Turbo Interleaving inside the cdma2000 and W-CDMA Mobile Communication Systems: A Tutorial

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1 Turbo Interleavng nsde the cdma2000 and W-CDMA Moble Communcaton Systems: A Tutoral Fabo G. Guerrero* Electrcal and Electroncs Engneerng School, Unversdad del Valle, Cal, Colomba (South Amerca). Cudad Unverstara Meléndez, Calle , Edfco 355, Ofcna 205, Cal, Colomba Phone: (572) ext 109; Fax: (572) ext 112 e-mal: fguerrer@unvalle.edu.co Marbell Sacanamboy Department of Computer Scence Engneerng, Unversdad Javerana, Cal, Colomba (South Amerca). Calle 18 No Cal, Colomba Phone: (572) e-mal: msacanamboy@puj.edu.co (We would welcome consderng ths work for possble publcaton) Abstract In ths paper a dscusson of the detaled operaton of the nterleavers used by the turbo codes defned on the telecommuncatons standards cdma2000 (3GPP2 C.S0024-B V2.0) and W-CDMA (3GPP TS V7.4.0) s presented. Dfferences n the approach used by each turbo nterleaver as well as dsperson analyss and frequency analyss are also dscussed. Two examples are presented to llustrate the complete nterleavng process defned by each standard. These two nterleavng approaches are also representatve for other communcatons standards. Keywords: Turbo codng, cdma2000, W-CDMA, 3G, nterleavng, dgtal communcatons. 1. Introducton Near one decade ago the IMT2000 ntatve of the Internatonal Telecommuncaton Unon dentfed fve base staton-moble staton ar nterfaces for the thrd-generaton moble communcatons systems (3G). It seems clear at the present however that the two technologes that wll be domnatng the global market of thrd generaton moble communcatons systems are cdma2000 and W-CDMA [1].

2 The salent feature of thrd generaton moble communcatons systems s ts hgh capacty for transmttng nformaton over the system data channels. By 1997 IMT2000 defned n Recommendaton ITU-R M.1225 test data rates of 2048 kbt/s, 144 kbt/s and 64 kbt/s for ndoors, pedestran and vehcular traffc respectvely [2] for purposes of evaluatng the thrd-generaton technologes. As expected, the contnung evoluton of moble technologes has left behnd these values wth much hgher speeds. For nstance, the Ultra Moble Broadband TM (UMB TM ) ar nterface specfcaton [3] s ntended to delver downlnk and uplnk data rates of 288 Mbt/s and 75 Mbt/s respectvely usng a bandwdth of 20 MHz. To offer these hgh data rates wth access termnals ncreasngly both small and functonal t s mperatve to work at the lmt of effcency n data transmsson. As t s well known n 1948 C. E. Shannon proved that the fundamental lmt of dgtal transmsson on channels wth whte nose s gven by the classc channel capacty formula C = W log 2 (1 + S / N), where C s the capacty n bt/s, W s the channel bandwdth n Hz, and S/N s the sgnal to nose rato at the recever. However, fndng an error correcton system able to acheve ths lmt meant extensve research for several decades. After more than forty years of research the concept of turbo codng developed by Claude Berrou and Alan Glaveux [4] fnally proved that t was possble to reach the lmt of channel capacty wth an encodng scheme that could be constructed n practce. Whle turbo codng s not the only technque known to be able to attan the channel capacty lmt [5] t s certanly the most commonly used channel codng technque for data channels n contemporary moble communcatons systems. Accordng to the nventors the turbo codng prncple was born from the expermentaton wth the feedback concept appled to the error correctng problem usng convolutonal codes [6]. At the core of a turbo codng system there s a fundamental consttutve element called nterleaver. An nterleaver s a system that changes the postons of nput data accordng to an establshed poston permutaton algorthm. Insde the turbo codng process the functon of the nterleavng block s to help n provdng codes vectors wth the hghest possble level of randomness (deally, ndependent vectors) [7] so that the resultng code resembles as close as possble the concept of random codng used by C. E. Shannon n [8] to prove the channel capacty theorem. Therefore the nterleaver s a fundamental element for the performance of a turbo code [9]. The understandng of nterleavng s a subject of hgh nterest to the specfcaton of physcal layers for both wred and wreless transmsson technologes. The am of ths artcle s to show n detal how the turbo nterleavers defned n the

