Performance of Modified Iterative Decoding Algorithm for Multilevel Codes in Adaptive OFDM System

Transcription

1 Internatonal Journal of Computer Informaton Systems and Industral Management Applcatons. ISSN Volume 6 (04) pp. - 0 MIR Labs, Performance of Modfed Iteratve Decodng Algorthm for Multlevel Codes n Adaptve OFDM System Atta-ur-Rahman Insttute of Sgnals, Systems and Softcomputng (ISSS), Islamabad, Pastan Baran Insttute of Informaton Technology (BIIT), PMAS-Ard Agrculture Unversty, Rawalpnd, Pastan ataurahman@bt.edu.p Abstract: In ths paper, the Modfed Iteratve Decodng Algorthm (MIDA) s nvestgated for decodng Mult-level codes. Adaptve Orthogonal Freuency Dvson Multplexng (AOFDM) system s used as system model for ths experment. MIDA s a hard decson decoder that was ntally proposed for decodng of Product codes and later for Mult-level codes by same authors. As Mult-level codes are matrx codes we have found that they have structural compatblty wth OFDM systems. In OFDM system each subchannel may have dfferent channel state nformaton (CSI) whch may be varyng over the tme. So a Multlevel code wth sutable combnaton of consttuent row codes can play a vtal role n combatng poor channel condtons on OFDM subchannels. A fuzzy rule based system (FRBS) s used for selecton of sutable most Multlevel code and modulaton symbol. Performance s shown by smulatons. Keywords: Modfed Iteratve Decodng Algorthm, Mult-level Codes, Bt Error Rate, Lnear Bloc Codes. I. Introducton Concatenated codes are manly categorzed nto two types. Frst the seral concatenated codes also called product codes [] and the second type s parallel concatenated codes also called turbo codes []. Product codes were frst presented by Elas n 954 [3]. The structure of Product codes s smple and powerful n whch nstead of usng one long bloc codes a number of small codes are concatenated that can be decoded n parallel fashon. These are matrx codes havng rows encoded by one bloc code and columns are encoded by another bloc code. Mult-level codes belong to the famly of Product codes. The only dfference s that n Mult-level codes each row may be encoded by a dfferent bloc code whle all the columns are encoded by same bloc code. Ths structure s sutable for many adaptve orthogonal freuency dvson multplexng (AOFDM) systems, where dfferent code rates may be assgned to dfferent subcarrers based upon ther channel state nformaton (CSI). Mult-level codes are also ute practcal n a sense that they have been used n many wreless standards nowadays especally n adaptve systems le WIFI (IEEE 80.n) [4] and WMAX (IEEE 80.6/e) [5]. Snce ther structural characterstcs are very much compatble wth OFDM systems, product codes are recommended for almost all 3 rd Generaton (3G) and 4 th Generaton (4G) systems ncludng wreless local area networs (WLAN) and HYPERLAN standards [6]. In hs PhD dssertaton, Al-Asary [6] proposed an teratve decodng algorthm for Product codes. That algorthm was based upon Lst Decoders for rows are columns and desgnated as the Maxmum Lelhood (ML) decoder of product codes [7]. ML decodng s an optmum decodng n whch complexty grows exponentally wth the codes sze and number of teratons. The modfed teratve algorthm (MIDA) was orgnally proposed for decodng of Product codes by Attaur-Rahman et al [8]. It s hard decodng algorthm that sgnfcantly reduces complexty of the basc teratve algorthm proposed by [6]. In [9], MIDA was proposed for Mult-level codes and the decoder s performance was nvestgated over an OFDM system. Moreover, the performance Mult-level codes wth dfferent parameters were demonstrated. It was shown that proposed scheme performs sgnfcantly better than the best scheme n the same area. In [0], an adaptve codng and modulaton scheme was proposed for OFDM systems n whch Product codes were used as forward error correcton (FEC) codes and Quadrature Ampltude Modulaton (QAM) as modulaton scheme. MIDA was used to decode the Product codes n ths scheme. A Fuzzy Rule Based System (FRBS) was used to select the sutable code rate and modulaton symbol dependng upon the channel state nformaton (CSI). It was shown through smulaton results that the proposed scheme performs sgnfcantly better than HYPERLAN/ standard scheme. Smlarly, n [, ], same Fuzzy Rule Based System s used for varous codng schemes le Convolutonal Dynamc Publshers, Inc., USA

