulated. The system is tested over different wireless fading channel models and with different FC-NC arrangements.The results of the tests have shown that combined FC and NC techniques improve throughput over the original system without FC by more than (70%) at relatively low signal-to-noise power ratios for the considered models of wireless channels. An optimum bit error rate performance (zero error) is achieved using the combined FC with NC over the original system (i.e using NC without FC) under different channel conditions. Keywords: Fountain Coding, Luby Transform, Network coding, Throughput, Butterfly network. 1. INTRODUCTION 1.1Fountain Code Concepts Practical networks transmission systems are characterized by packet erasure, which traditionally dealt with by retransmission based techniques. However, the tremendous growth that happened recently in data traffic, had led to great interest in erasure codes to overcome the usual problems encountered with the retransmission of the erased packets. Fountain codes (FC) are currently the dominant class of erasure codes [1]. Fountain coding principles are introduced by Byers et al. [2] in 1998. FC can be seen as a code that simulates the action of water falling from a spring into a container [3, 4]. In FC, the transmitter generates a potentially infinite amount of transmitted packets from the source node and the receiver can recover the message from any set of these packets [5]. From this point of view, the rate of a fountain codetends to zero, since the transmission is seen as time unlimited [6]. Thus the INTERNATIONAL JOURNAL OF COMPUTER ENGINEERING & TECHNOLOGY (IJCET) ISSN 0976 – 6367(Print) ISSN 0976 – 6375(Online) Volume 5, Issue 3, March (2014), pp. 54-63 © IAEME: www.iaeme.com/ijcet.asp Journal Impact Factor (2014): 8.5328 (Calculated by GISI) www.jifactor.com IJCET © I A E M E
  • 2. International Journal of Computer Engineering and Technology (IJCET), ISSN 097 ISSN 0976 - 6375(Online), Volume 5, Issue fountain codes are rateless codes. Luby T a class of fountain codes which are universally capacity be decoded with message-passing algorithms such as grows incrementally with time as decoding attempt is made after the arrival of each new pa 1.2 Network Coding NC is an approach used to improve transmission throughput of wireless networks in addition to some other advantages. NC has been suggested to combat the limitations on networks devices and channels in classical networks [7]. With network coding, the router will combine the packets instead of only store-and-forward the output messages by routing, thus maximizing t performance [8]. In its simplest form, NC relies on intermediate nodes to combine (using a linear coding scheme) the incoming packets from different source nodes and then to forward the linearly encoded packets to all destination nodes in a single transmission. Network coding can improve throughput, robustness, complexity, reliability and security [ improvement in resources such as energy efficiency, delay, wireless bandwidth and interference also can be obtained [8,9]. Each coding node serves as a relay node that combines the incoming packets, from different source nodes, in one encoded packet to be transmi Fig.1 shows an example of simple network, where nodes A and B want to exchange their packets a router. The classical network in Fig. packets generated by source nodes A & B via the relay node (R) to th On the other hand and with network coding defined by linear encoding of the incoming packets from source nodes, 3 transmissions are sufficient as in Fig Fig 1.3 Research Background The present research is an attempt to combine fountain coding with network coding so that the possible advantages from both techniques can be exploited. block error rate (BLER) performance in cooperative communication, through combining fountain code with network coding (NC). Based on this, the error means of integrating fountain code with NC simulation results that the proposed scheme can obtain lower BLER compared with detect and forward scheme. In [14] the authors networks. They proved that by applying NC to fountain transmissions was reduced over erasure channels and hence the effective throughput was increased. They demonstrated the role of analogue NC and optimal weight selection by applying an it over wireless with Rayleigh fading and AWGN channels. were proposed for transmitting a collection of packets through communication networks employing linear NC which generalized FCs and preserved the prop encoding/decoding complexity. They verified theoretically for certain cases and demonstrated numerically for the general cases that BATS codes achieved rates very close to the capacity of linear operator channels. The author in [16 International Journal of Computer Engineering and Technology (IJCET), ISSN 097 6375(Online), Volume 5, Issue 3, March (2014), pp. 54-63 © IAEME Luby Transform (LT) codes, originally invented