Error Control Coding in Optical Fiber Communication Systems: An Overview

Transcription

1 ACSIJ Advances in Coputer Science: an International Journal, Vol., Issue, No., March 05 Error Control Coding in Optical Fiber Counication Systes: An Overview Majid Hataian, Haid Barati, Saaneh Berenjian, Alireza Naghizadeh 3 and Behrooz Razeghi Departent of Coputer Engineering, Dezful Branch, Islaic Azad University Dezful, Iran ajid.hataian.h@ieee.org hbarati@iaud.ac.ir Departent of Coputer Engineering and Inforation Technology, Airkabir University of Technology Tehran, Iran saa.scientist@aut.ac.ir 3 Departent of Coputer Engineering, University of Guilan Guilan, Iran alireza.naghizadeh.a@ieee.org Departent of Electrical Engineering, Ferdowsi University of Mashhad Mashhad, Iran behrooz.razeghi.r@ieee.org Abstract In sending data fro one point to another, such as transferring data between various coponents of a coputer syste, due to the existence of electroagnetic waves and other issues such as noise and attenuation, inforation ay be changed in the iddle of the track. Therefore, it is critical for receiver to ensure the accuracy of the inforation. For this reason, error control coding plays an iportant role in counication channels. This is specially true for optical counication systes as one of the ost iportant edius used for data transission. In this paper, we present ethods of error control coding in optical fiber counication systes. For this purpose, we introduce two categories of error correction codes. The ost iportant types of error control coding techniques in optical fiber counications are: Reed-Soloon (RS), Bose-Chaudhuri-Hocquenghe (BCH), Product, and Low Density Parity Check (LDPC). Furtherore, an in-depth analysis for these error correction codes has been perfored. Keywords: Optical Fiber, Error Control Coding, Priitive Polynoial, Linear Block Codes, Convolutional Codes.. Introduction The basic of optical fiber is a very thin fiber that is soeties ade of plastic or ost often of glass which is responsible to transit the data. Nuerous advantages such as high bandwidth, low attenuation, low weight and high speed, are aong the factors that have led to the increasing use of this technology []. Optical fiber counication systes have the capacity to transit large volues of data at very high speed over thousands of kiloetres. Optical fibers provide uch greater bandwidth and offer low power loss copared to etal cables. They are also uch thinner and lighter which ake the easier to install. Along with these advantages, it is still possible to effectively increase transission capacity and decrease the costs with error control coding [,3]. Generally, error detection can be done in two ain fors. In the first approach, when the receiver detects an error in a essage, it autoatically requests the sender to resend the essage. This process is repeated until the essage can be received without error or the error continues beyond a predeterined nuber of transissions. This ethod is called Autoatic Repeat Query (ARQ). In the second approach, designed redundancy allows receiver to detect and correct a liited nuber of errors occurring in the essage without the need to request sender for additional repeat requests. The second ethod is called Forward Error Correction (FEC) [,5,6]. Error control coding consists of error detection and correction procedures. If during these processes an error was detected, it can be corrected. The error control coding is one of the ost iportant eleents of every odern optical fiber counication syste. In optical fibers, FEC systes are typically known as binary error correction codes. Error correction codes have been successfully used 70 Copyright (c) 05 Advances in Coputer Science: an International Journal. All Rights Reserved.