2 Rahman codes etc. It was found the fuzzy logc approach performs best n the envronments that are vague and unclear and mssng certan nformaton. In [3], a resource allocaton and resource levelng technue for heterogeneous SANETs (sensor actve networs) envronment, s presented. There ntroduced a RMU (resource management unt) that ensures a cooperatve communcaton and provdes features for an on-demand channel relocaton. In [4], Fuzzy Logc s used for sutable web access. In ths paper authors presented assessment methodology and model for performance measurement of dynamc webstes. It was named as Fuzz-Web; fuzzy logc s used for tang ntellgent decson regardng performance measurement. Rest of the paper s organzed as follows: Secton presents the basc model; structure and constructon of Mult-level Code s gven n Secton 3; Secton 4 s based on Iteratve Algorthm. Secton 5 presents the proposed Algorthm. Secton 6 s conssted of FRBS based adaptve codng and modulaton wth Mult-level codes, Secton 7 covers smulaton results whle secton 8 concludes the paper. II. System Model The system model consdered s an OFDM euvalent baseband model wth N number of subcarrers []. The freuency doman representaton of system s gven by y h. p. x z ;,,..., N () where y, h, p, x and z denote receved sgnal, channel coeffcent, transmt ampltude, transmt symbol and the Gaussan nose of subcarrer,,..., N, respectvely. The overall transmt power of the system s P total N p and the nose dstrbuton s complex Gaussan wth zero mean and unt varance. It s assumed that the complete channel state nformaton (CSI) at any subcarrer s nown to transmtter and recever ncludng whch row code s beng used at any subcarrer. It s also assumed that sgnal transmtted on the th subcarrer s propagated over an ndependent nondspersve sngle-path Raylegh Fadng channel and where each subcarrer faces a dfferent amount of fadng ndependent of each other. Hence, the channel coeffcent of th subcarrer can be expressed as: j h e ;,,..., N () where s Raylegh dstrbuted random varable of th subcarrer, and the phase s unformly dstrbuted over 0,, whle j s ota symbol snce phase s complex. Fg- contans the basc system model used for smulatons. In OFDM Systems one bg data stream s dvded nto a number of relatvely small data streams by nverse fast Fourer Transform (IFFT). These streams are modulated over orthogonal subcarrers and addton of adeuate cyclc prefx maes the system nter-symbol nterference (ISI) free. III. Transmtter Recever Mul-Level Codes Fgure. System Model As t s already descrbed that mult-level codes belong to the famly of Product codes, so n order to understand the mult-level codes, let s have a loo at constructon of Product codes. Consder two bloc codes A and A wth parameters [ n,, d] and [ n,, d ] respectvely, where n, and d ;, are the length, dmenson and mnmum Hammng dstance ( ) of the code d mn A (,) respectvely. Code A wll be used as row code whle A wll be used as column code. The rates of ndvdual codes are R and Rrespectvely gven by, R,, (3) n The product code Ω can be obtaned by codes A,, n the followng manner. Place nformaton bts n an array of rows and columns Encode rows usng code A, whch wll result n an array of n Now encode n columns usng code A, whch wll result n nnproduct code. The resultant product code Ω has the parameters [ nn,, dd ] and the rate wll be RR. In ths way long bloc codes can be constructed usng much shorter consttuent bloc codes. Ths concept can also be vewed as that product code Ω s ntersecton of two codes A and A. Where A s a code represented by all nnmatrces whose each row s a member of code A, smlarly A s a code represented by all nnmatrces who s each column s a member of code A. Ths can be wrtten as; Ω A A (4) Mult-level Encoder MIDA Decoder for Mult-level codes BPSK Modulator Channel BPSK Demodulator

