Journal of Wireless Networking and Communications 2016, 6(1): 10-20 DOI: 10.5923/j.jwnc.20160601.02 Performance Evaluation of Various Erasures Coding Techniques in Digital Communication N. M. El-Gohary1,*, M. A. M. El-Bendary2, F. E. Abd El-Samie3, M. M. Fouad1 1Department of Electonics and Communication, Faculty of Engineering, Zagazig University, Egypt 2Department of Communication Technology, Faculty of Industrial Education, Helwan University, Egypt 3Department of Electonics and Communication, Faculty of Electonics Engineering, Menofia University, Egypt Abstract Reducing error in wireless, satellite, and space communication systems is critical. In the wireless communication system, various coding methods are employed on the data transferred to induce high bit error rates. High speed wireless networks, in order to address the large latency and degraded network throughput due to the retransmission triggered by frame loss, the purpose of this paper is to study and investigate the performance of fountain codes that is used to encode and decode the data stream in digital communication. This is an intelligent solution that encodes a number of redundant frames from the original frames upon link loss rate so that a receiver can effectively recover lost original frames without significant retransmissions. Since then, many digital Fountain coding methods have been invented such as Tornado codes, Luby transforms (LT) codes and Raptor codes. Keywords Wireless communication systems, Fountain codes, Tornado codes, Luby transforms and Raptor codes ensures reliability by essentially retransmitting packets 1. Introduction within a transmission window whose reception has not been acknowledged by the receiver. It is known that such In civil and military applications, wireless networking protocols exhibit poor behavior in many cases, such as the technologies have been widely deployed such as 3G/4G and transmission of data over heavily disabled channels or IEEE 802.11 WLAN networks. However, wireless transmission of data from one server to multiple receivers or, communication suffers from frame losses due to shadowing, such as poor wireless or satellite links. Moreover, ack-based mobility, channel fading, and interferences. Frame loss protocols such as TCP perform poorly when the distance significantly undermines wireless network performance in between the sender and the receiver is long, since large that latency is enlarged and throughput is degraded. The distances lead to idle times during which the sender waits for large latency is induced by the retransmission of lost frames an acknowledgment and cannot send data. For these reasons, in the MAC layer [6]. other transmission solutions have been proposed. One class On the Internet, data is transmitted in the form of packets. of such solutions is based on coding. The original data is Each packet is armed with a header that describes the source encoded using some linear erasure correcting code. If during and the destination of the packet, and often also a sequence the transmission some part of the data is lost, then it is number describing the absolute or relative position of the possible to recover the lost data using erasure correcting packet in a given stream. These packets are routed in the algorithms. For applications it is critical that the codes used network from the source to the destination [16]. Due to are able to correct as many erasures as possible, and it is also various reasons, for example, buffer overflows at the critical that the encoding and decoding algorithms for these intermediate routers; some packets may get lost and never codes are very fast. Reed–Solomon codes can be used to reach their destination, other packets may be announced as partially recover for the inefficiency of random codes. lost if the internal check of the packet does not match. Reed–Solomon codes can be decoded from a block with the Therefore, the Internet is a very good real-world pattern of maximum possible number of erasures in time quadratic in the BEC. the dimension. There are faster algorithms based on fast Reliable transmission of data over the Internet has been polynomial arithmetic, but these algorithms are often too the subject of much research. Reliability is ensured by the complicated in practice. However, quadratic running times use of suitable protocols. For example, the present TCP/IP are still too large for many applications. Other codes are constructed with linear time encoding and * Corresponding author: [email protected] (N. M. El-Gohary) decoding algorithms that can come arbitrarily close to the Published online at http://journal.sapub.org/jwnc capacity of the BEC [16, 18]. These codes, called Tornado Copyright © 2016 Scientific & Academic Publishing. All Rights Reserved codes, are very similar to Gallager’s low-density Journal of Wireless Networking and Communications 2016, 6(1): 10-20 11 parity-check (LDPC) codes [19], but they use a highly the data using an error-correcting code (ECC) before unequal weight