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LDPC万福*简伟**吕一希***本文主要研究了低密度校验码(LDPC码)的编译码方法及其硬件实现在讨论几种主要的LDPC码的编译码方法的基础上,对LDPC译码错误产生原因进行了分析,提出了一种改进的置信传播译码算法最小和算法,该算法在几乎没有增加运算复杂度的情况下,明显地提高了译码性能同时,本文基于几何思想的LDPC码为例,提出了并串结合的FPGA实现方法,给出了仿真结果:低密度校验码置信传播译码算法最小和算法ResearchandRealizationofLDPCDecodingWanFuJianWeiLYixiAbstractThispaperputemphasisonthemethodofencodinganddecodingLDPCcode(lowdensityparitycheck)anditshardwarerealization.,OnthebasisofdiscussionofseveralmainPDPCencodinganddecoding,thecausesofwrongLDPChavebeenanalyzed,AnalgorithmofimprovedBeliefPropagationthushasbeenresulted,thatisMinSumalgorithm.Thisalgorithmimprovedobviouslythedecodingperformancewithoutadditionalcomplexityofoperation.Meanwhile,AwayofseriesandparallelcombinedFPGArealizationhasbeenraisedwiththeemulationresultunderthealgebraideaofLDPCcode.Keywords:lowdensityparitycheckbeliefpropagationminsum(LDPC)Gallager,,,Turbo,LDPC,LDPC1/210000,LDPCTurbo,LDPCLDPCLDPC******120074,,LDPCLDPC,FPGA,LDPCLDPCLDPC,,,,,,,,图1LDPC码编码阵1,TBDACEH,,HH,HHx=(x1,x2,x3),x3:(1)y=D!x3;k=T!y;s=A!k+z(2)x2=(A!T!B+C)-1!s;x1=T!(B!x2+y)(3)xEncode,LDPC,LDPC,LDPC220074,LDPC,,LDPCLDPC,LDPC,:(1);(2);(3),,BF(BitFlipping),,(BeliefPropagation),BP,BP,BP,MinSum1LDPC,,4,,,,4,,H,qxmlrxml,qxmllm,lx;rxmllm,mL(pl)=lnpl(1)pl(0)=lnexp(2x22)exp(-2x22)=2x2(1)y=12ln(k1k2),k1+k2=1tanh(y)=exp(2y)-1exp(2y)+1tanh(12L(rkml))=tanh(12ln(r1mlr0ml))=r1ml-r0ml(2)(1),(2)tanh(12L(rkml))=∀l#L(m)\ltanh(12ln(q1mlq0ml))=∀l#L(m)\ltanh(12L(qkml))(3)L(rkml)=2tanh-1[∀l#L(m)\ltanh(12L(qkml))](4)L(qkml)=(qkml)!(qkml)(5)320074(qkml)=sign(qkml),!(qkml)=|qkml|L(rkml))=2tanh-1[∀l#L(m)\l(qkml)[∀l#L(m)\ltanh(12!(qkml))](6)=[∀l#L(m)l(qkml)][2tanh-1(ln-1∃l#L(m)llntanh(12!(qkml))]F(x)=-lntanh(12x)F(x)=F-1(x),,(6)L(rkml)=[∀l#L(m)\l(qkml)F[∃l#L(m)\lF!(qkml))](7),,,,,,2(MinSum)BP,F(x)=-lntanh(12x),F(x)=F-1(x)图2F函数曲线2F(x),F(x)x,,∃l#L(m)\lF(!(qkml))!(qkml),(8)∃l#L(m)\lF(!(qkml))%F(∀minl#L(m)\l!(qkml))(8)(8)(6),,∀,3325560686LDPC,AWGN,100,,,,,LDPC420074图3MinSum与BP译码算法的性能比较LDPC,,,,,,,LDPC,,,,FPGA,LDPC1LDPC,LDPCLDPC,5LDPC4(640,1024)LDPC,5,85:8(128!128),8!8(16!16),8,8!816!16,8520074图4LDPC码校验矩阵LDPC,LDPC(5)1,,,64,1,;,,LDPC,,LDPC2LDPC4LDPC5图5迭代结构示意图5,LDPCk2RAM,k2(VNU),5k(CNU),2L;,,N=L!k2,M=5k!L,MNLDPC6200743LDPC:L=16,k=8,M=5!L!k=640,N=L!k!k=1024,8(4,4),8,5LDPC,,:(1);(2)k!k=645!k=40,L!k!k/k/k=L=16,5!L!k/k/5=L=16;(3)2!8!8!640=80k;(4)N!f/2L/Iternum,f,Iternum图6(640!1024)的LDPC码纠错性能6BPSK,10,AWGN,,,,,LDPC,,80k,1032*fLDPCLDPC,,,LDPC,LDPCLDPC,,LDPC(下转第31页)720074,,,,,,ST8257I2SDSP,DVB&∋&∋,,,PW328DVBC,,(上接第7页)FPGA,LDPC,FPGA,LDPC1.&-∋..19912.&∋..19923T.Etzion,A.TrachtenbergandA.Vardy.&WhichCodesHaveCycleFreeTannerGraphs,∋IEEETransactionsonInformationTheory,Vo.l45.No.6,pp.2173~2181,Sep.t1999.4NiclasWiberg.&CodesandDecodingonGeneralGraphs∋,DepartmentofElectricalEngineeringLinkopingUniversity5J.ChenandA.Dholakia.&ReducedComplexityDecodingofLDPCCodes,∋IEEE.2002.3120074