3 Performance of Modfed Iteratve Decodng Algorthm for Multlevel Codes n Adaptve OFDM System 3 Fgure. Structure of the Product code Now as far as mult-level codes are concerned the rows of these codes are encoded by a set of bloc codes havng same dmensons but dfferent code rates whle column s mostly encoded by one bloc code. Consder a set of lnear bloc codes; that s C [ A ]; S, where S s cardnalty of the set. A [ n,, d ] are the elements of the set, where and d ;,..., S are the dmenson and mnmum Hammng dstance d mn of the code respectvely and n represents code length. The dmensons of all codes taen must be same n order to mae the mult-level code a matrx code. The rates of ndvdual row codes are gven by, R,,,... S (5) n The column code B [ nc, c, dc ] where nc, c and d c represents dmenson, sze and mnmum dstance of the column code. The multlevel code Θ can be defned as set of all matrces whose rows belong to set C and whose columns belong to code B. IV. Iteratve Algorthm The dea of Iteratve decodng algorthm for Product code was orgnally proposed by Al-Asary [6], for reference purpose t s restated here. The decoder s conssted of two sub-decoders, namely one for rows whle other for columns. The receved n n matrx R can be wrtten as; R = X+ N (6) where X and N are transmtted and nose matrces of dmensons n n respectvely. The receved matrx s fed to row and column decoders n successon at each stage of teratve algorthm. At frst row decoder gves ts suggested soluton, whch s further fed to column decoder, whch after processng returns ts suggested soluton, ths process contnues n all stages of decoder untl a stoppng crteron met. A detal of these sub-decoders s gven n turn. Fg-3 shows the flowchart of teratve decodng algorthm and fg-4 shows the status of th state of the teratve decoder. A. Row Decoder Ths decoder receves a matrx and as a result provdes another matrx as a soluton n whch rows of the ncomng matrx are corrected. At the th stage of teratve decoder ths sub-decoder taes the prevous nn soluton S as nput and creates a lst L that conssted of n sub-lsts, where each sub-lst s mantaned for the correspondng row n S. As we have already mentoned that we have to nowledge that whch row s encoded by whch consttuent code from set C. Each sub-lst contans those code words n code space of A whose dstance from that row s less than or eual to e A, n ascendng order, where e A s referred as decodng radus of row decoder correspondng to bloc code n set C. The lst L at decoder s stage can be represented as the Cartesan product of all sub-lsts, namely; n j ( ) e A j,: j L ( S, A ) (7) Where j e A s a sub-lst that contans the canddates for the jth row n matrx S. After the lst s prepared, decson wll be taen as descrbed below. B. Decson crtera for row decoder Row decoder returns ts suggested soluton T, n the followng way; mn D ( tr, ) mn(, ) T arg t L D ( t, R ) (8) where D, are, defned as; D = some dstance defned le Hammng dstance D( T, R ) ; dstance of th stage row soluton and receved matrx D( S, R ) ; dstance of th stage column soluton and receved matrx So n other words the row decoder at stage chooses the member of lst L that s closest to R, but at a dstance greater than the solutons suggested n prevous stages,.e., mn(, ). Then ths suggested soluton wll be further processed by column decoder. C. Column Decoder Smlar to that of row decoder column decoder concerns wth the columns of receved matrx R. At th stage of teratve decoder ths sub-decoder taes the prevous nn soluton T that was suggested by th stage row decoder, as nput and creates a lst L that conssted of n sub-lsts, where each sub-lst s populated for the correspondng column n T. Each sub-lst contans