2 ACSIJ Advances in Coputer Science: an International Journal, Vol., Issue, No., March 05 in wireless and wired counications to offer an error free transission with high spectral efficiency [7,8]. In this paper, four types of error control coding ethods include: RS, BCH, Product and LDPC codes are introduced. The atheatical structure of the is deonstrated and coding/decoding concepts for each of the is explained. The rest of this paper is organized as follows. Section describes abnoralities in optical fiber channels. Section 3 explains types of error correction codes. Section is about fundaental atheatical concepts of error control coding. Section 5 presents Reed-Soloon, BCH, Product, and LDPC codes as the ost iportant techniques for error control coding in optical fibers. Finally, Section 6 concludes this paper.. Abnoralities in Optical Fiber Channels. Dispersion Dispersion takes place when the pulses pass through the optical fiber. By overspreading these pulses, it liits the available bandwidth. Dispersion in optical fibers can be divided into two types, Interodal (ultipath) and Intraodal (chroatic). Interodal dispersion is caused by different distance lengths of the odes in the fiber and different effective velocities which results in flattening of the transitted pulses through the fiber. This type of dispersion occurs in ulti-ode fibers and is known as odal dispersion. Intraodal dispersion is a ter used to describe the spreading of a light pulse as it travels down a fiber when light pulses launch close together (high data rates). In this way, they spread too uch and result in errors and loss of inforation. Intraodal dispersion occurs in single-ode fibers and causes the pulse broadening in these fibers [].. Noise Noise is an ever present part of all systes. Any receiver ust confront with noise. In analog systes, noise spoils the quality of the received signal. But in digital counication systes, noise debilitates the throughput. The reason is that, noise requires retransission of packets or redundant coding to recover the data in the presence of errors. Cobination of electronic circuits, optical coponents such as add/drop ultiplexers, optical crossconnects and fiber optics are factors that have led to the occurrence of noise. We have two types of noise: - External noise: noise whose sources are external such as an-ade noise or industrial noise, atospheric noises, etc. - Internal noise: noise which is discovered within the receiver or counication syste such as shot noise, theral noise (white noise), iscellaneous internal noise, etc []..3 Nonlinear Effects In an optical fiber, light is restricted to a very sall lateral sector. For this reason, even ild optical powers lead to high optical intensities. Since, light propagates over considerable distances in a fiber, nonlinear effects often have vital effects. This is especially true about fibers which are used to transit short pulses. In fact, it can be argued that these effects are dependent on the intensity of light. Scattering and Kerr effects are instances of nonlinear effects. For exaple, Self-Phase Modulation (SPM) is one of the consequences of the Kerr effect. SPM occurs when a light wave in the fiber experiences a nonlinear phase delay which results fro its own intensity. Cross-Phase Modulation (CPM) occurs when two different waves with two different wavelengths, propagate together in a fiber [,5].. Attenuation In optical fiber, attenuation is the reduction in intensity of the light bea with respect to distance it travels through a fiber. Attenuation also affects the propagation of waves and signals in optical fibers. It is defined as the ratio of the optical output power (after light propagates the distance d ) to the input power (overall optical throughput of an optical fiber) and it can be written as [], P(o) P(i) t d () e where, t is the total attenuation coefficient and it can be obtained as follows: 0 P (db/ k) log (i) t 0 d P(o) 3. Types of Error Correction Codes Error correction codes are generally divided into two categories: Linear Block and Convolutional Codes. In the following, we introduce these two types of error correction codes. 3. Linear Block Codes These codes are called linear because linear cobinations of codewords and the word itself belongs to linear block () 7 Copyright (c) 05 Advances in Coputer Science: an International Journal. All Rights Reserved.

3 ACSIJ Advances in Coputer Science: an International Journal, Vol., Issue, No., March 05 codes. In linear block codes, in order to protect data against errors, inforation source data is divided in fors of blocks with length k sybols. If we assue that U ( u, u,..., u k ) is one of these blocks, thus its associated codeword would be V ( v, v,..., v n ),where n k. The first k sybols of the codeword V is the data block itself. In other words: v u, v u,..., v k u k (3) The n k reaining sybols, are parity sybols of the code. In a way that the codeword V satisfies H. V O. H is called the code's parity atrix and is defined by H [A In k]. A is a n k diensional atrix that is peranently fixed and In k is the identity atrix of degree n k [9,0]. 3. Convolutional Codes In convolutional codes, the initial data string is called U and the generated data string is V. For each k sybols of U, n sybols of V are generated. In convolutional codes, U and V represent strings of inforation blocks while in linear block codes, U and V represent blocks of inforation. That is in convolutional codes, U and V consist of k and n sybols block strings, respectively. The iportant thing is each n sybols block of V is dependent on the previous blocks of the initial data in addition to the k sybols initial data at the sae tie. Convolutional codes are represented with (n,k,). Soe of the ost popular convolutional codes decoding algoriths are Fano, Viterbi and ZJ [,].. Fundaental Matheatical Concepts of Error Control Coding The field F is a set of eleents on which we can apply addition, subtraction, ultiplication and division operations. A field with a liited nuber of eleents is called a Finite Field or Galois Field (GF). In the fields, addition and ultiplication have the characteristics of associative, distributive and coutative. When we talk about field we ean the nuber of eleents it contains. Thus, one field is defined by {0,} which is called binary field and is represented by GF (). But, GF ( ) includes all bits cobinations which we represent with different powers of that are the priitive eleents of GF. In this case, GF( ) includes ebers as following [3]: 0 0,,,,..., () Each GF has a Priitive Polynoial of degree, with as its root. Generally, in digital counication systes which work with binary data, error correction codes are constructed by eleents of binary field GF () or generalized field GF ( ). Typically, non-binary codes such as Reed-Soloon consist of GF ( ) and binary codes such as BCH consist of GF (). For exaple, consider that we want to represent the ebers of GF ( ). We assue that the priitive polynoial of this GF is as following [3]: x x (5) Therefore, the ebers of this GF are: 0 0,,,,..., (6) For representing the ebers of a GF, there are different ethods. One of these ethods is Standard Basis [3,] representation. In this ethod, each position of a bits vector, represents a power of. Thus, the rightost place 0 relates to, the next place relates to and so on. As an exaple, description for representing the ebers of GF( ) in binary for, is as follows. Since, therefore we have a bits vector that each of its digits represent a power of. According to the above definitions, we have: In the next step, we ust find the other ebers of GF fro these five ebers. As it is entioned, is the root of the priitive polynoial, so if we put as x in the priitive polynoial, the answer of the equation is zero, we have: (8) We know that in GF, addition and subtraction are equivalent and both are equal to XOR, so we have: (7) 7 Copyright (c) 05 Advances in Coputer Science: an International Journal. All Rights Reserved.