by Luby [2], are ountain codes which are universally capacity-achieving for erasure channels. passing algorithms such as Belief Propagation (BP) with decoding graph a new packet is received at the destination node decoding attempt is made after the arrival of each new packet [4]. NC is an approach used to improve transmission throughput of wireless networks in addition to some other advantages. NC has been suggested to combat the limitations on networks devices and With network coding, the router will combine the packets instead forward the output messages by routing, thus maximizing the overall system ]. In its simplest form, NC relies on intermediate nodes to combine (using a linear coding scheme) the incoming packets from different source nodes and then to forward the linearly encoded packets to all destination nodes in a single transmission. Network coding can improve ity, reliability and security [9,10]. In wireless networks further improvement in resources such as energy efficiency, delay, wireless bandwidth and interference also Each coding node serves as a relay node that combines the incoming packets, nodes, in one encoded packet to be transmitted to all destination nodes [ 1 shows an example of simple network, where nodes A and B want to exchange their packets The classical network in Fig.1(a) needs 4 transmissions to perform complete receptions of packets generated by source nodes A & B via the relay node (R) to their intended destination nodes. On the other hand and with network coding defined by linear encoding of the incoming packets from ufficient as in Fig.1(b) [12]. Figure-1 two node network. The present research is an attempt to combine fountain coding with network coding so that th techniques can be exploited. The authors in [13 block error rate (BLER) performance in cooperative communication, through combining fountain code with network coding (NC). Based on this, the error-tolerant coding scheme was proposed by means of integrating fountain code with NC in cooperative communication. They showed by simulation results that the proposed scheme can obtain lower BLER compared with detect and the authors proposed a transmission strategy of FCs over cooperative relay ed that by applying NC to fountain-coded packets, the required number of transmissions was reduced over erasure channels and hence the effective throughput was increased. They demonstrated the role of analogue NC and optimal weight selection by applying an it over wireless with Rayleigh fading and AWGN channels. In [15] batched sparse (BATS) codes for transmitting a collection of packets through communication networks employing linear NC which generalized FCs and preserved the properties such as ratelessness and low encoding/decoding complexity. They verified theoretically for certain cases and demonstrated numerically for the general cases that BATS codes achieved rates very close to the capacity of linear 16] proposed a series of new encoding and decoding algorithms International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), invented by Luby [2], are achieving for erasure channels. LT code can ropagation (BP) with decoding graph received at the destination node, and a new NC is an approach used to improve transmission throughput of wireless networks in addition to some other advantages. NC has been suggested to combat the limitations on networks devices and With network coding, the router will combine the packets instead he overall system ]. In its simplest form, NC relies on intermediate nodes to combine (using a linear coding scheme) the incoming packets from different source nodes and then to forward the linearly encoded packets to all destination nodes in a single transmission. Network coding can improve In wireless networks further improvement in resources such as energy efficiency, delay, wireless bandwidth and interference also Each coding node serves as a relay node that combines the incoming packets, tted to all destination nodes [11]. 1 shows an example of simple network, where nodes A and B want to exchange their packets via omplete receptions of eir intended destination nodes. On the other hand and with network coding defined by linear encoding of the incoming packets from The present research is an attempt to combine fountain coding with network coding so that 13] investigated the block error rate (BLER) performance in cooperative communication, through combining fountain tolerant coding scheme was proposed by in cooperative communication. They showed by simulation results that the proposed scheme can obtain lower BLER compared with detect and proposed a transmission strategy of FCs over cooperative relay coded packets, the required number of transmissions was reduced over erasure channels and hence the effective throughput was increased. They demonstrated the role of analogue NC and optimal weight selection by applying and analyzing batched sparse (BATS) codes for transmitting a collection of packets through communication networks employing erties such as ratelessness and low encoding/decoding complexity. They verified theoretically for certain cases and demonstrated numerically for the general cases that BATS codes achieved rates very close to the capacity of linear ] proposed a series of new encoding and decoding algorithms