4 4 Rahman those code words n B whose dstance from that column s less than or eual toe B n ascendng order, where e B s referred as decodng radus of column decoder. The lst L at decoder s stage can be represented as the Cartesan product of all sub-lsts; n j ( ) eb :, j j L ( T, B ) (9) j where s a sub-lst that contans the canddates for the eb jth column n matrx T. After the lst preparaton, decson wll be taen n the followng manner. D. Decson crtera for column decoder Column decoder returns ts suggested soluton S, n the followng way mn D ( sr, ) mn(, ) S arg s L D ( s, R ) (0) Where D, are, same as defned above. So n other words the column decoder at stage chooses the member of lst L that s closest to R, but at a dstance greater than the solutons suggested n prevous stages, than s, mn(, ). E. Stoppng Crtera Ths row/column decodng at each stage wll go on n turn tll the number of stages that are adjusted by the user. Then the last stage soluton wll be the ultmate decodng soluton. Yes Receved Code Matrx R Row Decoder Column Decoder Iteraton++ Iteraton<=MaxIteraton No Fgure 3. Flow chart of teratve decoder DECISION Fgure 4. th stage of teratve decoder V. Proposed MIDA for Mult-level Codes Proposed Modfed Iteratve Decodng Algorthm s a revsed verson of Iteratve decodng algorthm proposed by [6]. It s a hard decson decoder. Syndrome decodng of lnear bloc codes s used for complexty reducton [9]. In ths way number of rows/columns, for whch lsts are to be bult, s reduced sgnfcantly. Man changes n prevous Iteratve decodng algorthm are: In row decoder rows wll be frstly passed through a Syndrome chec. If the Syndrome of any row results n 0 (.e. row s correct), then no sub-lst wll be populated for that row and the row tself wll be returned as a decoded soluton. Mathematcally, where S H 0 (). T j,: H s party chec matrx of the correspondng row code A ;,,..., S In column decoder each column wll be checed by Syndrome decoder. If the Syndrome of any column results n 0 (.e. column s correct), then no sub-lst wll be populated for that column and the column wll be return as a decoded soluton. Mathematcally, T H 0 () T :, j. B where HB s party chec matrx of the column code B Sub-lsts, wll be generated only for those ea eb rows and columns respectvely, who s Syndrome wouldn t result n 0. Decodng rad of rows decoder wll be chosen as ( t ); where t s error correcton capablty of A A row code A ;,,3,..., S n set C. Decodng radus of column decoder wll be chosen as ( t B ); where t B s error correcton capablty of column code B So the Eu-7 and Eu-9 wll be changed to two new Eu-3 and Eu-4 whch help great reducton n decodng complexty for the same state of art. ~ n j ( ) e (,:, ); A j n n j L S A (3) ~ n j ( ) e ( :,, ); B j n n j L T B (4) Smlarly the Eu-8 and Eu-0 wll be converted to;

5 Performance of Modfed Iteratve Decodng Algorthm for Multlevel Codes n Adaptve OFDM System 5 ~ mn ~ T arg t L D ( t, R ) (5) D ( tr, ) mn(, ) mn ~ ~ S arg s L D ( s, R ) (6) D ( sr, ) mn(, ) Proposed MIDA Algorthm for Multlevel Codes Let R be the receved code matrx nxn. whle ( Max no of teratons ) do a) If ((each row of R s the member n the correspondng row code n set C) and (each column of R s the member n column code B)) then go to step b, otherwse to step c b) Return R as the decoded soluton and go to step c) Mar those rows n R that are members n the correspondng row code n set C and those columns that are member of column code (usng Syndrome chec), respectvely d) Mae lsts for unmared rows ( n ) and columns ( n ) usng Eu-3 and Eu-4, wth decodng rad ( t A ) and ( t B ) respectvely e) Tae decsons for suggested soluton n row/column decoders at th stage of teraton usng Eu-5 and Eu-6 respectvely. f) R S g) go to. Ext VI. Adaptve Codng and Modulaton usng FRBS Adaptve codng and modulaton for OFDM system usng Fuzzy Rule Base System was orgnally proposed by [0]. We are