A Novel Effcen Soppng Creron for BICM-ID Sysem Xao Yng, L Janpng Communcaon Unversy of Chna Absrac Ths paper devses a novel effcen soppng creron for b-nerleaved coded modulaon wh erave decodng (BICM-ID) sysem. The new creron s based on he absolue value of he dfference of log-lelhood-rao (LLR) ha beween he oupus of he () h eraon and he (-1) h of he sof-npu sof-oupu (SISO) decoder. Smulaon resuls comparng he proposed scheme wh he wdely used cross-enropy (CE) soppng creron show ha alhough a lle more eraon, he proposed scheme can ge excellen performance as CE n erms of b-error-rae (BER) and can ge codng gans a hgh sgnal-o-nose raos (SNRs). More mporanly, he proposed new creron doesn need any exponenal compuaon, whch has grealy reduced he complex compuaon n he BICM-ID recever. In addon, dealed dscussons regardng varous parameers ha may affec he decodng performances are also provded. 1. Inroducon B-nerleaved coded modulaon wh erave decodng (BICM-ID) s a smar scheme for s remarable performances boh n AWGN and n Raylegh fadng channels [1]. The erave decodng algorhm a he recever especally maes he BICM-ID a very promsng echnque for he capably of achevng large codng gans whou bandwdh expanson [2, 3]. The erave decodng process s beween he sof-npu sof-oupu (SISO) decoder and he demapper, whch s dfferen from urbo eraon. In urbo recever, he erave process s beween s wo nner SISO decoders. The smlary of he wo erave decodng algorhms s ha hey are boh desgned o acheve he global opmum hrough a sep-by-sep local search. In he eraon cycle, he b-error-rae (BER) decreases as he eraon number ncreases, bu he ncremenal mprovemen gradually dmnshes. The convenonal erave decodng algorhm s a scheme wh fxed eraon number M. Usually M s se wh he wors corruped frames n mnd. However, mos frames need less eraon o converge. Afer a ceran number of eraons, he sysem ges very lle performance mprovemen wh any furher eraon. Thus, o reduce he long decodng delay and he decodng power, he soppng crerons, whch can mely sop he unnecessary eraons, are pu forward [4-9], such as he cross-enropy (CE) soppng creron [4], he sgn-change-rao (SCR) soppng creron [5], he hard-decson-aded (HDA) soppng creron [5], he measuremen of relably (MOR) soppng creron [6], he convoluon-sum (CS) soppng creron [7], he bbased paral eraon creron [8], he Mn-CorrEx soppng creron [9] ec. Alhough hey are proposed nally for urbo recever, f properly modfed, hey can also be used for BICM-ID recever o reduce he unnecessary eraons. Reference [10] has modfed he CE soppng creron successfully o be appled o he BICM-ID recever. Ths paper proposes an effcen soppng creron ha based on he absolue value of he dfference of log-lelhood-rao (LLR), whch s beween he oupus of he () h eraon and he (- 1) h of he BICM-ID SISO decoder. The paper s organzed as follows: Secon 2 nroduces he srucure of BICM-ID recever. Secon 3 gves a general revew abou he wdely used CE soppng creron and secon 4 nroduces our proposed novel effcen soppng creron. Secon 5 provdes he smulaon resuls, whch ncludes he comparsons of our proposed soppng creron wh CE soppng creron and he fxed scheme. In addon, dealed smulaons abou varous parameers ha may affec he decodng performances are also conduced. Fnally, secon 6 concludes he paper. 2. The srucure of BICM-ID recever The srucure of BICM-ID recever s shown n Fgure 1. Before beng appled o he SISO decoder, he exrnsc nformaon L e (c ()) of he demapper s denerleaved. The denerleaved oupu s consdered as he a prornformaon L a (c ()) of he SISO decoder, where c ( ( ) 0) La( )) log c ( ( ) 1) c (() 0, r La()) c Lc e(()) log Lc a(()) c (()1, r La()) c (2) Copyrgh 2012, Infonomcs Socey 612