distribution for the implied graphs. transmission. The receiver used the additional In computer networks, fountain codes are ideally suited redundancy added the code to recover the original data. for transmitting information. A server sending data to many • Automatic repeat request (ARQ): (referred also to as recipients can perform Fountain code for a given piece of backward error correction): Every block of data data to generate an infinite stream of packets. As soon as a received is checked using the error detection code used, receiver requests data, the packets are copied and forwarded and if the check fails, retransmission of the data is to the receiver. In a broadcast transmission model, there is no requested – this may be done repeatedly, until the data need for copying the data since any outgoing packet is can be executed. This is an error control technique received by all the receivers. In other types of networks, the whereby an error detection scheme is combined with copying can be done actively by the sender, or it can be done requests for retransmission of incorrect data. by the network. An example, if multicast is enabled; the FEC and ARQ may be combined, this is called hybrid recipient collects the output symbols, and leaves the automatic repeat-request (HARQ), such that minor errors transmission as soon as it has been received by them. That are corrected without retransmission, and major errors are time, it uses the decoding algorithm to recover the original corrected via a request for retransmission. There are many symbols. That, the number is the same regardless of the different families of error-correcting codes of major channel characteristics between the sender and the receiver. importance for recording applications is the family of More loss of symbols just translates to a longer waiting time Reed-Solomon (RS) codes. to receive the packets. This paper surveys the channel coding methods in the 2.2. Binary Erasure Channel physical layer and Digital Fountain code proposals in the The Binary Erasure Channel (BEC) is a channel model application layer. The following paper is arranged as follows. where the receiver either receives the transmitted bit or is Section 2 presents the RS codes architectures, applications informed with the erasure of the bit, that is, the bit was not and limitations. Section 3 discusses the fountain codes received or erased. Therefore, the receiver has no idea about properties, the related erasure channel and construction. the transmitted bit with a certain probability p, and is exactly Section 4 Recent advances have produced powerful fountain sure about the transmitted bit with a certain probability 1-p. codes, such as Tornado codes, Luby Transform (LT) codes According to Shannon, the capacity of BEC is 1-p, which and Raptor codes. Finally, section 5 discusses the advantages means that for the alphabet size of 2k, where k is the number of fountain code over Reed Solomon code. Finally section 6 of bits in the alphabet, no more than (1− p) k bits/symbol can presents the conclusion. be reliably communicated over the binary erasure channel [20]. Feedback from the receiver to the transmitter will not 2. Developing Background Related increase the capacity of the channel and reliable Work and Motivations communication should be possible at this rate. Automatic Repeat Request (ARQ) schemes have so long been used as a 2.1. Error Correction Control (ECC) classical approach to solve the reliable communication In information and coding theory with applications in problem. However, redundant number of feedbacks used in computer science and telecommunication system, error the case of erasures causes improvident usage of bandwidth, detection and correction are techniques that enables reliable network overloads and impossible delays. Also known as and efficient delivery of digital data over communication rateless erasure codes are a class of erasure codes with the channels. Many communication channels are subject to property that a potentially limitless sequence of encoding channel noise, and thus errors may be inserted during symbols can be generated from a given set of source symbols transmission from the source to a receiver. Error detection such that the original source symbols can ideally be techniques permit detecting such errors, while error recovered from any subset of the encoding symbols of size correction enables regeneration of the original data in many equal to or only slightly larger than the number of source cases. symbols. The term fountain or rateless refers to the fact that Error correction control is accomplished by adding these codes do not exhibit a fixed code rate. redundant symbols to the message. These redundant symbols make it possible for the receiver to detect and /or 2.3. Reed-Solomon Code correct some of the errors that may occur in the received Reed-Solomon (RS) code is a forward error-correcting message. The main challenge is to ensure the required code first invented in 1960 by Irving Reed and Solomon [1].