4 ACSIJ Advances in Coputer Science: an International Journal, Vol., Issue, No., March (9) Thus, the other ebers of the GF are deterined as follows: ( ) ( ) Error Control Coding in Optical Fiber Counication Systes (0) If we assue T is the tie it takes for k sybols to be transferred without coding, T / k is the tie it takes for one sybol to be transferred. After coding k sybols in a n sybols codeword, n sybols are transferred in tie T and therefore the period of sybol is T / n which is lower than T / k. In every error detection and correction syste, soe excess inforation called redundant is sent along with the original inforation. We represent the syste that converts the k bits essage to a codeword with length n, by the pair ( nk, ). The width of each sybol after coding is reduced by the k/ n factor, and also the required bandwidth for the transfer of sybols is increased by the factor n/ k, called the Bandwidth Expansion Ratio. In addition, we call k/ n the code rate and represent it by R c. In case of optical fiber counication systes that work in very high data rates ( Rc 0.8), selection of the coding ethod that results in low overhead is very iportant. If R is closer to, eans that the bandwidth has been used in a ore efficient way. If R is closer to 0, eans that we have ore redundancy [,,0]. The structure of an optical fiber counication syste is shown by Fig.. 5. The Reed-Soloon Code The Reed-Soloon (RS) code is a subset of cyclic codes which are a subset of linear block codes theselves. RS is one of the ost widely used error correction codes in optical fiber counications. This code can correct / (n k) errors. RS is based on GF atheatical structure and like other error correction codes, transfors an inforation packet with length k to a codeword with length n. But RS differentiates itself with other codes such as Haing or Parity. In this code, the nuber k does not ean k bits, but eans k sybols that each sybol is a bits eber of GF ( ). Therefore in RS code, a k bits string will be transfored to a n bits codeword. Which is defined as RS (n, k). In the RS, the nuber n relates to which is shown as follows ( n is the length of the block) []: n () The RS corrects up to / (n k) errors in a n sybols inforation packet. But capability of correcting / (n k) errors does not ean correcting / (n k) bits, it eans / (n k) sybols contain errors. A string of inforation including eleents of GF can be represented by a polynoial of X. The coefficients of different powers of X are the ebers of GF theselves. Assue that the string B includes the sybols b0, b, b and b 3. This string can be represented by the following polynoial []: B( X ) b X b X b X b () 5.. The RS Encoder The encoding process is done with a Generator Polynoial. The generator polynoial has n k t tande roots. These roots are: t,.,..., (3) where, 0 can be any nuber. But it ust be selected carefully, because a good selection can result in optiization of soe decoding stages. In other words, the generator polynoial gx ( ) is defined as follows: t g( X ) ( X )( X )...( X ) () Fig.. Structure of an optical fiber counication syste. 73 Copyright (c) 05 Advances in Coputer Science: an International Journal. All Rights Reserved.