3 cdma2000 EV-DO Revson B (3GPP2 C.S0024-B V2.0) [10] and W-CDMA (3GPP TS V7.6.0) [11] standards work, what are ther man characterstcs, and what are the desgn prncples used by each one. Ths artcle has been wrtten wth a tutoral approach n mnd. The artcle s organzed as follows: Secton 2 provdes an overvew of the turbo nterleavers defned n cdma2000 and W-CDMA standards. In Secton 3 two detaled examples of the turbo nterleavng done by each standard are descrbed. Secton 4 shows a dsperson analyss for each nterleaver. Fnally, n secton 5 the man fndngs and observatons of ths work are presented. For a full dscusson of the theory of the nterleavers descrbed n ths artcle references [12] and [13] can be consulted. 2. Descrpton of the cdma2000 and W-CDMA turbo nterleavers W-CDMA and cdma2000 use dfferent strateges for the nterleavng carred out by ts turbo codng systems. The cdma2000 nterleaver s based on the prncple of generatng the nterleavng postons through a counter that generates addresses whch are modfed through a preset table and a functon that reverses the order of the bts. The resultng address vectors determne the permutaton of the nput data. In cdma2000 the nput to the nterleaver and the output data form the nterleaver are defned as arrays (vectors) of length Nturbo. The values that the Nturbo varable can take are defned by the standard. In W-CDMA the nput and output of the nterleaver are treated as matrces whose dmensons (rows and columns) depend on the total length of the nput data, K. The values the varable K can take are also defned by the standard. The nterleavng process takes place n two steps. Frst the postons of the bts for each row are permuted. Then the row postons are permuted (wthout changng the bts n each row). In summary, the Amercan standard (cdma2000) treats nput bts as an array (or vector), whle the European standard (W-CDMA) treats the nput data as a matrx. To change postons the Amercan standard uses a counter whle the European one uses permutaton patterns of rows and columns. The followng sub-sectons descrbe n detal the operaton of the cdma2000 and W-CDMA nterleavers. 2.1 cdma2000 turbo nterleaver Fgure 1 shows the flow dagram of the nterleaver used by the cdma2000 turbo encoder, whch has as nput the packet_sze varable whch s used to determne from Table 1 both then n y Nturbo parameters. The value of n s a nterleavng parameter defned as an nteger n the range 3 n 7. Nturbo s the actual number of nformaton bts n the nterleavng block and must satsfy the relatonshp Nturbo 2 n+5.

4 The packet sze s sx bt longer than Nturbo because the sx tral bts are used to force the turbo encoder to the ntal state after the codfcaton of the Nturbo data bts s complete. Table 1. Turbo nterleaver Parameter Packet _sze n N turbo The parameters n Table 1 are defned for reverse lnk channels.e. channels gong from the moble staton to the base staton. For forward lnk channels the (base staton to moble) n s n the range 5 n 7 and the values of packet sze and Nturbo are dfferent. The nterleavng algorthm s the same for the reverse lnk as well as the drect lnk.

5 Input packet sze - Physcal Layer (Table 1) Determne n, and N turbo (Table 1) Counter n+5 bts = 0 N_teratons = 0 MSB = Counter [(n+4):5] LSB = Counter [4:0] MSB = (MSB + 1) [n-1:0] LSB [n-1:0]= Table_Lookup (LSB, n) T = {MSB * LSB} [n-1:0] MSB_address = bt_reversal ( Counter[4:0]) LSB_address = T Tempt_address [n+4:0] = MSB_address LSB_address Tempt_address < N turbo No Yes Output_address = Tempt_address Counter = Counter+1 Yes N_teratons < 2 n+5 No Produce output bts Fg. 1. Flow dagram for the cdma2000 standard's turbo nterleaver algorthm Fgure 1 shows the sequental tasks that are performed wthn the nterleaver proposed n the cdma2000 standard. The frst task s to calculate the MSB address by takng the n least sgnfcant bts of the value of the address counter n most sgnfcant bts plus one. Then Table 2 s ndexed usng the counter's fve least sgnfcant bts. Ths lookup table ndexng provdes an LSB address of n bts. Table 2. cdma2000 turbo nterleaver lookup table Index n=3 n=4 n=5 n=6 n=

6 The next step s to take the n least sgnfcant bts of the product of the prevously obtaned MSB and LSB addresses whch wll consttute the lower part, namely LSB_address, of the fnal address. The hgher part of the fnal address, namely MSB_address, s obtaned by bt-reversng the fve least sgnfcant bts of the counter. MSB_address and LSB_address are then concatenated formng the fnal address whch s stored at the Output_address vector f the fnal address s less than Nturbo, otherwse the address s dscarded. The counter s ncreased by one and the process s repeated untl the Nturbo nterleavng addresses are obtaned. The algorthm s desgned so that wth 2 n+5 teratons s always possble to obtan the Nturbo requred addresses,.e. t s not possble for the teratons to end wthout havng obtaned all the nterleavng addresses.