utlzng the same technue here for adaptng Mult-level code rate and modulaton scheme wth respect to the changng channel state envronment at OFDM subcarrers. The adaptaton mechansm s shown n fg-5. Smlar wor s done n [] and [] for convolutonal codes. FRBS was used to choose the optmum modulaton code par for the gven channel state nformaton at ndvdual subchannels of OFDM system after each transmsson nterval. Transmtter of PHY Layer Feedbac Channel OFDM Channel New Modulaton Code Par PHY layer Recever Channel Estmates Qualty of Servce Demand per Subcarrer Ln Adaptaton per subcarrer usng FRBS Sgnal s transmtted through the OFDM physcal (PHY) layer (ar nterface). After passng through the channel, PHY layer recever obtans the channel estmates. Along wth the channel estmates, ualty of servce demand s fed to the ln adaptaton bloc (LAB). LAB whch s actually Fuzzy Rule Based System (FRBS) suggests the optmum modulaton code par that maxmzes the OFDM system throughput whle satsfyng certan constrants. A. Codng Scheme Codng schemes used for ths framewor are set of Mult-level codes. The set of row codes and column codes used n ths paper are lsted n table. All of these codes are BCH codes. TABLE I. CODING PARAMETER Sr Row Code Column Code Product Code Code rate C [63,63,] [63,57,3] [3969,359,3] 0.9 C [63,57,3] [63,57,3] [3969,349,9] 0.8 C3 [63,5,5] [63,57,3] [3969,907,5] 0.73 C4 [63,36,] [63,57,3] [3969,05,33] 0.5 C5 [63,63,] [63,63,] [3969,3969,] C6 [63,57,3] [63,63,] [3969,359,3] 0.9 C7 [63,5,5] [63,63,] [3969,33,5] 0.8 C8 [63,36,] [63,63,] [3969,68,] 0.57 So set of code s conssted of four dfferent product codes. That s C { C }; 8 (7) The reasons for selecton of these codes are as under. All codes are of same length would be helpful n hardware mplementaton Same length of row codes mae t possble for decodng snce f we use dfferent length codes then upon recevng receved matrx may not be formulated B. Modulaton Scheme The modulaton scheme used for ths experment s Quadrature Ampltude Modulaton (QAM) whch s recommended by many OFDM standards. Followng set of modulaton schemes s used. That s M {, 4,8,6,3, 64,8} (8) So wth these codng and modulaton sets we have twentyeght possble modulaton code pars (MCP) by a Cartesan product of the sets C and M. Ths can be gven by the expresson. P Cx M {( c, m ); c C, m M } (9) j j After decdng modulaton and codng schemes for ths framewor, all of the possble combnatons of modulaton code pars are plotted n subseuent fgures. In fg-6, all modulaton schemes namely from QAM to 8QAM are plotted usng Product Code C5 as lsted n table. Smlarly, n fg-7 and fg-8 dfferent QAM modulatons are plotted usng Product codes C and C3 respectvely. Fgure 5. Proposed Adaptaton Model

6 6 Rahman Ths table shows the facts extracted for smulated performance of dfferent codes and modulaton pars n prevous secton. It can be stated as for a gven receved SNR and a fxed QoS, whch MCP maxmzes the throughput. Receved sgnal to nose rato s expressed n level to level 9 and Qualty of Servce are gven le poor, med, good and hgh that s 3 4 0,0,0,0 respectvely. Fgure 6. Performance of dfferent QAM schemes usng C5 as row code Fgure 9. Looup Table for FRBS Creaton Fgure 7. Performance of dfferent QAM schemes usng C Fgure 8. Performance of dfferent QAM schemes usng C3 We have used a fuzzy rule base system (FRBS), whch s capable of decdng the best modulaton code par (MCP) for the next transmsson, based upon the heurstcs. Fuzzy logc s best suted for the stuatons that are vague, ambguous, nosy or mssng certan nformaton. There are many ways we o buld a Fuzzy Rule Base System, we have used table looup scheme for ths purpose. The looup table s gven n fg-9. C. Rate Optmzaton In order to maxmze the rate for OFDM system followng constraned optmzaton problem s consdered. N max RTotal r N s.t, BER BER and Total N P p P Total T T (0) where r (log ( M )) R s the product of code rate and modulaton bts/symbol over th