5 ACSIJ Advances in Coputer Science: an International Journal, Vol., Issue, No., March 05 For encoding a string i(x) with k sybols in RS ethod, we ust take these steps [9,]: Step : i(x) will be shifted by n k sybols to the left. Which creates n k sybols with a value of zero in the right side of i (X). It can be done by ultiplying i(x) by n k X. Fig. shows this procedure. Fig.. Method of ultiplying i(x) by n k X n k Step : In this step, we ust divide i( X ). X by the generator polynoial gx ( ) The reainder is shown by rx ( ). Step 3: rx ( ) will be placed in the n k n k and deterine its reainder. epty places in the right side of i( X ). X. In this way, a codeword is created that we call it cx ( ) and is as follows: Then, i can be written as follows: (8) i (,,,,,,,,,,) We can write polynoial i(x) as follows: i(x)= α X α X α X α X α X α X α X α X α X α X (9) Step : In this step, the generator polynoial g (X), should be deterined. So, we ust select the roots of 3 g (X). The roots of g (X) is selected as,, and 5 (how to deterine has been explained earlier). Because each of these four roots have one less factor than the previous one and the calculation becoes easier. g(x) is created as below: 3 g( X ) ( X )( X )( X )( X ) g(x) X X X X Step : For encoding the string i (X) (0), we have to divide i( X ). X by g (X) and deterine the reainder: r( X ) i( X ) X od g( X ) r( X ) X X X 0 () n (5) c( X ) i( X ) X r( X ) To further clarify this process, we provide an exaple by RS (5,), we have: n 5, k (6) n k t, Step 3: We write c (X) as follows: c( X ) i( X ) X r( X ) c(x) = (α X α X α X α X α X α X α X α X α X αx X ) α X α X α X () As previously entioned, RS code can detect ( n k) error sybols. It also can correct ( n k) / error sybols. In other words, RS (5,) can detect ( n k) or ()=6 error bits and correct ( n k) / or ()/=8 error bits. Assue that we want to encode the following bits string: i ( ) (7) In this way, codeword is created as follows: ( ) (3) It can be seen, the length of c (X) is 60 bits. This eans the initial inforation which was bits, is transfored to 60 bits. 7 Copyright (c) 05 Advances in Coputer Science: an International Journal. All Rights Reserved.

6 ACSIJ Advances in Coputer Science: an International Journal, Vol., Issue, No., March The RS Decoder Decoding is the duty of the receiver. Iediately after receiving a codeword, the receiver detects whether an error occurred or not. The steps for error correction and detection in the RS coding ethod, are as below [,3,]:. Calculating the Syndroe Decoder.. Deterining the Error Locator Polynoial (ELP) for calculating the error location in the codeword. 3. Deterining the Error Evaluator Polynoial (EEP) for calculating the aount of errors in each location. Correcting the errors (if any). In the following, the ethod for calculating syndroe decoder is explained. We entioned that after taking the encoding steps, a polynoial appears which is divisible by g (X), thus its reainder after the division by g (X) is zero. In this way, if the data which is received by the receiver is divisible by g (X), it indicates that no errors occurred. Otherwise, it is concluded that soe errors have occurred and the codeword is invalid. It is also clarified that g (X) can be written in for of Eq. (). Also the roots of g (X) are shown by Eq. (3). In this case, if we call the codeword which is received by the receiver v (X), the roots of g (X) are also the roots of v (X). So, to deterine whether an error has occurred, it is sufficient to see whether t,,..., are the roots of v (X) or not. For this purpose, just have to place these roots instead of the variable X in v (X). If the value of v is zero with this placeent, it indicates that no errors have occurred, otherwise we will know there is an error. So in general, for error detection, we ust deterine the value of v (X) for each root of g (X). The whole procedures which are explained so far is called syndroe calculation and can be suarized as: 0 S0 v( ) 0 S v( ) 0 t St v( ) () We call S0, S,..., St the syndroes of v (X). If all the S 's are zero, it eans that we have no errors. Otherwise, there is an error and we ust correct its location and value. 5. The Bose-Chaudhuri-Hocquenghe (BCH) Code As it is entioned before, since the BCH code acts on bits, so it is naed binary. On the contrary, the RS code acts directly on sybols so it is called non-binary [5]. The BCH code is a rando error correction code. This code is capable of correcting errors occurred randoly in the inforation string. The BCH and RS codes are also called rando and burst error correction codes, respectively. The BCH code can also be called a generalized odel of Haing code that is capable of correcting ultiple errors whereas the Haing code is only capable of correcting one error. The BCH code siilar to the RS code, is based on GF atheatical structure. In a BCH code, for positive integers 3 and t, we have a BCH code with the following characteristics [,5,6]: n, n k t,d t (5) in where, n indicates the length of codeword (block), n k t indicates nuber of parity bits and din t represents the iniu distance of code. It should be obvious that this code can correct any cobination of t errors in a block with length of n. A code with this characteristic is called a BCH code with capability of correcting t errors. The generator polynoial for this code is deterined by its roots which belong to GF ( ). If is the priitive eleent of GF ( ), the generator polynoial g (X) is a polynoial with the least degree and with coefficients of GF () which its roots are as follows: 3 t t,,,...,, (6) It is iportant to understand that the ost iportant concern about the BCH codes, is their difficult decoding [,6,7]. 5.3 Product Codes Product codes can be called the first group of cobinational codes which presented with the ai of ore error correction capability. These codes are ade by cobination of two block codes ( n, k, d) and 75 Copyright (c) 05 Advances in Coputer Science: an International Journal. All Rights Reserved.