7 2.2 W-CDMA turbo nterleaver The turbo nterleaver of the W-CDMA standard s based on a rectangular nput bt matrx. Ths matrx s permuted both by columns and rows before the output bts are delvered. The nput bts are denoted as x x, x, x, x,..., x 1, K where K s the number of nput bts, where 40 K Fgure 2 shows a flow dagram of the algorthm used by the W-CDMA turbo nterleaver. Input K 40 K 5114 No Yes Determne R, C dmensons of rectangular matrx Wrte nput bts x 1,x 2,..,x K row by row R C > K No Yes Add (R C K) padded bts Determne rows permutaton pattern {T()}, = 0,1,.., R-1 Determne ntra-row permutaton pattern {U (j)}, j = 0,1,..,C-1 Permute columns usng permutaton pattern U and permute rows usng permutaton pattern T Read rectangular matrx column by column R C > K No Yes Prune (R C K) padded bts Produce output bts x' 1, x' 2,.., x' K Fg. 2. Flow dagram for the W-CDMA standard's turbo nterleaver algorthm As shown n Fg. 2, after verfyng that the length of K s n the range establshed by the standard, then both the number of rows R, and the number of columns C of the rectangular matrx are determned accordng to the rules gven n Tables 3 and 4.

8 Table 3. Rules for determnng the number of rows R R K 5 40 K ( 160 K 200 ) ( 481 K 530 ) 20 K = any other value Table 4. Rules for determnng the number of columns C K P C 481 K C = p = 53 K R ( p +1) Mnmum p (see Table 5) C = C = C = p 1 p f p + 1 f ( K R ( p 1) ) ( R ( p 1) < K R p) f (( R p) < K ) As shown n Table 4 when K s outsde the range 481 K 530, p s the lowest prme number such that ( p +1) K R and C s calculated accordng the thrd column of Table 4. The values for the prme number p are shown n Table 5. Table 5. Lst of prme number p and prmtve roots v p v p v p v p v p v The matrx s flled wth the K nput bts by rows from top to bottom. If R C > K, then the matrx s zero (or one) padded. The row permutaton pattern whch s represented by the vector ( ) { 0,1,..., R 1} bts K as showed n Table 6. T and depends on the number of nput

9 Table 6. Rules for determnng the row permutaton pattern K R Inter-row permutaton patterns ( ) { 0,1,..., R 1} 40 K ,3,2,1, 0 ( ) ( 481 K 530) ( ) ( 3161 K 3210) K 10 9,8,7,6,5,4,3,2,1, 0 K 20 19,9,14,4,0,2,5,7,12,18,16,13,17,15,3,1,6,11,8, 10 K = any other value 20 19,9,14,4,0,2,5,7,12,18,10,8,13,17,3,1,16,6,15, 11 T The next task s to calculate the permutaton pattern for the columns n each row. Ths pattern s defned by the matrx ( j) j { 0,1,..., C 1} U as ndcated n Table 7. Table 7. Column permutatons Patterns Condton Column permutaton pattern ( ) j { 0,1,..., C 1} C = p U ( j) = s( ( j r ) mod ( p 1) ), j = 0,1,... ( p 2), U ( p 1) = 0 C = p+1 U ( j) = s( ( j r ) mod ( p 2) ), j = 0,1,... ( p 2), U ( p 1) = 0 and U ( p) = p K = R C, exchange U R 1 ( p) wth U R 1 ( 0) C = p-1 U ( j) = s( ( j r ) mod( p 1) ), j = 0,1,... ( p 2) U j In Table 7 the varable s corresponds to the base sequence ( ) j { 0,1,..., p 2} pattern and s defned by the eq. (1): ( 1 ) mod( p) ), j = 1,2,... ( p 2), ( 0) = 1 ( j) s v s( j ) s = s (1) where v s the prmtve root as defned n Table 5. The varable r s the sequence of permuted prme ntegers defned n equaton (2): r = q, = 0,1,..., R 1 ( ) T (2) s j used to generate the column permutaton Where the subscrpt T () s the row permutaton vector gven n Table 6 and q s the sequence of prmes determned by the lowest prmes q such that c. d ( q, 1) 1 g. p =, q > 6 and, q > q( ), = 1,2,..., R 1. 1 U j and then The orgnal nput matrx s frst column permuted wth the column permutaton pattern ( ) j { 0,1,..., C 1} wth the row permutaton patterns ( ) { 0,1,..., R 1} T. Fnally data are read by columns from left to rght. If extra zero

