Convolutonal nterleaver for unequal error protecton of turbo codes Sna Vaf, Tadeusz Wysock, Ian Burnett Unversty of Wollongong, SW 2522, Australa E-mal:{sv39,wysock,an_burnett}@uow.edu.au Abstract: Ths paper descrbes constructon of a convolutonal nterleaver as a block nterleaver and dscusses ts applcaton to turbo codes wth equal and unequal error protecton technques. Based on smulatons, dfferent convolutonal nterleaver structures sutable for turbo codes wth unequal error protecton capablty are suggested. Fnally, based on conducted smulatons the best method s selected. Keywords: Convolutonal nterleaver, Unequal error protecton, turbo codes.. ITRODUCTIO Compresson has become the norm n moble communcatons; currently speech domnates but vdeo and general multmeda compresson s fast becomng mportant. A vtal characterstc of a compressed data stream s the unequal perceptual mportance of the compressed parameters. In turn, ths leads to unequal effects of errors durng transmsson. Thus Unequal Error Protecton (UEP) has become an mportant part of desgn of channel encoders for multmeda content. Amongst the known channel codes, turbo codes have the hghest performance n drect bt error rate reducton terms. Turbo codes are produced by the parallel concatenaton of two or more convolutonal code generators separated by one or more nterleavers []. The reducton n BER resultng from such codes s drectly dependent on the desgn of a sutable nterleaver. In the lterature, several technques for mplementng UEP usng turbo codes have been proposed. In [2], sngle nterleaver for all levels and, n [3], one nterleaver for each level are suggested, whle [4] dscusses optmzaton of the sngle nterleaver soluton. The nterleavers suggested n [2-4] are from the block nterleaver famly. In a block nterleaver, data bts are wrtten nto the memory column-wse and read row-wse (or vce versa). Another type of the block nterleaver s a sem random nterleaver, where after fllng the whole nterleaver memores the bts are read n a sem random manner, not rowor column-wse. Both types of nterleavers are used wth turbo codes and the total delay at the end of nterleavng process s twce of the nput data length. The non-block nterleavers (such as the convolutonal nterleavers [5]) have better performance n terms of BER reducton durng turbo decodng process. Addtonally, they ntroduce a shorter delay, whch smplfes the de-nterleavng procedure. It s also mportant to note that convolutonal nterleaver performance s data dependent and that they allow for a contnuous operaton, whch s a vtal consderaton for turbo codes. In ths paper, we ntroduce method that returns the memores of appled convolutonal nterleaver to the known state at the end of each data block, resultng n the convolutonal nterleaver performng effectvely as a block nterleaver. Therefore, the nterleaved block-by-block data are ndependent from each other, whch enable to use the conventonal teratve decodng methods n the decoder. The organzaton of the paper s as follows: In Secton 2, the structure of turbo codes and the poston of the nterleaver are descrbed. In Secton 3, the performance of a new convolutonal nterleaver wth the calculaton of dstance parameter of turbo codes s presented. In Secton 4, some structures of nterleaver sutable for UEP n turbo codes are descrbed. Secton 5 concludes the paper. 2. TURBO CODES STRUCTURE Turbo encoders consst of two or more Recursve Systematc Convolutonal (RSC) encoders separated by one or more nterleavers. Fgure shows a turbo encoder (rate /3) structure wth two RSC encoders. Input data IT RSC encoder Systematc data Fgure : Turbo encoder structure Party data Party data 2