7 ACSIJ Advances in Coputer Science: an International Journal, Vol., Issue, No., March 05 ( n, k, d ). This results are generated in a new block code with the for of ( n n, kk, dd ) [8,9] Product Codes Encoder A product code can be considered as a two-diensional array. Its rows and coluns are apped by the first and the second codes, respectively. Fig. 3 shows how to for a two-diensional array with eleents of two block codes. Fig.. How to find a non-zero iniu weight of codeword C 5.3. Product Codes Decoder Fig. 3. Creation of the two-diensional array in product codes. A product code which is shown by C, is encoded using the first location of inforation bits in a k k atrix. Each colun of the atrix k k is encoded by coponents ( n, k, d ) of code C. The result of encoding is stored in a n k atrix. Each row of the n k atrix is encoded by coponents ( n, k, d ) of code C and the result of encoding is stored in a n n atrix. Therefore, we have a ( n n, kk ) code. For decoding, first we need to decode all the coluns by a decoder for C and all the rows by a decoder for C, respectively. However, this ethod only ensures that errors d with a weight of d dd. can be decoded. Fig. 5 shows how a product code can be decoded. The goal is to find the iniu distance of codeword C. We should find the sallest non-zero weight of codeword C. Assue that a codeword in its non-zero situation, for instance, in situation (i, j). In this case, the weight of colun j is at least d. Thus, we have d non-zero rows, including rows i. Each of these rows at least have weight d. It can be concluded that the weight of codeword C would be d d. Fig. deonstrates this proble. As we entioned before, the sallest non-zero weight of codeword C should be found. The represented black squares depict the non-zero situations [9]. Fig. 5. Methods of finding errors in product codes for decoding. (a) occurrence of a single error, (b) occurrence of two errors in different rows and coluns, (c) occurrence of two errors in the sae rows and (d) occurrence of two errors in the sae coluns. For exaple, we assue the codes C and C with coponents (3,,) and (5,,), respectively. Because the difference between n and k in these codes is, we conclude that each of the above codes has a redundancy bit. The product code resulting fro the two above codes is (5,8,). 76 Copyright (c) 05 Advances in Coputer Science: an International Journal. All Rights Reserved.