10 (or one) bts where ntally padded these bts must be removed (the number of bts removed equals ( R C) K, producng the bts x ' 1, x' 2, x' 3, x' 4, x' 5,..., x' K. 3. Examples of operaton 3.1 Turbo nterleaver standard cdma2000 In ths example a packet sze packet sze 256 s used. Followng the algorthm descrbed n Fg. 1 we have: _ = 1. From Table 1 n =3 and Nturbo = Start the counter of n+5=8 bts at zero,.e. counter = Save the three most sgnfcant bts of counter n the MSB varable. 4. Save the fve least sgnfcant bts of counter n the LSB varable. 5. Add 1 to MSB,.e. MSB = 001 for the frst teraton 6. Use Table 2 wth the fve LSBs of counter and column n (ndex = for the frst teraton) and store the n-bt result n LSB,.e. LSB = 001 for the frst teraton. 7. Take the n least sgnfcant bts of the MSB x LSB product and store t n T. 8. Bt reverse the fve least sgnfcant bts of counter and save t n MSB_address,.e. MSB_address = for the frst teraton 9. Concatenate MSB_address and LSB_address=T nto Temp_address,.e. Temp_address = for the frst teraton 10. If Temp_address < Nturbo then delver vald output_address,.e. output_address= for the frst teraton 11. Add 1 to counter 12. Go to step 3 Table 8 shows the sx addresses whch are dscarded durng the process because of beng greater than the value of Nturbo. Table 8. Example of nvald nterleavng addresses Address Counter MSB LSB MSB = MSB+1 LSB = Table2[LSB,n] MSB_address = reverse(lsb counter) LSB_address = MSB x LSB x011 = x011 = 110 Tempt_address = [MSB][LSB] = 251base = 254base 10

11 x011 = x011 = x011 = x011 = = 252base = 250base = 253base = 255base10 For ths example, the nput vector has 250 data, whose values for smplcty are consecutvely numbered from one to two hundred and ffty. As the nput vector s relatvely large n sze only some postons wth ther values are shown n Table 9. Fgure 3 shows the nterleaved output data vector. Table 9. cdma2000 example nput vector { } Fg. 3. cdma2000 output data after nterleavng As can be seen n Fgure 3 the nput data has been totally nterleaved from ther orgnal postons. For nstance at poston 16 s the element 242 and at poston 242 s the element 233, whereas at the same postons n the nput vector n Table 9 are the data 16 and 242 respectvely. Fgure 4 shows the results of ths example plotted n a Cartesan plane, where the x-axs represents the ndex and the

12 y-axs the poston of the output data. Output bt poston Output bt poston Data before nterleavng cdma Input bt poston Data after nteleavng cdma Input bt poston Fg. 4. Input vector vs output vector before and after nterleavng 3.2 Turbo nterleaver standard W-CDMA For ths example a value of K = 250 nput data s used. From Table 3 the number of rows R must be 20 and from Table 4 the number of columns C must be 13. Ths value for C s found as follows: from Table 5 the smallest prme such that ( + 1) p s p = 13; accordng to the rules n Table 4 as < condton R ( p + ) < K R p meets the 1, then C = p = 13. The rectangular matrx has then = 260 elements. In ths example the nput values, for smplcty are chosen to be the ntegers from 1 to 250 whch are wrtten by rows nto the nput matrx. Snce the matrx sze s greater than K the empty postons are flled wth zeros as shown n Table 10. Accordng to the rules n Table 6 the row permutaton pattern ( ) { 0,1,...,19 } s = 19,9,14,4,0,2,5,7,12,18,10,8,13,17,3,1,16,6,15, 11 T for ths case T. Smlarly, as n ths example C = p permutaton patterns accordng to the rules n Table 7 are determned by equaton (3): ( j) s( ( j r ) mod ( 13 1) ), j = 0,1,...,12, U ( 12) = 0 = U (3) Table 11 shows the base sequence whch has been generated usng Eq. (1) and whch s used n Eq. (3)., the column To obtan the sequence of permuted prme ntegers r the sequence of prme numbers q s needed. The sequence q must g. =, q > 6 and q > q( ), 1,2,..., 19 satsfy the condton c. d (,13 1) 1 q 1 =, n ths example gvng as a result