The nput and RSC coded data are referred to as systematc and party data, respectvely (see Fgure ). The nterleaver permutes the nput data pror to the second RSC encoder to generate dfferently encoded data compared wth the codeword of the frst RSC encoder [6]. If a trells termnaton or truncaton s performed on RSC encoders and block nterleaver s used, the turbo code performance can be evaluated as that of one block code (L(n+m), kl) where L, m and k/n represent the nterleaver length, the number of RSC encoder memores or encoder states, and the code rate, respectvely [6]. In ths paper, the trells termnaton s performed on the frst RSC encoder, whch returns ts memory contents to zero state, whle trells truncaton s performed on the second RSC encoder that leaves ts memory states open. As t has been shown n [7] wth an employment of convolutonal nterleavers, whch create less delay than block nterleavers and mantan synchronzaton between the nterleaver and denterleaver, turbo codes performance mproves. Moreover, utlzaton of the contnuous behavour n the stream-orented turbo codes s sutable for long data length wth RSC encoders havng hgh number of states [8-9]. In order to use the convolutonal nterleaver n turbo codes equvalent to a block code, the nterleaver memores should be reset at the end of each block to the specfc value to create segmented nterleaved data for the second RSC encoder. The new scheme can be used n turbo codes wth unequal error protecton property and the proposed technque s descrbed n the next sectons. 3. COVOLUTIOAL ITERLEAVER STRUCTURE A convolutonal nterleaver conssts of T parallel lnes, wth dfferent delay n each lne that represents nterleaver perod [5]. In general, each successve lne has a delay whch s M symbols duratons hgher than the prevous lne. The structure for M= and T=3 s llustrated n Fgure 2. Fgure 2: Convolutonal nterleaver structure wth T=3 and M=. In a smlar manner to the trells termnaton technque (whch emts stored data from memores), an nserton of a certan number of zeros at the end of a data block can solate the nterleaved data block. Ths guarantees a data block of a specfc length and generates ndependent blocks of data for the RSC encoder. For the data length L=6 and the convolutonal nterleaver wth M= and T=3, the nterleaved data would be X 0 0 X4 X2 0 0 X5 X3 0 0 X6. Snce the applcaton of convolutonal nterleaver n turbo codes requres an nserton of stuff bts that reduces channel bandwdth usage, an optmsaton should be performed on the nterleaver to control the number of those bts, whch can be equal to the number of appled memores. For ths purpose one block s added after the nterleaver to control the data at the nterleaver output deletng extra zero stuff bts that are nserted at the end of each block. In ths case, the memory contents at the end of each block have zero value that stays tll the begnnng of the next block. Fgure 3 shows the structure of the optmsed convolutonal nterleaver. Followng the prevous example, the optmsed nterleaver output s: X 0 0 X4 X2 0 X5 X3 X6. Input data Fgure 3- Optmsed Convolutonal Interleaver. The same procedure can be repeated to obtan a second set of sutably nterleaved data for the second RSC encoder. More optmsaton can be done to the zero stuff bts nserton for the systematc and the frst party data after the trells termnaton procedure of the frst RSC encoder, as t s not necessary to transmt zero stuff bts n the mentoned data parts. However, these bts need to be consdered for the second RSC because of ther nfluence on the performance of the nterleaver. To verfy performance of the new convolutonal nterleaver and compare t to conventonally employed nterleaver such as rowcolumn nterleavers, the dstance parameter d ) of the turbo encoder of Fgure was ( calculated. Based on ths parameter, the Bt Error Rate (BER) for addtve whte Gaussan nose (AWG) can be expressed as: [0] E BER ω b erfc( d R ) () 2L where s the number of codeword wth weght d, ω s the average weght of the data sequences wth weght length, E Convolutonal Interleaver s the code rate. b 0 d Zero deleton 0 Interleaved data, L s the nterleaver s the sgnal to nose rato per bt and R In [] and [2] two dfferent algorthms for dstance computaton of turbo codes wth dfferent RSC encoder structures have