8 ACSIJ Advances in Coputer Science: an International Journal, Vol., Issue, No., March Low Density Parity Check (LDPC) Codes Low Density Parity Check (LDPC) codes are fro the block codes faily that their parity check atrix ( H ) has a sparse atrix for. A sparse atrix is a atrix that its non-zero eleents are far fewer than its zero eleents. Generally, LDPC codes are organized into two regular and irregular groups. In the regular group, the nuber of nonzero eleents in all rows and all coluns in the atrix H are equal. LDPC codes are one of the ain rivals for Turbo codes. Both of the are used in current optical counications [0,]. ek is introduced by the pair of vertexes ( vi, vj) at its ends. Edges and vertexes are also called branches and nodes, respectively. The nuber of branches connected to each node is called the degree of the node and is shown by dv ( i ). For exaple, structure of the Tanner graph for the Haing code (7,) is shown by Fig LDPC Codes Encoder In this section, the creation of LDPC codes based on RS codes is explained. If we assue that is the priitive eleent of GF (q) such that s q p is a power of a prie nuber, and also we pick the positive integer p such that p q, the generator polynoial of code RS( q, q p, p ) on GF (q) is deterined as follows []: p g( X ) ( x )( x )...( x ) p g( X ) g0 gx gx... X (7) In Eq. (7), gi GF( q). It is iportant to note that in Eq. (7), the polynoial has the lowest degree aong other polynoials of the related code and all its p coefficients are non-zero. If we truncate this code by deleting q p inforation sybols, a reduced code RS( q,, p ) is created that only has two inforation sybols and the nuber of its codewords will be q. The generator atrix of such code has two rows and is written as below [3]: Gb g0 g g... 0 [ ] 0 g0 g g... (8) 5.. LDPC Codes Decoder LDPC codes are decoded in a repetitive anner. Decoding in LDPC codes is done using a graph naed the Tanner graph. The edges in the graph, are those routes that inforation goes through. This graph is used to represent the atrix H []. A graph G(V, E) V consists of the set of vertexes { v, v,...} and set of edges E e e {,,...}. Each edge Fig. 6. Structure of the Tanner graph for the Haing code (7,). Bit-flipping is a decoding algorith for LDPC codes [,5]. This ethod is based on the principle of restoration of syndroe equations by reversing soe bits of the received string. The ipleentation steps of this algorith are as follows: Step : All vi nodes (also called variable nodes) send their inforation to c j nodes connected to the. Step : c j nodes (also call parity nodes), calculate the su of the received bits and return the result (zero or one) to every node connected to the. Step 3: vi nodes, select a new value based on the ajority vote by receiving this inforation fro parity nodes connected to the and with the respect to their current value. Step : The algorith repeats fro Step until either all the syndroe equations are satisfied or the preset nuber of repeats is reached. For exaple, assue that the received string on the receiver is V (000). The given atrix H for this graph is as follows: (9) Also, the Tanner graph for the given atrix H is shown by Fig Copyright (c) 05 Advances in Coputer Science: an International Journal. All Rights Reserved.

9 ACSIJ Advances in Coputer Science: an International Journal, Vol., Issue, No., March 05 shown. As we can see, each ethod has its pros and cons. For exaple, RS and BCH have burst errors and rando error correction capability. Product codes have less processing delay. LDPC codes suitable for long codeword lengths. They also support a fully parallelis decoding and this is very well when considering long codewords. Fig. 7. Exaple of the Tanner graph with received string V (000) on the receiver. Step : The inforation of string V is sent to the parity nodes and it can be seen that the values of the parity nodes after the inforation was sent, will be C 0, C 0, C, C. 3 Step and 3:In these steps, we look at parity nodes with value. If the parity nodes with value are connected to a variable node, the value of that variable node will becoe 0, by doing XOR the value of parity nodes connected to the variable node. According to this assuption, only the value of the variable node V becoes 0. Because the two parity nodes C and C with value are connected to V. Step : Since the string 000 has been transfored to 0000 and this new string is again sent to the parity nodes, and because all the parity equations are satisfied and C C C3 C 0, the decoding stops. 6. Conclusions Error control coding is an iportant proble in odern counication systes. Since optical fibers are widely used for exchange of inforation all around the world, providing appropriate solutions for error control coding is crucial. In this paper, four types of error control coding ethods which are used in optical fiber counication systes were introduced. RS is coonly used in ost long haul optical fiber counication systes and is capable of correcting burst errors. BCH code is capable of correcting rando errors which occur during transission. Product codes have significantly less processing delay and are very useful in optical fiber. LDPC codes have good distance properties, particularly for long codeword lengths, therefore suitable in optical fiber counication systes. The structure of these ethods were described and coding/decoding approaches were explained with a lot of practical exaple. Based on contents described so far, we present Table. In this table the advantages and disadvantages for ost iportant criteria of each ethod is Table. Types, advantages and disadvantages of error control codes Codes Type Advantages Disadvantages Burst Errors correction and low Reed- Alphabet size is Linear coputational Soloo as large as their Block coplexity with n length predictable decoding capabilities BCH Product LDPC Linear Block Cobina tional Linear Block Rando Errors correction and ease of decoding by syndroes Decreased Bit Error Ratio perforance and significantly less processing delay Good distance properties, particularly for long codeword lengths. They also support a fully parallelis decoding and this is very well when considering long code-words. Coplex decoding Coplex atheatical structure Coplex encoding and inflexibility References [] E. A. B. Saleh and M. C. Teich, Fundaentals of photonics, John Wiley and Sons Inc, 99. [] B. P. Sith and F. R. Kschischang, Future prospects for FEC in fiber-optic counications, IEEE Journal of Selected Topics in Quantu Electron, vol. 6, no. 5, 00, pp [3] D.J. Costello, J. Hagenauer, H. Iai and S.B. Wicker, Applications of error-control coding, IEEE Transactions on Inforation Theory, vol., no. 6, 998, pp [] G. Gho, L. Klak and O. M. Kahn, Rate-Adaptive coding for optical fiber transission systes, IEEE Journal of Lightwave Technology, vol. 9, no., 0, pp [5] S. Cho, Adaptive Forward Error Correction Schee for 78 Copyright (c) 05 Advances in Coputer Science: an International Journal. All Rights Reserved.