1 1) L 1 e Subsung (5) and (6) no (4), we ge CE: H cˆ cˆ 1 1 [ ( ), ( )] Fgure. 1 The srucure of BICM-ID recever Smlarly, he exrnsc nformaon of he SISO decoder s hen nerleaved and fed bac o he demapper as he a pror nformaon of he nex eraon. We noe ha L a (c ()) s se o be zero durng he frs eraon as he assumpon ha he npu aes value 0 or 1 wh he same probably. A he las eraon, he hard decson of he nformaon bs ulmaely made based on he sgn of s LLR value. The erave process won sop unl he prese maxmum eraon number M s reached. Ths s he convenonal fxed eraon number scheme. We call fxed scheme. 3. The ypcal CE soppng creron CE (cross-enropy) s a measuremen of how close wo dsrbuons are. For he dsrbuons p and q of a fne alphabe χ, CE s defned as p( x) H[ p, q] p( x)log qx ( ) x In BICM-ID, assume ha L ( ^c represens he LLR of he decoded b c (=1, 2, 3,,N) afer he h eraon and L -1 ( ^c represens he LLR of he (-1) h eraon respecvely. Thus, he CE value beween he decodng oupus of he wo consecuve eraons s H cˆ cˆ 1 1 [ ( ), ( )] ( ˆ c 0)log 1 1 ˆ c ( ˆ c 1)log 1 1 ˆ c where 0) ( 0) 1) ( 1) L L e 0) 1 e N 1 L ) L ) 1 e 1e 1e 1 1 1 1 L log L ) L ) As he eraon connues, he oupus beween he wo consecuve eraons and -1 come o be approxmaely he same. Therefore, he CE value becomes smaller and smaller. When he eraon proceeds o a ceran exen, alhough he eraon number connues ncreasng, he CE value won decrease any more. Ths means ha he eraon has reached he decodng lm. Then, he erave decodng process can be ermnaed. We usually se a hreshold o effecvely sop he unnecessary eraons: 1 1 N 1 1 L ) L ) ( ˆ ) 1 L c e T () log L ) L ) 1 1e 1e hreshold 4. The proposed novel effcen soppng creron As nroduced n Secon 1, he erave decodng process converges when he eraon proceeds o a ceran exen. We suppose ha he erave decodng process converges a eraon, hen, we have sgn( L 1 )) sgn( L )) Meanwhle, he dfference beween he magnudes of L ( ^c and L -1 ( ^c s very small, whch s less han 1.0. Therefore, he LLR() s small enough o ermnae he erave process, where ΔLLR( ) L 1 ) L ) We use ΔLLR () as he decson elemen of wheher o connue he erave process or no, where 1 ΔLLR( ) L ) L ) Copyrgh 2012, Infonomcs Socey 613
Thus, our proposed soppng creron can be descrbed as: Compare ΔLLR () wh a hreshold, whch s a predeermned suffcenly small value. (In hs paper, we se he hreshold as 10-3 ΔLLR (1) ). The erave cycle s sopped when 3 ΔLLR( ) 10 ΔLLR( 1) In he proposed creron, here s no complex exponenal compuaon n he erave process, whch s much easer for he mplemenaon of he BICM-ID recever. 5. Smulaon resuls We frs nroduce he smulaon envronmens: BICM-ID sysem; rae 1/2 convoluonal code; 8SK modulaon; S mappng; Raylegh fadng channel; frame sze 2048. For soppng crerons, he maxmum eraon number Q s se o be 10. For fxed scheme, he fxed eraon number M s also se o be 10 for comparson. For CE soppng creron, when T()<10-4 T(1), sop eraon. For our proposed novel effcen soppng creron, when 3 ΔLLR( ) 10 ΔLLR( 1), sop eraon. As shown n Table 1, alhough he proposed soppng creron needs abou 0.31~2 more eraon numbers han CE creron, can save as much as 5 eraon numbers n low and hgh SNRs (sgnal-onose raos) compared wh he fxed scheme. Meanwhle, Fgure 2 shows can ge as excellen performance n erms of BER as CE and he fxed. The superory exsng n our proposed creron s ha whou complex exponenal compuaon as CE, can ge codng gans compared wh CE creron and he fxed a hgh SNRs as shown clearly n Fgure 3. When BER s below 10-6, he proposed soppng creron can ge nearly 0.15dB codng gans han CE soppng creron. Meanwhle, here s nearly no BER performance degradaon beween he proposed creron and he oher wo schemes a oher SNRs. Fgure 2 shows ha he BER performance curve of our proposed creron almos concdes wh he curves of CE and he fxed a oher SNRs. Fgure 4 ~ 6 and Table 2 ~ 5 are a seres of smulaon resuls