  • 3. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 3, March (2014), pp. 54-63 © IAEME 56 that had the ability to diminish the complexity of Random NC and Rateless Codes, while they approached the optimality bound. After a theoretical analysis of the proposed techniques, they analyzed in various applications for content distribution in peer-to-peer networks, distributed storage systems and network management and monitoring. In the present work, the research is concerned with the performance evaluation and analysis of fountain coding with network coding over wireless networks. The main intension here is to discover the likely advantages of fountain coding when combined with network coding. The remaining parts of the paper are organized as follows: In the next section LT encoder and decoder are described. The model of the network used is to be described in the third section. The topology of network and other main assumptions are given in this section. The fourth section shows the simulation tests results in the form of error probability and the increase in throughput versus channel SNR. The last section deals with the main concluding remarks of the work. 2. LUBY TRANSFORM CODE 2.1 Encoder Operation Each encoded packet ‫ݕ‬௡ is produced from the source packetsܵଵ; ܵଶ; ܵଷ;…; ܵ௞ as follows [17]: - Randomly choosing a degree ݀௡ of the source packets from a degree distribution µ (d); the appropriate choice of µ depends on the source file size K (where the degree distribution will be described in paragraph c). - Choose, uniformly at random, ݀௡ distinct input packets, and set ‫ݕ‬௡ equal to the bitwise sum, modulo-2 addition of those ݀௡ packets. This sum can be done by successively modulo-2 addition of the packets together. This encoding operation defines a sparse-graph connecting encoded packets to source packets.It isassumed that, both the encoder and the decoder have synchronized clocks (to choose identical random degrees and set of connections). So that the degree of each received packet, and to which source packets is connected in the graph are known at the decoder side. 2.2 Decoding Algorithm The decoder's task is to recover S୩ from y୬=S୩Gୢ , where Gୢ is the degree distribution matrix associated with the graph [16]. According to the erasure channel and the BP decoding algorithm used, all messages are either completely uncertain messages or completely certain messages. Uncertain messages assert that a message packet S୩ could have any value, with equal probability, certain messages assert that S୩ has a particular value, with probability one. This simplicity of the messages allows a simple description of the decoding process. The following are the main steps used in decoding of LT code [18]: - Find the node y୬ that is connected to only one S୩ packet. If there is no such y୬ node, this decoding algorithm halts at this point, and fails to recover all the source packets. - Set S୩ =y୬. - Add S୩ to all y୬ that are connected to S୩: y୬ = y୬ + S୩ … (1) For all n such that G୬୩ ୢ = 1. - Remove all edges connected to the S୩ packet. - Repeat the above until all S୩ are determined. The above LT decoding process is illustrated in Fig.2, where each packet is just one bit. There are three source packets (shown by the upper circles) and four received packets (shown by the lower rectangles), which have the values; [yଵ;yଶ;yଷ;yସ] = [1011] at the start of the algorithm [3, 17]. At the first iteration, the only y୬ node that is connected to a sole source bit is the first yଵ node (panel- a). Source bit Sଵ is then set accordingly as in panel-b. Now, the yଵ node is discarded followed by adding the value of Sଵ (i.e. 1) to the all y୬ nodes to which it is connected as in panel-c.
  • 4. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 3, March (2014), pp. 54-63 © IAEME 57 Sଵis then disconnected from the graph. At the start of the second iteration (panel-c), the fourth y୬ node is connected to a sole source bitSଶ. Sଶis then set to yସ (0, in panel-d), and add Sଶ to the two y୬ it is connected to (panel-e). Finally, as panel-e shows, two y୬ nodes are both connected to Sଷ, and they agree about the value of Sଷ, which is restored as in (panel-f). 