subcarrer. s the avalable transmt power. BER T s target BER that depends upon a specfc ualty of servce (QoS) reuest or applcaton reurement. The possble QoS assumed are 4 3 BER T 0,0,0,0 whle N s total number of subcarrers n OFDM system. The above cost functon s optmzed by the proposed Fuzzy Rule Base System. It wll be decded that whch modulaton code par s sutable for transmsson based upon the average channel state nformaton (CSI) at the subcarrers and the Qualty of Servce demand. We have used the table loo-up scheme for desgn of ths fuzzy rule base system usng the followng steps. The nput-output pars needed for desgn of FRBS are provded n fgure 8. They are of the form; p p p ( x, x ; y ); p,,3... M () PT

7 Performance of Modfed Iteratve Decodng Algorthm for Multlevel Codes n Adaptve OFDM System 7 p p where x represents receved SNR, x represents p reured BER (QoS) and y represents the output MCP suggested by FRBS, so the rule format wll be gven as; {IF ( x s Good and x s L7) THEN y s P5} Followng s the bref descrpton of dfferent components of fuzzy rule based system used. Desgn of the FRBS s carred out n MATLAB 7.0 standard Fuzzy System Toolbox. The nterface of the toolbox s gven n fg-0 and fg-. E. Fuzzfer Standard trangular fuzzfer s used wth AND as MIN and OR as MAX. F. Rule Base Rule base contans rules aganst all the IO pars. As there are nne sets (L to L9) for frst nput varable named SNR and about four sets (low, medum, good and hgh) for nput varable QoS. Hence there are 36 rules n rule base. G. Inference Engne Standard Mamdan Inference Engne (MIE) s used that wll nfer whch nput par wll be mapped on to whch output pont. H. De-Fuzzfer Standard Center Average Defuzzfer (CAD) s used for defuzzfcaton. Ths s because t fulflls all the reurements of a good de-fuzzfer. Le t s computatonally lght and ts performance s better than ts peers. Fgure 0. Fuzzy Rule Edtor Fgure. Fuzzy Sets for nput varable receved SNR Fgure 3. Fuzzy Sets for nput varable QoS Fgure. Fuzzy Rule Base System at a glance D. Fuzzy Sets Suffcent numbers of fuzzy sets are used to cover the nput output spaces. There are two nput varables average receved SNR and QoS that represents a BER. There s one output varable for modulaton code par MCP. All of these nput and output varables are depcted n fg-, fg-3 and fg-4 respectvely. There are nne, four and eghteen fuzzy sets used for the varables SNR, QoS and MCP, respectvely, where SNR and QoS are nput varables whle MCP s output varable. Fgure 4. Fuzzy Sets for output varable Modulaton Code Par

8 8 Rahman Fgure 5. Rule surface Fg-5 shows the rule surface that shows that by ncreasng SNR the throughput s maxmzed. Also on the other hand for poor QoS throughput s more than that of hgh QoS. A combned effect of both nput varables namely SNR and QoS can be seen n that fgure. For the hghest value of SNR and lowest value of QoS, throughput of the system approaches to 5bts/s/Hz. VII. Smulaton Results The components of multlevel codes used n the smulaton are gven n the table-i, whle smulaton parameters are gven n table-ii. There are four row codes wth dfferent code rates but same code length because accordng to structure ultmately t should become a matrx. Two dfferent column codes are nvestgated n frst case code rate s one that s no redundancy s ntroduced whle n second case there s redundancy overhead of sx bts. Then obvously the mult-level codes wth [63, 57, 3] bloc code performs better than that of mult-level codes wth [63, 63, ] bloc code. The scheme s tested for a range of sgnal to nose rato (SNR) and bt error rate (BER) s calculated whch s demonstrated n fg-6. The smulaton parameters are chosen same as that were n [6] so that proposed decoder s performance can be hghlghted. Smulaton results show vtalty of proposed algorthm over the basc algorthm wth a reduced complexty. The comparson s gven between conventonal teratve algorthm and proposed modfed teratve decodng algorthm