LDPC码在二进制对称信道下的性能分析

第42卷第1期东北师大学报(自然科学版)Vol.42No.12010年3月JournalofNortheastNormalUniversity(NaturalScienceEdition)March2010l2009-06-29SE1S(60802060).TeV(1978),3,pV3,=,1VY2I;SC(1964),3,q,pV3=,1VY/|).cI|1000-1832(2010)01-0059-04LDPC=/?s李玉祥1,2,梁国龙2,殷敬伟2(1.哈尔滨工程大学理学院,黑龙江哈尔滨150001;2.哈尔滨工程大学水声技术国防科技重点实验室,黑龙江哈尔滨150001)K1低密度校验码(LDPC)是一类线性分组纠错码,和积传递算法是LDPC码迭代译码算法中的常用算法.在此基础上研究了二进制对称信道(BSC)下LDPC码的消息传递迭代译码算法,对其误码特性进行了仿真,并用密度进化方法仿真了校验节点a变量节点的概率密度在迭代过程中的收敛情况.结果表明在给定的信道门限下LDPC码具有良好的纠错性能.1oM低密度校验码;密度进化;和积算法ms|TN911.2S120#10DSA0LDPC-K/PjKBp1.R.G.Gallager1962Mn54LDPC2,1996MD.J.MacKayVCI4?,rLDPC/PjK?3-4.dI,BP%rHp?V3Klq9,7%rE,?VCv?.r5ELDPCrEB,6srEv?E.=Hq/,LDPCrE,iEv?s.1LDPClLDPCBnLsF.nHvs0,Bls1,7OnVBn.BnM1,cd,#.nHc/10M,VLDPCs?5d?5.TBnBd,M,Bd,9M,*?5LDPC,5d?5LDPC.BVULDPCZE(n,Q,C)l,:n,Q3n(c1),Cn(c1).2LDPCBSC/rEBSCm1U.(=|,-HY1.,?/00H,l1+|/10qp,/00q1-p;7?/10H,l1+|/00qp,/10q1-p,p1.D2,7W%sBECGa-llagerrE#|rE.Y东北师大学报(自然科学版)第42卷m1qp=V!.M5q,ELDPCs.LDPCBSC/rE:(1)S9.M5q.L(un)=logp1-p,x=1;log1-pp,x=0.N1Vd:L(un)|YlM01,VU|01,L(un)v01V?v.,L(un)VrT.Q,Hm,n=1B(m,n),Knym(un)=L(un),+myn=0.(2)Vnm#nIN(m),9+myn(un)=2artanhFncIN(m)ntanhKncym(un)/2.Mn#mIM(n),9Knym(un)=L(un)+EmcIM(n)m+mcyn(un).n,9K(un)=L(un)+EmIM(n)+myn(un).(3)k%TK(un)0,5xn=1;TKn(un).3:k3.1lHqHq/6:(1).!=sYxy,TMqp(y|x=1)=p(-y|x=-1),5.(2)n.Ti|?1(b1,bdc-1),nh|Q,5n.(3)M.TM|QM,5M.BPrEHqH,VLrpq.3,rpq.31,yNVL!.0313.3.2Vh.E,hzq=smH.MnlVH.h,sY9Hh,V7LCh.(?,n5LS3,:1LLR(LogLikelihoodRatio)L(x)=logp(x=0)p(x=1).Tp(x=0)p(x=1),*LLR;5.03,5q1+q.sh.rq,lpl(ql)lQH,M(n)n(M)hqf.m2E60第1期李玉祥,等:LDPC码在二进制对称信道下的性能分析n_hLLR.q,MMF,qMq.yN,nhqfwr-1hMqf.wrnMM.ql=p(wr-1)l,|VU.(nsQ(x),ql=EiQip(i-1)l=Q(pl).(1)Mn,M_hLLR.yNMhqfwc-1hnqf#qf.pl=p0q(wc-1)l.:wcMMn,p0VUqf.(MsK(x),:pl=p0EiKiq(i-1)l=p0K(ql).(2)h.Em2.4_T#s4.1LDPCBSC?sBSCHq/,(3,6)?5LDPC_s,20000,q0.5.m3VPGQq01010,01020,01030,01040,01050,01060,01070,01080HqQMf,q9v,qv9F.,:VUq,VU(Q.qlH,1Vz+.4.2V_sm4VUq0.080H20QMnqf.m52Qa10Qa20Q28QMqf,VV,hqv,phql,rl.V28Q,qt0.r7SH,Mnq+%.h.rEBQ,qMM,qv.yN,V_f/,LDPC,6h.Vhqs,Hq,sr?.m3BSC/LDPC+wLm420QHMnqm52,10,2028QHMq5=/LDPC?Ke.N$=/(3,6)?5LDPC,+_.iZE_n,MqQ9Fqlf.NZEs61东北师大学报(自然科学版)第42卷K,ss4Z_./B|LDPC=W1,LDPCL=LYd4IN.ID1CHUNGSY,FORNEYJGD,RICHARDSONTJ,etal.Onthedesignoflow-densityparity-checkcodeswithin0.0045dBoftheShannonlimitJ.IEEECommunicationsLetters,2001,5(2):58-60.2GALLAGERRG.Low-densityparity-checkcodesR.Cambridge:MITPress,1963:25.3MACKAYDJC,NEALRM.NearshannonlimitperformanceoflowdensityparitycheckcodesJ.ElectronicLetters,1996,32(8):1645-1646.4MACKAYDJC.Gooderror-correctingcodesbasedonverysparsematricesJ.IEEETransonInformTheory,1999,45(2):399-431.5FRANLRK,BRENDANJ.Factorgraphsandthesum-productalgorithmJ.IEEETransonInformTheory,2001,47(2):498-519.6RICHARDSONT,SHOKROLLAHIM,URBANKER.Designofcapacity-approachingirregularlow-densityparity-checkcodesJ.IEEETransonInformTheory,2001,47(2):619-637.7DIC.Finite-lengthanalysisoflow-densityparity-checkcodesonthebianryerasurechannelJ.IEEETransonInformTheory,2002,48(6):1570-1579.AnalysisofLDPCcodeperformanceoverbinarysymmetricchannelLIYu-xiang1,2,LIANGGuo-long2,YINJing-wei2(1.CollegeofScience,HarbinEngineeringUniversity,Harbin150001,China;2.NationalLaboratoryofUnderwaterAcousticTechnology,HarbinEngineeringUniversity,Harbin150001,China)Abstract:Low-DensityParity-Checkcode(LDPC)isakindoflinearblockerror-correctingcodes.Sum-productalgorithmisaniterativedecodingalgorithmscommonlyusedinLDPCcodedecoding.Thispa-perstudiesintotheLDPCcodemessagepassingiterativedecodingalgorithmunderthebinarysymmet-ricchannel(BSC)andsimulatesthebiterrorprobability,thensimulatestheconvergenceofchecknodespandvariablenodespprobabilitydensityintheiterativeprocessusingthemet