2.3 Robust Soliton Distribution The possibility of always finding new degree-one rows during the process is importantto the BP algorithm. The degree distribution of LT codes is designed to keep the expected number of degree- one rows equal to 1 at each iteration. It is theoretically approved that, the best distribution is the Ideal Soliton Distribution (ISD) defined by the following probability distribution [4]: ρሺdሻ=ቊ 1/K for d ൌ 1 భ ౚሺౚషభሻ for d ൌ 2, 3, … , Kቋ … (2) It has been shown in [4] that, this distribution performs poorly in practice because of the large variance for the probability of finding degree-one rows during the BP decoding process. To solve this problem, Luby proposes Robust Soliton Distribution (RSD), originated by ISD with two parameters added. RSD relies on using two parameters c and δ, in order to ensure that the expected number of the degree-one received nodes during the BP decoding process is about [4]: m = c logୣሺK/δሻ √K … (3) Using these parameters, the positive function (߬ ሺ݀ሻ) is calculated: ߬ ሺ݀ሻ = ‫ە‬ ۖ ‫۔‬ ۖ ‫ۓ‬ ೘ ಼ భ ೏ ݂‫݀ݎ݋‬ ൌ 1, 2, … , ቀ ௄ ௠ ቁ െ 1 ೘ ಼ logሺ೘ ഃ ሻ ݂‫݀ݎ݋‬ ൌ ሺ ௄ ௠ ሻ 0 ݂‫݀ݎ݋‬ ൐ ሺ ௄ ௠ ሻ ۙ ۖ ۘ ۖ ۗ … (4) Finally, the RSD (µሺdሻ) is given by [4]: µሺdሻ= ρሺୢሻାτ ሺୢሻ ୞ … (5) Figure-2 decoding example for LT code with K=3 andN=4 [3, 17]
  • 5. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 3, March (2014), pp. 54-63 © IAEME 58 where Z is given by: Z ൌ ෍ ሺρሺdሻ ൅ τ ሺdሻሻ ୢ ...(6) 3. SYSTEMMODEL The network considered in the present work is a wireless network that is interconnected by wireless links. Fig.3 illustrates the basic model used here. S1 and S2 are source nodes, while D1 and D2 are destination nodes. The aim here is to deliver all packets generated from different source nodes to its destination ones with least number of transmissions to increase the overall throughput of the network. S1 and D2 (also S2 and D1) are out of each other's communication range, thus they have a data to be exchanged through the relay node V. The network coding process is applied at packet level (in the network layer) to improve throughput.The relay node creates queues for the arrived packets from each different source. The queue is used here to make the packets ready to be encoded with NC if such opportunity is met. Finally, the relay node sends the network coded packets to the destination nodes in First in First out (FIFO) principle. Figure-3 network model. Each wireless link together with the required operation at each pair of connected nodes can be represented by the transmission model of Fig.4. This represents a general case for all nodes shown in Fig.3. The source output is either FC-NC coded packets if the source node is a relay node with network coding opportunity, or else FC coded packets without NC (network coding block is not used) that transmit directly from source nodes (S1 and S2) to their corresponding destination nodes (D1 and D2). Also, there is a possibility that source node is a relay node without network coding opportunity. This latter case occurs when there are no packets in the queue of one of the sources at the relay node. In either case, when coding is involved at the relay node, the jth coded packet at the relay node r୨ is given by: ‫ݎ‬௝ ൌ ܽ௞ ْ ܾ௞ … (7) whereܽ௞and ܾ௞are the generated packets at source nodes S1and S2, respectively, and ْdenote mod-2 addition.Whether NC is used or not, the contents of the transmitted packets are encoded with FC code (as described in section 2.1) and dealt with as bit stream at the physical layer. The bit stream is then modulated using Binary Phase Shift Keying (BPSK) modulation.
  • 6. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 3, March (2014), pp. 54-63 © IAEME 59 Figure-4 the system model. LT code which is a class of FC is used in this paper. Therefore at the receiving nodes (whether NC is used or not) the received packets are decoded using LT decoder (as in section 2.2). Following the reconstruction of the received packets at the receiving node in the network considered here, it is either passed to the higher layer, if the packets are network uncoded, or else decoded if the intended destination node has sufficient information to do so. At each destination node, the received network coded packet from the relay node is used with the aid of the packet received by direct transmission (network uncoded packets) from its intended source. This means that destination node D1, for example, which already received the packet, can decode the packet as shown below: a୩ ْ r୩ ൌ a୩ ْ a୩ ْ b୩ ൌ b୩ … (8) Similarly, the packet is decoded at the destination node D2. For more details about the complete algorithm steps for NC and LT code of the intended network can be found in [19]. 