been proposed, whch are manly useful for large nterleaver sze. Fgure 4: Free dstance computaton algorthm Snce n UEP turbo codes technque nput data s segmented to shorter lengths, we can compute d from the defnton. Ths nvolves fndng a L codeword wth mnmum weght among 2 possble L codewords of length L. Among all 2 cases, only codewords that create low weghts have been consdered. Snce nput data are transferred drectly to the encoder output as systematc bts and puncturng s not performed on them, weght of the nput data corresponds to the weght nformaton part of codeword. It should be noted that the tal bts due to trells termnaton of the frst RSC are consdered as a part of the systematc data, whch affects the codeword weght. Algorthm starts d calculaton for all possble data streams of length L and mnmum weght,.e. one. Then, the correspondng codeword weghts are calculated. The obtaned mnmum weght from the frst codeword set s consdered as dstance at the frst step. In the next step, nput stream weght s ncreased by one unt,.e. stream wth weght of 2 at the second step, and ther dstance s computed. The mnmum d value among two relevant computed values s consdered as d at the end of second step. Agan, for the stream wth one unt d hgher weght,.e. weght 3 s computed and the mnmum d between prevous and current calculaton s selected. Ths procedure s contnued tll the computed dstance n the related step s less or equal to the weght of the current nput stream. The obtaned d at the end of the procedure s consdered as d of the turbo code. Fgure 4 shows the appled d =0, d_[0]=3 L =+ Compute d_ (d_[]) for all possble codewords wth weght of (W[]) d_[]=mn { d_[], d_[-] } Yes d_=d_[] d_[] < W[] computaton algorthm. o Based on the descrbed procedure, d has been calculated for the turbo codes mplemented by the structure presented n Fgure wth the rowcolumn and convolutonal nterleavers of the length of 6 and 64 and the rate of /3. The plot of the E b calculated BER versus for the mentoned nterleavers s presented n Fgure 5. For the low sgnal-to-nose rato (SR) the convolutonal nterleavers have better performance than the block ones. In order to mprove the performance for hgh SRs, nterleaver structure wth longer perod s suggested and dscussed n detals n the next secton. It should be noted that ncreasng the perod and data separaton ncreases the number of stuff bts whch can potentally reduce usage of the channel bandwdth. Data separaton nto shorter blocks has the same dsadvantage, too. Thus, ncreasng the perod and data separaton should be done n a reasonable way mnmsng the overhead but mantanng the advantages. Fgure 5: BER for convolutonal and block nterleaver szes of 6 and 64 wth rate: /3. 4. ITERLEAVER FOR UEQUAL ERROR PROTECTIO For turbo codes wth unequal error protecton, the fxed nterleaver perod s consdered for all levels, and, dependng on the requred protecton level, the length of the data block at each level s altered. As an example, we consder three protecton levels for data wth length of 2048 bts. Specfcatons of these levels have been presented n Table. We assume that 2048 bts are splt nto 5 groups. At the begnnng of each group, 64 bts of data are allocated the protecton level. Then, there are some blocks of length L=42 wth the protecton level 2, and the remanng blocks of length L=32 are allocated the protecton level 3. 0
Unequal error protecton s obtaned by puncturng encoded stream dfferently at dfferent protecton levels. Part Lev. (L=64) Lev.2 (L=42) Lev.3 (L=32) 3 6 2 3 6 3 3 7 4 3 7 5 4 7 Table : Dstrbuton of 2048 bts nto three protecton levels. The nserton of stuff bts to clear the nterleaver memores affects the effectve code rates, of course. Therefore, the effectve code rate at each level can be calculated as: L R eff = R (2) L + S Where L, ( ) S denote lengths of data block and the k number of stuff bts, respectvely, whle R =, n =, 2, 3 s the code rate after puncturng at the relevant protecton level. Hence, for the code rates of /3,/2, and 2/3, because of bt stuffng, we get the effectve code rates of 0.32,0.47, and 0.6, n the consdered example (see Table ). In order to verfy UEP turbo codes performance, an average rate for the mentoned example s calculated. Wth employment