10 ACSIJ Advances in Coputer Science: an International Journal, Vol., Issue, No., March 05 Real-Tie Counication in Satellite IP Networks, KSII Transactions on Internet & Inforation Systes, vol., no. 6, 00, pp. -6. [6] M. Zhang, Z. Wang, M. Guo, A Method of Cobining Scrabling Technology with Error Control Coding to Realize Both Confidentiality and Reliability in Wireless MM Counication, KSII Transactions on Internet & Inforation Systes, vol. 6, no., 0, pp [7] I. B. Djordjevic, M. Arabaci and L. L. Minkov, Next generation FEC for high-capacity counication in optical transport networks, IEEE Journal of Lightwave Technology, vol. 7, no. 6, 009, pp [8] J. Clienta, V. Herranzb and C. Pereab, Linear syste odelization of concatenated block and convolutional codes, Elsevier Linear Algebra and its Applications Journal, vol. 9, no. 5 6, 008, pp. 9. [9] K. Fenga, L. Xua and F. J. 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Guoleia, Interleaved Processing of Bit-Flipping Decoding For LDPC Codes, Elsevier Procedia Engineering Journal, vol. 5, 0, pp Majid Hataian received his B.S. degree in Coputer Hardware Engineering in 03. He is currently working toward the M.S. degree in Coputer Systes Architecture Engineering in Dezful Branch, Islaic Azad University, Iran. His ajor research experiences and interests include Wireless Networks and Mobile Counications, Cryptography and Data Protection, Security Issues in Wireless & Ad-hoc Networks and Machine Learning Techniques. Haid Barati received his B.S. degree in Coputer Hardware Engineering, M.S. degree in Coputer Systes Architecture Engineering and Ph.D. degree in Coputer Systes Architecture Engineering in 005, 007 and 0 respectively. Currently he is faculty of Islaic Azad University, Dezful Branch, Iran. His ajor research experiences and interests include Mobile Ad-Hoc Networks, Interconnection Networks & Energy-Efficient Routing and Security issues in Wireless Sensor Networks. Saaneh Berenjian is an inforation technology engineer. Her research interests are in the areas of Intrusion Detection systes, Autoated Intrusion Response Systes, Security protocols and Cryptographic algoriths where she is aiing to expand her research at security in e-health systes. She has worked in ISEC lab under the supervision of Dr. Mehdi Shajari since 0. She has graduated with a M.Sc. in IT engineering fro the Departent of Coputer Engineering and Inforation Technology, Airkabir University of Technology. Alireza Naghizadeh received his M.S. in Inforation Technology fro University of Guilan, Iran in 03. His current research interests are distributed and PP networks, specializing in security, anonyity, gae theory, network anageent and network architectures. He presents his papers in several acadeic seinars, workshops and has published over research papers in international journals and conferences. Behrooz Razeghi was born in Mashhad, Iran, in 989. He received the B.Sc. degree (First-class Honours) in Electrical and Counication Engineering fro Sadjad University of Technology, Mashhad, Iran, in 0. He is currently a research assistant in the Departent of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran. During his undergraduate studies, his research was focused on electronic circuits and 79 Copyright (c) 05 Advances in Coputer Science: an International Journal. All Rights Reserved.

11 ACSIJ Advances in Coputer Science: an International Journal, Vol., Issue, No., March 05 control systes. His current research interests fall into the broad areas of wireless counication, inforation theory, counication theory, coputer network, inforation theoretic learning, and optiization ethods in counications and networking. He is the author or co-author of ore than 5 technical papers published in scientific journals and presented at international conferences. He has been a eber of Technical Progra Coittees for several conferences and served as reviewer for nuerous IEEE international journals and conferences. 80 Copyright (c) 05 Advances in Coputer Science: an International Journal. All Rights Reserved.