for mult-level codes wth and wthout column redundancy respectvely. If we ntroduce column redundancy then t means we have to scarfy some subchannels for carryng the redundant nformaton. In ths way we have to compromse the throughput but a better bt error rate (ualty of servce) s guaranteed. Smlarly, f there s no column redundancy then code rate wll not be compromsed but bt error rate may be more. TABLE II. SIMULATION PARAMETER Sr. Parameter name Value Codng Schemes Multlevel Code Code rates, 0.9, 0.8, Modulaton, 4, 8, 6, 3, Schemes 64, 8 QAM 4 Bts/symbols n,, 3, 4, 5, 6, 7 Sr. Parameter name Value modulaton 5 Total MCPs 4x7=8 5 OFDM Standard used HYPERLAN/ 6 Number of subchannel Mnmum throughput MCP Maxmum throughput MCP 9 Adaptaton 0 Adaptaton Crtera 0.57x=0.57bts/ s/hz x7=7bts/s/hz Both modulaton and code Fuzzy Rule Base System Moreover, as t s already told that we have assumed that complete channel state nformaton s avalable at both transmtter and recever. So the nformaton that whch row s encoded by whch component code s already avalable to the decoder. So as code matrx receved lst of approprate code wll be populated accordng to the procedure descrbed n prevous sectons. Smlarly, t can be seen that the natve decodng algorthm demands almost 5dB more n terms of sgnal to nose rato for possessng the same performance. If we observe the bt error rate at 5dB sgnal to nose rato then a sgnfcant dfference s notable. That s more than two order dfference and proposed scheme gves a 5dB gan over the prevous wor. Hence proposed scheme outperforms compare to natve scheme. In fg-7, proposed scheme s compared for varous ualty of servce (QoS) le average BER=0e-, 0e-, 0e-3 and 0e-4. In ths way QoS was fxed ntally then dependng upon the receved sgnal to nose rato (SNR), most approprate modulaton code par (MCP) was chosen usng Fuzzy Rule Base System (FRBS), for entre OFDM system, then the product of modulaton rate and code rate so called modulaton-code-product s consdered as throughput s plotted. In fg-8, proposed scheme s compared wth the Adaptve Codng scheme proposed by Al-Asary n ths PhD dssertaton [6], where HYPERLAN/ standard was compared, the adaptaton crtera was based upon SNR thresholds. As smulaton results reveal, proposed scheme profoundly performs better than that of proposed by Al- Asary as well as HYPERLAN/ standard. In frst graph, t s revealed that the performance wth the Multlevel codes havng zero column code redundancy ends up n a hgh code rate that s 00Mbps at 30dB SNR. But obvously n ths way Qualty of Servce may be lttle compromsed. In second graph of fg-8 codes wth column code havng redundancy would cause lttle degradaton n system throughput that t went down to 80Mbps because n ths case we have to scarfy subcarrers for redundancy but wth an mproved QoS compared to prevous case. Both cases outperform compare to scheme proposed by Al-Asary [6] and HYPERLAN/ standard.

9 Performance of Modfed Iteratve Decodng Algorthm for Multlevel Codes n Adaptve OFDM System 9 Fgure 6. Performance comprarson of proposed algorthm Fgure 7. Comparson of proposed scheme for varous QoS n a HYPERLAN/ envronment Fgure 8. Comparson of proposed scheme wth dfferent schemes VIII. Conclusons In ths paper performance of modfed teratve decodng algorthm (MIDA) for Mult-level codes s nvestgated for an Adaptve Orthogonal Freuency Dvson Multplexng (AOFDM) envronment. In whch, a Fuzzy Rule Based System s employed for adaptng the transmsson parameters. MIDA s a suboptmum teratve decodng algorthm that reduces the complexty of ts natve counterpart n whch Lst Decodng s employed. By usng the concept of Syndrome Decodng, MIDA sgnfcantly reduces the search space. It s also noted that the performance of MIDA s as good as orgnal teratve decodng algorthm for Multlevel codes. Proposed scheme was compared wth OFDM HYPERLAN/ standard as well as wth a smlar wor namely Adaptve Codng for OFDM System by Al- Asary [6] and sgnfcance of proposed scheme s shown by usng smulaton results. Sgnfcance of proposed scheme s due to the followng factors,. Wde range of consttuent row codes for Multlevel codes.. A relatvely low complexty decoder for Multlevel codes. 