of puncturng at each level, the average code rate can be calculated as [3]: c = av = c R (3) k R = k the nterleaver. Takng nto account the number of blocks and block lengths at each level, the average length s gven by: Where c = c L = (4) = L L and ; =, 2, 3 are the length of data block and the number of blocks at each level, respectvely. Hence, the average length of turbo encoder s L 4bts. Snce an nterleaver wth 3 lnes and 3 stuff bts has been consdered, the length of the average data per block s approxmately: L data 4 3 = 38 bts. Based on the presented d n Table 3 for data dstrbuton of Table, Fg.6 gves the BER performance of the turbo codes at dfferent levels of protecton. At level wth the lowest number of data bts, we expect that the protecton s better than at other levels. Ths happens for low SRs but at hgh SRs t s smlar to that of level 2. The level 2 protecton at low SRs has weaker performance than the overall performance of the code. Ths s caused by the multplcty of dstance n level 2 due to ts data length and the puncturng. Lev. Lev.2 Lev.3 Overall d 6 5 2 3 8 2 ω 3 3 2 3 Table 3- Free dstance specfcatons wth nserton of stuff bts after tal bts to the nterleaver. Where, c represents the number of levels. Based on the data n Table 2 the effectve aggregate rate s 2048 determned as: R eff av = 0.53. 49 2048 + 62 Level Length (bts) Code rate Effectve Code rate 320 /3.32 2 672 /2.47 3 056 2/3.6 Average 2048.53.49 Table2: Specfcaton of three protecton levels. A smlar calculaton can then be performed to obtan the specfcaton for average block length of Fgure 6: BER for UEP turbo codes wth the nterleaver of Fgure 2 and nserton of stuff bts after the tal bts. In order to remove degradatons n the mentoned parts of level and 2, ther dstances
should be ncreased. One soluton s to consder the effect of stuff bts n the systematc and the frst coded party data. In ths case, trells termnaton s Fgure 7: BER for UEP turbo codes wth the nterleaver of Fgure 2 and nserton of stuff bts before tal bts. done after the entry of stuff bts to the frst RSC encoder. In order to consder tal bts effect for the second RSC encoder and to avod changng of the nterleaver memory states, whch are n the reset condton, the tal bts are transferred through the frst lne of nterleaver that has no memory. Fgure 7 shows smulaton results for the dentcal data structure of prevous example to verfy performance of the new nterleaver based on relevant computed d n Table 4. Lev. Lev.2 Lev.3 Overall d 8 4 2 3 2 ω 3 2 2 2 Table 4- Free dstance specfcatons wth nserton of stuff bts before tal bts to the nterleaver. Another method (referred here to as method 2) of achevng UEP s to consder a varable perod nterleaver whch alters the number of stuff bts at dfferent levels. Fgure 8 shows a convolutonal nterleaver confgured accordng to ths method. In ths example, the number of blocks at each level s the same as that of Table. The data requrng the hghest protecton level (level ) s dstrbuted on 5 lnes of the nterleaver wth 6 stuff bts. Meanwhle, level 2 and 3 data are dstrbuted on 4 and 3 lnes of the nterleaver, respectvely. Level Level 3 Level 2 Fgure 8: Interleaver structure n method 2. Agan, two alternatve schemes usng the new structure,.e. nserton of stuff bts after or before the tal bts are consdered and ther smulaton results compared wth the fxed perod nterleaver for all the levels. Table 5 and Fgure 9 show the computed d and the performance for protecton levels when stuff bts are nserted after tal bts, respectvely. Consderng the dfferent stuff bts length of dfferent levels, average value of stuff bts for overall level has been calculated, whch approxmately equals 3. Lev. Lev.2 Lev.3 Overall d 7 5 2 3 4 2 ω 2 2.25 2 3 Table5- Free dstance specfcatons wth nserton of stuff bts after tal bts to the nterleaver. In ths scheme d n level 2 occurs multple tmes but ts performance at low SRs s equal to that of the overall performance of the code. Also at level, degradaton s observed at hgh SRs. Wth nserton of stuff bts before tal bts, an