4. SIMULATION RESULTS&ASSESSMENT Simulation tests were performed to evaluate the performance of systems considered here with and without network coding. The performance measure covers both the evaluation of Bit Error Rate (BER) and the equivalent normalized throughput. These are determined for different SNR's. The SNR is taken here as the ratio of the average energy per information bit to AWGN noise power spectral density (Eb/No). The BER rate is taken as the ratio average number of errors in receiving the data at all destination nodes to the total number of data bits transmitted by the source nodes [20].Three different channels are considered here, the ideal AWGN channel, flat fading channel and multipath fading channel with three paths. The characteristics of the latter are given by; delays for the paths are 0, 0.4, and 0.9 µs, while their gains are 0, -5, and -10 dB, respectively. The multipath fading channel is known in the literature as SUI-3 and widely used to model wireless networks. Details of the actual channel modelling and complete system simulation can be found elsewhere [20].Four different systems are considered in this work, these are:System#1 neither FCnor NCis used, System#2without FC but NC is used, System#3 FC is used but without NC,System#4bothFC& NC are used. The performances of the systems are presented in Fig.5& 6. The BER performance is only shown for the cases were FC is not used (i.e only for System#1 & System#2), since the error will be vanished with fountain coding. This is based on the assumption that FCdecoders (for System#3& System#4) at the destination nodes and the relay node have enough encoded packets. Thus it will produce zero errors for the range of SNR considered in the tests. ThereforeFig.5 shows the BER performances for the systems without FCs. Fig.5 (a) shows the BER performance for the systems without FC code over AWGN channel. This figure shows that both systems (with and without NC)
  • 7. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 3, March (2014), pp. 54-63 © IAEME 60 have the same BER performance at high SNR, with slight difference in favour of NC based system (System#2) at low SNR.This is due to the fact that AWGN channel dose not introduce any distortion. It is clear from Fig.5 (b) and (c) that for both fading channels the improvement of NC at high SNR is relatively large. With fading, more SNR is required to achieve the same BER rate as compared with the case of AWGN channel as expected. Summarizing the BER performance for the channels tested in Fig.5 one can say that the use of FC improves the error performance (no error) on the expense of the overhead in transmitting packets. There is animprovement in systemsthat use NC over fading channels whether FC is used or not. a) AWGN channel. b) Single path fading channel. c) SUI-3 channel. Figure-5 BER performancesfor system#1 & system#2 Combining FC with NC should improve the throughput in addition to BER performance. Thus Fig.6 provides the performances of different systems, in the form of the resultant throughput, against SNR. In most literature the general definition of the throughput is given by the average rate of data that transmitted successfully from a given source node to its intended destination in a specifiedamount of time. Therefore, the throughput (Th) measure considered here is calculated as
  • 8. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 3, March (2014), pp. 54-63 © IAEME 61 the percentage of all correctly received packets from source nodes (or relay node) to their intended destination nodes in a specified amount of time multiplied by the nominal bit rate. Thus; Th = ே௢.௢௙௖௢௥௥௘௖௧୪୷ ௥௘௖௘௜௩௘ௗ௣௔௖௞௘௧௦ ே௢.௢௙௧௥௔௡௦௠௜௧௧௘ௗ௣௔௖௞௘௧௦ ൈ ܾ݅‫݁ݐܽݎݐ‬ … (9) The bit rate considered in the work is 10 Mbps. The three channel models are also considered in the throughput tests. As expected the measured throughput is directly proportional to SNR in general. Further, the improvement in throughput also depends on the topology of the network considered [11]. Fig-6shows that there is always an increase in throughput for the network coded systems over that achieved with uncoded counterparts. Further, the throughputs for FC coded systems (system#3& System#4) at relatively low SNRs are greater than those systems without FC (system#1& System#2).This is due to the fact that FC code always provides the least BER, thus allow more correct packets to be delivered to the destination nodes whether NC is used or not. The advantage of NC is vital, whether the system uses FC code or not, where the throughput performance is improved over all ranges of SNRs. The throughput in either case will reach a steady state value at very high SNR. This is determined by the network topology and the type of coding used. The percentage increase in throughput could be used to compare different systems tested here. For the system using both FC& NC (System#4)this percentage is about 35% as compared to NC without FCsystem (System#2) over AWGN channel at very low SNR ( Eb/No = 0 dB). a) AWGN channel. b) Single path fading channel. c) SUI-3 channel Figure-6 Throughput performance of different systems