3. Every subcarrer may be assgned a dfferent code rate and dfferent modulaton scheme dependng upon CSI 4. Wde range of modulaton code pars to handle almost all possble channel condtons. 5. A Fuzzy Rule Base System to choose sutable most combnaton of code and modulaton scheme based upon a specfc Qualty of Servce and average receved channel power to nterference nose rato (CINR). 6. A constraned optmzaton problem s focused, that s solved by employng Multlevel codes wth MIDA decoder under supervson of FRBS. Acnowledgement Ths research wor was supported by Hgher Educaton Commsson (HEC), of Pastan. References [] F. J. MacWllams and N.J.A. Solane, The theory of Error Correctng Codes, North-Holland, 977. [] C. Berrou, A. Glaveux, and P. Thtmajshma, Near Shannon lmt error-correctng codng and decodng: Turbo-codes (), n IEEE Int. Conf. Communcatons ICC 93, vol., no. 3, pp , May 993. [3] P. Elas, Error-free codng, IEEE transacton on Informaton Theory, vol. 4, pp. 9-37, 954. [4] IEEE Std 80.6TM-004, Part 6: Ar nterface for fxed broadband wreless access systems, Oct 004. [5] IEEE Std 80.6Etm-005, Part 6: Ar nterface for fxed and moble broadband wreless access systems, Feb [6] Al-Asary, O., Codng and teratve decodng of concatenated mult-level codes for the Raylegh fadng channel, Doctoral thess n Rado communcaton systems, Stocholm, Sweden, 006. [7] D. Chase, A class of algorthms for decodng bloc codes wth channel measurement nformaton, IEEE Trans Inform. Theory, vol. 8, no., pp 70-8, Jan. 97. [8] Atta-ur-Rahman, Ghour, S.A., Adeel, H., Waheed, A., Performance of Modfed Iteratve Decodng Algorthm for

10 0 Rahman Product codes, Internatonal Conference on Computatonal Aspects of Socal Networs (CaSoN ), pp. 47-5, 9- Oct. 0, Salamanca, Span [9] Atta-ur-Rahman, Quresh I.M., Muzaffar M.Z., Naseem M.T., Performance of Modfed Iteratve Decodng Algorthm for Multlevel Codes. IEEE Internatonal conference on Computatonal aspects of Socal Networs (CaSoN ), pp.99-04, November -4, 0, Sao Paulo, Brazl. [0] Atta-ur-Rahman, Quresh I.M. and Muzaffar M.Z. Adaptve Codng and Modulaton for OFDM Systems usng Product Codes and Fuzzy Rule Base System. Internatonal Journal of Computer Applcatons (IJCA), Vol. 35(4), pp.4-48, December 0. [] Atta-ur-Rahman, Quresh I.M., Mal A.N., A Fuzzy Rule Base Asssted Adaptve Codng and Modulaton Scheme for OFDM Systems, J. Basc Appl. Sc. Res. Vol. (5), pp , 0. [ISI Indexed Journal] [] Atta-ur-Rahman, Quresh I.M., Mal A.N., Adaptve Resource Allocaton n OFDM Systems usng GA and Fuzzy Rule Base System, World Appled Scences Journal (WASJ), Vol. 8(6), pp , 0. DOI: 0.589/dos.wasj [ISI Indexed Journal] [3] M. Vodel, M. Lppmann and W. Hardt, Resource Allocaton and Resource Levelng n Hetrogeneous SANET Envronments. Internatonal Journal of Computer Informaton Systems and Industral Management Applcatons. Vol. 5, pp , 03. [4] R. Re and I. Kallel, Fuzz-Web: A Methodology Based on Fuzzy Logc for Assessng Webstes. Internatonal Journal of Computer Informaton Systems and Industral Management Applcatons. Vol. 5, pp. 6-36, 03. Author Bography Dr. Atta-ur-Rahman has receved hs BS degree n Computer Scence from Unversty of the Punjab Lahore, Pastan n 004; MS degree n Electronc Engneerng from Internatonal Islamc Unversty Islamabad, Pastan n 008 and PhD degree n Electronc Engneerng from ISRA Unversty, Islamabad Campus, Pastan n 0. Currently he s worng as Assstant Professor as well as Deputy Drector (Academcs) at Baran Insttute of Informaton Technology, Rawalpnd, Pastan. Hs research nterests nclude Dgtal/Wreless Communcatons, Dgtal Sgnal Processng, Informaton and Codng Theory, Softcomputng, Artfcal Intellgence, Evolutonary Computng and Fuzzy & Hybrd Intellgent Systems.