of dealed dscussons abou he parameers ha may affec he decodng performances usng proposed soppng creron. Table 2 and Fgure 4 mae a jon dsplay ha QSK modulaon performs he bes boh n erms of BER and average eraon numbers. When BER s a 10-4, QSK modulaon can ge approxmaely 0.8dB and 1.2dB codng gans han 8SK and 16QAM respecvely. When SNR s 5.5dB, QSK can save abou 1.94 and 5.29 eraons han 8SK and 16QAM. When SNR s 7dB, he superory of QSK s nearly 1.02 and 2.36. A low SNRs, alhough 16QAM needs less eraon, s BER performance s he wors. However, when SNR s hgh enough, 16QAM can surpass 8SK n erms of BER and only requre less han 2 eraon numbers for compensaon. Consder 8SK modulaon as a represenave, besdes he reduced eraon numbers, he proposed soppng creron can ge as excellen BER performance as he fxed and even beer a hgh SNRs. Table 1. Comparson of average eraon numbers Fxed scheme CE soppng creron roposed soppng creron 0(dB) 10 4.06 5.04 1 10 4.87 5.97 2 10 6.09 7.47 3 10 9.44 9.97 4 10 9.65 9.96 5 10 5.55 7.51 5.5 10 4.60 6.42 6 10 4.10 5.83 6.5 10 3.74 5.23 7 10 3.29 5.02 7.5 10 3.09 5.00 8 10 3.03 5.00 8.5 10 3.01 4.98 9 10 3.00 4.81 Fgure. 2 BER performance comparson Fgure. 3 BER performance comparson a hgh SNRs Copyrgh 2012, Infonomcs Socey 614
Table 2. Comparson of average eraon numbers regardng varous modulaons Fxed 16QAM QSK 8SK 8SK 0(dB) 10 4.17 7.16 5.04 1 10 4.84 10 5.97 2 10 5.11 10 7.47 3 10 6.34 8.57 9.97 4 10 8.94 5.74 9.96 5 10 10 4.95 7.51 5.5 10 9.77 4.48 6.42 6 10 8.50 4.10 5.83 6.5 10 7.21 4.01 5.23 7 10 6.36 4.00 5.02 7.5 10 6.01 4.00 5.00 8 10 5.70 4.00 5.00 8.5 10 5.14 4.00 4.98 9 10 5.01 4.81 Table 3. Comparson of average eraon numbers regardng varous mappngs Fxed S SS MSEW Gray S 0(dB) 10 5.04 4.00 4.00 6 1 10 5.97 4.49 4.44 7.16 2 10 7.47 5.09 5.06 8.99 3 10 9.97 6.17 6.19 9.63 4 10 9.96 8.89 8.69 8.34 5 10 7.51 10 10 6.20 5.5 10 6.42 9.42 9.39 5.39 6 10 5.83 7.84 7.85 4.92 6.5 10 5.23 6.84 6.85 4.53 7 10 5.02 6.13 6.13 4.15 7.5 10 5.00 5.99 4.04 8 10 5.00 4.02 8.5 10 4.98 4.00 9 10 4.81 4.00 mappng performs he bes n erms of BER a low o medum SNRs. When BER s a 10-4, compared wh SS and MSEW, S mappng can ge nearly 0.2dB codng gans. Meanwhle, can save eraon numbers a medum SNRs as well. Clearly, Gray mappng sn suable for BICM-ID. Tae S mappng as a represenave, he scheme ha employs proposed soppng creron no only can grealy reduce he eraon numbers, bu also can acheve codng gans a he same me compared wh he fxed. Table 4. Comparson of average eraon numbers regardng varous decodng algorhms Fxed MA MA Lnear- MA Max- MA Consan- MA 0(dB) 10 5.04 7.23 10 10 1 10 5.97 8.63 10 10 2 10 7.47 10 10 10 3 10 9.97 10 10 10 4 10 9.96 9.92 9.96 9.94 5 10 7.51 7.52 7.86 7.52 5.5 10 6.42 6.41 6.52 6.46 6 10 5.83 5.86 5.86 5.84 6.5 10 5.23 5.22 5.23 5.23 7 10 5.02 5.01 5.02 5.02 7.5 10 5.00 5.00 5.00 5.00 8 10 5.00 5.00 5.00 5.00 8.5 10 4.98 4.98 4.97 4.98 9 10 4.81 4.80 4.77 4.80 Fgure. 4 BER performance comparson regardng varous modulaons and mappngs I can be seen obvously from Table 3 and Fgure 4 ha SS and MSEW mappng schemes can ge he bes BER performance a hgh SNR secons, bu need more eraon numbers for compensaon. S Fgure. 5 BER performance comparson regardng varous decodng algorhms As shown n Table 4 and Fgure 5, he max-log- MA algorhm performs he wors a medum SNRs boh concernng he BER performance and he average eraon numbers. When BER s a 10-2, oher decodng algorhms can acheve more han 0.5dB codng gans han max-log-ma algorhm. A relavely hgh SNR secons, he four decodng algorhms have almos he same performances consderng boh BER and eraon numbers. A low SNRs, needng he leas eraon numbers, MA algorhm clearly shows s superory. Copyrgh 2012, Infonomcs Socey 615