13 [ 1,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79 ] q =. The permuted sequence r s then: r = q, = 0,1,...,19, = [ 17,61,19,59,13,23,71,29,43,7,41,79,31,47,11,73,67,53,37,1 ] ( ) rt ( ) T Table 12 shows the column permutaton patterns produced by Eq. (3). Table 13 shows the rectangular matrx after applyng the permutaton pattern U and Table 14 after applyng the permutaton pattern T. Table 15 shows the resultng output after readng the matrx column by column. It can be observed at the frst column of Table 15 the sx fll-n zeros. Fgure 5 shows the end result after prunng the fll-n zeros. Fgure 6 shows ths example's results plotted n a Cartesan plane where the x-axs represents the ndex and the y-axs the poston of the output data. Table x13 matrx before nterleavng Table 11. Base sequence for row permutatons ( ) j { 0,1,...,,11 } s j

14 Table 12. Column permutaton matrx U ( j) Table 13. Rectangular matrx after column nterleavng

15 Table 14 Rectangular matrx after both column and row nterleavng Table 15. Rectangular matrx after readng column by column

16 { } Fg. 5. W-CDMA nterleaved output data Output bt poston Output bt poston Data before nterleavng W-CDMA Input bt poston Data after nteleavng W-CDMA Input bt poston Fg. 6. Input vector vs output vector before and after nterleavng, packet sze = Some test vectors wth bnary dgts As example vectors Tables 16 and 17 shows the results for the one hundred ones followed one hundred and ffty zeros vector, and the complementary vector (one hundred ffty zeros followed by one hundred ones) for W-CDMA and

17 cdma2000 respectvely. The notaton used for both nput and output vectors uses bnary and hexadecmal format to avod the ambguty that may cause the sze of the nput data not beng a multple of four. Table 16. W-CDMA and cdma2000 nterleavng test vectors. Input data: 100 ones and 150 zeros Input FFFFFFFFFFFFFFFFFFFFFFFFF 16 Output W-CDMA 00 2 B03E0B01E1607C2C0F8581F0B03E1603C2C0F8580F0B03E1603C2C0F82C0F8 16 cdma A8A8A8A A2A2A2A A8A8AAA Table 17. W-CDMA and cdma2000 nterleavng test vectors. Input data: 150 zeros and 100 ones Input Output 3FFFFFFFFFFFFFFFFFFFFFFFFC W-CDMA CC154CC169982D3305A66094CC169982D3304A66094CC129982D cdma2000 2AAA2A2A AA8AAA AAA2A2A2AAA2AAA AA8A8 A8 16 In Table 16 and 17 t can easly be seen that the nput data are nterleaved n a dfferent way by the turbo nterleaver of each standard. For nstance, n W-DCMA t appears several tmes consecutve ones at the output (nbbles B16 and C16, for example) but they never come from consecutve postons at the nput vector. In cdma2000 t never appears for ths example consecutve ones at the output vector. 4. Dsperson analyss Although the output produced by nterleavers (Fgures 3 and 5) seem to have elements of randomness, t should be notced that the transformaton T [x] = y between nput and output postons s both determnstc and bjectve,.e. the mappng s fxed, one to one and for all y there s a sngle x and vce versa. Because of ths reason t s more useful to calculate the average nterleavng dstance, defned as the average value of the dstance between the nput and output postons, L avg, as well the standard devaton of these dstances. Table 18 shows the values of L avg and standard devaton for dfferent lengths of nput data. As shown n Table 18 the values of L avg and standard devaton are very smlar for the two compared standards.