mprovement s obtaned at relevant protecton levels, as llustrated n Fgure 0. The resultng dstances have been presented n Table 6. In comparson wth the prevous method, level 2 has been mproved near to the level graph n Fgure 8 whle level protecton shows better performance than the other levels. Method 2 has mproved performance but at the expense of an ncrease n stuff bts and hence redundancy level. Thus, a compromse needs to be found between optmsaton of turbo code performance and the number of utlzed stuff bts. As one optmsaton, combnaton of two mentoned schemes s suggested. For nstance, n method 2 and level, we apply zero stuff bts nserton before tal bts to get more protecton. But n level 2 we nsert them after the tal bts that have acceptable behavour wth less redundancy. Also smulaton shows that the level 3 protecton performance of turbo codes n both sub-methods are dentcal, whch can be due to puncturng effect at short data length. Therefore, for ths level, format of stuff bts nserton after tal bts s recommended. 5. COCLUSIOS In ths paper, we proposed a technque, whch ntalzes convolutonal nterleaver memores by the nserton of stuff bts at the end data of blocks of specfc lengths. Ths process results n a sem-block
nterleaver structure for turbo codng. The performance of ths new structure has been compared wth that of conventonal block nterleavers and appled to unequal error protecton turbo codes. Two major methods were proposed and tested. In each method, two schemes dependng on nserton of stuff bts before or after the tal bts were nvestgated. The results show that a stuff bt nserton before the tal bts n the nterleaver wth varable perod wll produce the best performance. Further work wll consder fndng a sutable compromse between the turbo-code performance and the stuff-bt redundancy. REFERECES []- C.Beerrou, A.Glaveux, P.Thtmajshma, ear Shannon lmt error-correctng codng and decodng: turbo codes, ICC 993, pp.064-070, May 993. [2]- A.Barbulescu, S.S.Petrobon, Rate compatble turbo codes, IEE Electroncs letters, vol.3, no.7, pp. 535-536, 30 th March 995. [3]- M.Salah,R.A.Ranes, A.Temple, T.G.Baley, A general nterleaver for equal and unequal error protectons of turbo codes wth short frames, Internatonal conference on nformaton technology: Codng and computng 2000, pp-42-45. [4]- M.Grangetto, E.Magl, G.Olmo, Embeddng Unequal Error Protecton nto turbo codes, 35 th Aslomar conference on Sgnals, Systems and Computers, 200, vol., pp. 300-304. [5]- G.D.Forney, Burst-correctng codes for the classc bursty channel, IEEE Trans. Commun, vol.com-9, pp. 772-78, Oct.97. Fgure 9: BER for UEP turbo codes wth nterleaver of Fgure 8 and nserton of stuff bts after tal bts. Lev. Lev.2 Lev.3 Overall d 9 5 2 3 2 2 ω 3 2.5 2 2 Table 6- Free dstance specfcatons wth nserton of stuff bts before tal bts to the nterleaver. [6]- S.Dolnar, D.Dvsalar, Weght dstrbutons for turbo codes usng random and non-random permutatons, TDA progress report 42-22, pp.56-65, Aug,5,995. [7]- E.K.Hall, G.Wlson, Stream-orented turbo codes, IEEE Trans Inform. Theory, vol.47, no.5, pp.83-83, July 200. [8]- S.Benedetto, G.Montors, Performance of contnuous and blockwse decoded turbo codes, IEEE trans. Letters, vol.,no.3, pp.77-79,may 997. [9]- M.Brellng,L.Hanzo, The super-trells structure of turbo codes, IEEE Trans. On nform.theory, vol.46,no.6,pp.222-2228, Sep 2000. [0]-L.C.Perez, J.Seghers, D.J.Costello, A dstance spectrum nterpretaton of turbo codes, IEEE Trans Inform Theory,vol.42,pp. 698-709, ov.996. []- J.Seghers, On the dstance of turbo codes and related product codes Fnal Rep. Dploma project ss95,no 663,Swss Federal Insttute of Technology, Zurch, Swtzerland,Aug. 995. Fgure 0: BER for UEP turbo codes wth nterleaver of Fgure 8 and nserton of stuff bts before tal bts. [2]-R.Garello, P.Perlen, S.Benedetto, Computng the dstance of turbo codes and serally concatenated codes wth nterleavers: Algorthms and applcatons, IEEE Journal on selected areas n commun., vol.9, no.5,may 200,pp.800-82.
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