Lewse, wh he same decodng algorhm, he proposed creron has obvous advanages over he fxed boh on BER performance and on average eraon numbers. Table 5. Comparson of average eraon numbers regardng varous nerleave dephs Fxed 512 1024 2048 4096 8192 2048 0(dB) 10 5.41 5.07 5.04 5.00 5.03 1 10 6.23 6.24 5.97 5.91 5.96 2 10 8.53 7.84 7.47 7.47 7.33 3 10 9.96 9.97 9.97 10 10 4 10 9.65 9.83 9.96 9.99 10 5 10 7.57 7.42 7.51 7.60 7.58 5.5 10 6.45 6.42 6.42 6.40 6.40 6 10 5.78 5.78 5.83 5.91 5.97 6.5 10 5.31 5.27 5.23 5.17 5.10 7 10 5.09 5.04 5.02 5.00 5.00 7.5 10 5.01 5.00 5.00 5.00 5.00 8 10 4.95 4.99 5.00 5.00 5.00 8.5 10 4.82 4.92 4.98 5.00 5.00 9 10 4.62 4.71 4.81 4.90 4.97 6. Conclusons Ths paper pus forward a novel effcen soppng creron for BICM-ID sysem. Dealed dscussons concernng varous parameers ha may affec he decodng performances are also provded. Compared wh he fxed scheme, he new smple soppng creron can no only sgnfcanly reduce he eraon numbers bu also can ge much codng gans n erms of BER a he same me. Alhough he eraon number s a lle more han CE creron, can oban large codng gans as compensaon. Anoher advanage compared wh CE s ha doesn need any exponenal compuaon, whch can grealy decrease he compuaon complexy a he recever. Above all, he excellen performances and he smplcy for recever mplemenaon mae he new proposed creron more oponal n BICM- ID sysem. 7. Acnowledgemens Ths paper s suppored by he ey projec of Chnese Mnsry of Educaon (No.106042) and he projec sponsored by he Scenfc Research Foundaon for he Reurned Overseas Chnese Scholars, Sae Educaon Mnsry (2007[24]). 8. References [1] Samah S.S, Goff S, and Sharf B.S, Comparave sudy for b-nerleaved coded modulaon wh erave decodng, IEEE AICT, May 2009, pp. 316-318. [2] X. L, J. Rcey, B-nerleaved coded modulaon wh erave decodng, Communcaons Leers, IEEE, vol. 1, no. 6, Nov 1997, pp.169-171. Fgure. 6 BER performance comparson regardng varous nerleave dephs I s revealed clearly from Fgure 6 ha as he nerleave deph ncreases, he BER performance mproves. When BER s a 10-2, he 1024 case can acqure abou 0.35dB codng gans compared wh he 512 scheme. Lewse, 4096 compares wh 2048 and 2048 compares wh 1024 boh can ge nearly 0.1dB codng gans. 8192 has an approxmaely 0.3dB superory compared wh 4096 scheme. Table 5 and Fgure 6 mae a jon show ha a relavely hgh SNR secons, he four nerleave curves converge o approxmaely he same performance bound boh concernng BER and average eraon numbers. Smlarly, regard he 2048 nerleave deph as a represenave, he proposed soppng creron ges superor performances n erms of boh BER and average eraon numbers. [3] X. L and J. Rcey, B-nerleaved coded modulaon wh erave decodng usng sof feedbac, IEE Elecronc Leers., vol. 34, no. 10, May 1998, pp.942-943. [4] J. Hagenauer, E. Offer, and L. ape, Ierave decodng of bnary bloc and convoluonal codes, IEEE Trans. Inform. Theory, vol. 42, Mar. 1996, pp. 429 445. [5] R. Y. Shao, S. Ln, and M..C. Fossorer, Two smple soppng crera for urbo decodng, IEEE Trans. Commun., vol. 47, Aug 1999, pp.1117-1120. [6] Fan-Mn L, An-Yeu Wu, A new soppng creron for effcen early ermnaonn Turbo decoder desgns, ISACS 2005, Dec 2005, pp.585-588. [7] Le L, Qn Wang, Cheng Youn Lu, A novel soppng creron for Turbo decodng, ICICIC 06, Frs Inernaonal Conference on, vol. 1, 2006, pp.201-205. [8] J. Wu, Z. Wang, B. Vojcc, aral erave decodng for bnary Turbo codes, Communcaons, IEEE Trans. Vol.57, No.11, Nov.2009, pp.3298-3306. Copyrgh 2012, Infonomcs Socey 616
[9] L Shan, Xe Le, Chen Hufang, and Wang Kuang, A new soppng creron for Duo-bnary Turbo codes, CMC. IEEE, Vol.2, 2010, pp.271-274. [10] S. Zhang, J. L, C. Ca, A varable erave decodng scheme for BICM-ID based on cross-enropy, WCS 2009. Inernaonal Conference on, Nov. 2009, pp.1-4. Copyrgh 2012, Infonomcs Socey 617