18 Smlarly, as noted at the hstograms of nterleavng dstance versus frequency of Fgure 7 and 8 for 250 data, the dsperson patterns are statstcally smlar. Patterns obtaned for hgher nput values have smlar behavor. Tabla 18. L avg dstance of nterleavng Length of nput data L avg Standard devaton cdma2000 W-CDMA cdma2000 W-CDMA The nterleavng process does not mean that all postons must change at the output. For example, n cdma2000 for an nput sze equal to 506 postons 68, 84 and 338 appear at the same postons at the nterleaver's output. For W-CDMA for the same nput sze (506) t happens the same wth poston Frecuency Dstance of jump Fg. 7. Interleavng dstance versus frequency for W-CDMA, packet sze = Frecuency Dstance of jump Fg. 8. Interleavng dstance versus frequency for cdma2000, packet sze = 250

19 5. Conclusons In essence the prncple of nterleavng used n cdma2000 s based on manpulatng a counter whose value defnes the mappng poston at the output. Instead, the turbo nterleaver used by the W-CDMA standard s based on a permutaton method usng prme numbers for generatng permutatons for both rows and columns n a rectangular matrx. Whle output vectors appear to be randomly dstrbuted, the transformaton whch defnes the mappng between nput and output postons n both W-CDMA and cdma2000 turbo nterleavers s bjectve and of determnstc nature,.e. mappng between nput and output s fxed. Consderng the nterleavng average dstance and the varance of nterleavng dstance (Table 18) t can be observed that the W-CDMA and cdma2000 turbo nterleavers have a very smlar behavor even when ther nterleavng algorthms are substantally dfferent. The dstrbuton of dstances, as can be seen at the hstograms of Fg. 7 and Fg. 8, corroborate that the dsperson patterns of the W-CDMA and cdma2000 turbo nterleavers are statstcally qute smlar. References [1] The acceleratng mgraton to 3G technologes, CDMA development group, The Smart Money Is On 3G, August 2006, Avalable: Consulted December 13th [2] Gudelnes for evaluaton of rado transmsson technologes for IMT-2000, Recommendaton ITU-R M.1225, [3] Physcal Layer for Ultra Moble Broadband (UMB) Ar Interface Specfcaton, 3rd Generaton Partnershp Project 2, Standard 3GPP2 C.S verson 2.0. August [4] C. Berrou, A. Glaveux, P. Thtmajshma. Near Shannon lmt error-correctng codng and decodng: Turbo codes, Proc Int. Conf. Commun. Geneva pp [5] D. J. Costello, G. D. Forney, Jr. Channel Codng: The Road to Channel Capacty, Proceedngs of the IEEE, Vol. 95, No. 6, pp Jun [6] C. Berrou, A. Glaveux. Reflectons on the Prze Paper: Near Shannon lmt error-correctng codng and decodng: Turbo codes IEEE Inform. Theory Socety Newsletter, Vol pp

20 [7] G. Battal. A Conceptual Framework for Understandng Turbo Codes IEEE Journal on Selected Areas n Communcatons. Vol. 16, No.2, pp Feb [8] C. E. Shannon. A mathematcal theory of communcaton, Bell Syst. Tech. J. Vol pp and [9] C. B. Schlegel, Lance C. Pérez, Trells and turbo codng. New York, NJ: IEEE Press, 2004, ch. 10. [10] cdma2000 Hgh Rate Packet Data Ar Interface Specfcaton, 3rd Generaton Partnershp Project 2, Standard 3GPP2 C.S0024-B verson 2.0. Apr [11] Multplexng and channel codng (FDD) (Release 7), 3rd Generaton Partnershp Project Standard 3GPP TS verson Sept [12] O. Takeshta, D. Costello. New Determnstc Interleaver Desgns for Turbo Codes IEEE Transactons on Informaton Theory. Vol pp [13] A. Shbutan, H. Suda, F. Adach. Complexty reducton of turbo codng, Proceedngs, IEEE Vehcular Technology Conference VTC'99 Fall pp Fabo G. Guerrero, receved a B.Eng. degree n telecommuncatons engneerng from Unversdad del Cauca, Popayan, Colomba (South Amerca), 1992, and a M.Sc. degree n Real-Tme Electronc Systems from Bradford Unversty, UK, Currently, he works as telecommuncatons assstant lecturer n the Department of Electrcal and Electroncs Engneerng of Unversdad del Valle, Cal, Colomba (South Amerca). Hs research nterests nclude dgtal communcatons, telecommuncaton systems modelng, and next generaton networks. He s member of the Communcatons Socety of the IEEE and has served as revewer for several nternatonal journals. Marbell Sacanamboy, She receved hs 5-year Dploma n Electroncs Engneerng n 1999 from the Unversdad Javerana, Cal, Colomba (South Amerca). Currently she s a M.Sc. student at the Electrcal and Electroncs Engneerng School of the Unversty of Valle, Cal. She s wth the Department of Computer Scence Engneerng, Unversdad Javerana, Cal. Her research nterests nclude dgtal desgn for communcaton systems, fuzzy logc, and computer archtectures.