  • 9. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 3, March (2014), pp. 54-63 © IAEME 62 The corresponding percentages over single path fading channel and SUI-3 channel are at least 70%. While the percentageincrease in throughput of the combined FC and NC (System#4) compared to that using FC without NC (System#3) is more than33%, 34%, and 31%over AWGN, single path fading, and SUI-3 channels, respectively. This is valid for SNR greater than 10 dB as shown in the Fig.6.Apart from the better BER performance provided by FC code, it is clear that combining FC with NC will provide improvement in throughput at relatively low SNRs. 5. CONCLUSION A combination of fountain coding (FC) and network coding (NC) arrangementwas studied here aiming to improve system performance.The simulation results have shown that the packet loss in NC can be reduced further with the use of FC. Further improvement in throughput can be achieved also by combining FC with NC especially at low SNRs. The percentage improvements in throughput become clear when models of fading channels are used. As much as 70% increase in throughput can be obtained at relatively low SNRs when FC-NC system is used over the considered models of wireless channels.Finally,the results reveals that FC-NC system reserves the advantages of both Fountain Coding(low BER) andNetwork Coding (throughput improvement) at all ranges of SNRs over wireless fading channels. REFERENCES [1] J. Qureshi, C. Foh, & J. Cai, "Primer and Recent Developments on Fountain Codes", Cornell University Library, arXiv: 1305.0918v1 [cs.IT], May 2013. [2] J. Byers, M. Luby, M. Mitzenmacher, & A. Rege, “A Digital Fountain Approach to Reliable Distribution of Bulk Data,” SIGCOMM, pp. 56–67, September 1998. [3] D. MacKay, " Fountain Codes", IEE Proc. Com., UK, Vol. 152, No. 6, pp. 1062-1068, December 2005. [4] M. Luby, "LT Codes", Proc. 43rd, IEEE, Foundations of Computer Science, pp. 271–282, 16– 19 November 2002. [5] J. Maria, J. Cordeiro, & B. Shishkov, "Software and Data Technologies", 6th International Conference, ICSOFT 2001, Seville, Spain, July 18-21 2011. [6] J. Moreira & P. Farrell, "Essentials of Error-Control Coding", J. Wiley & S. Ltd, England, 2006. [7] G. Kramer, “Lecture on Network Coding and Information Theory,” Alcatel Lucent, Sep. 2007. [8] R. Ahlswedeet al., "Network information flow," IEEE Transactions on Information Theory, Vol. 46, No. 4, pp. 1204-1216, July 2000. [9] S. Katti, “Network Coded Wireless Architecture,” Ph.D. Thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Aug. 2008. [10] C. Fragouli& E. Soljanin, “Network Coding Fundamentals”, Foundations and Trends in Networking, Boston, Vol. 2, Issue 1, 2007. [11] T. Ho& D. Lun, “Network Coding: An Introduction,” Cambridge University Press, New York, 2008. [12] I. Qazi& P. Gandhi, “Performance Evaluation of Wireless Network Coding under Practical Settings”, Tech. Report TR-07-150, University of Pittsburgh, 2007. [13] M. Yang, J. An, X. Li & L. Yuan, "Combined Fountain Code with Network Coding in Cooperative Communication", IEEE Networks Security Wireless Communications and Trusted Computing (NSWCTC), Vol. 2, pp. 24-27, China, April 2010. [14] E. Kurniawan, S. Sun, K. Yen, & K. Chong, "Network Coded Transmission of Fountain Codes over Cooperative Relay Networks", Institute for Infocomm Research, Connexis, Singapore, May 2010.
  • 10. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 3, March (2014), pp. 54-63 © IAEME 63 [15] S. Yang & R. Yeung, "Coding for a Network Coded Fountain", IEEE International Symposium on Information Theory Proceedings, pp. 2647-2651, The Chinese University of Hong Kong, Hong Kong SAR, China, 2011. [16] V. Bioglio, "Data Dissemination in Distributed Systems Using Rateless Codes", Ph.D. Dissertation, Univerisita' DegliStudi di Torino, Dipartimento di Informatica, Torino, Italy, 2011. [17] D. MacKay, "Information Theory, Inference, and Learning Algorithms," 1st Ed., Cambridge University Press, Cambridge, UK, 2005. [18] I. Reed and G. Solomon, "Polynomial Codes Over Certain Finite Fields," Journal of the Society of Industrial and Applied Mathematics, Vol. 8, No. 2, pp. 300-304, June 1960. [19] Z. Abduljabbar, "Performance Evaluation of Fountain Codes Based Network Coding," M.Sc. Thesis, Al-Nahrain University, Iraq, February, 2014. [20] A. Mahmood, "Combined Multi Input Multi Output and Network Coding for Wireless Networks", M.Sc. Thesis, Al-Nahrain University, Iraq, June 2012. [21] B. Sklar, “Digital Communications: Fundamentals and Applications”, 2nd Ed.,Prentice Hall, 2001. [22] Kalpana Chikatwar, Ramesh D and Satish Kannale, “Design of ARQ And Hybrid ARQ Protocols For Wireless Channels Using Bch Codes” International Journal of Advanced Research in Engineering & Technology (IJARET), Volume 4, Issue 3, 2013, pp. 49 - 54, ISSN Print: 0976-6480, ISSN Online: 0976-6499. [23] S.R.Shankar and Dr.G.Kalivarathan, “Feasibility Studies Of Wireless Sensor Network and It’s Implications” International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 2, 2012, pp. 105 - 111, ISSN Print: 0976-6545, ISSN Online: 0976-6553. [24] S.R.Shankar and Dr.G.Kalivarat han, “Prediction of A Reliable Code For Wireless Communication Systems” International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 1, 2013, pp. 19 - 26, ISSN Print: 0976-6545, ISSN Online: 0976- 6553.