RS编码rs(204,188)设计原理

11.9.2 RS(204,译码器的设计RS数字电视）准中信道编/解码采用RS(204,188)；ATM网络中使用RS(128,124)作为前向纠错编码ForwardErrorCorrecting,FE。本节将以DVB标准中定义的RS(204,BMpipeline结构的译码的所有技术细节。考虑到译码器的可扩展性、可维护性，实例中尽可能RS译码器。应用背景（signal-to-noiserat。在大多数应用中，将RS码与卷积码级联使用进行纠错。接收机都能将误码纠正过来。必须指出，信道编码并非指信号经上变频发送出去后，在传输信道中（有线、卫星或地面Reed-Solomon编码等都可划为信道编码。典型的数字电11-73所示。在图11-73中，外编码多为具有很强突发纠错能力的RS(n,k,t)编码，n为（缩短）码长，k为信息位，t为能纠正误码的最大的码位，且RS外码编码的特点是纠正与本组有关的误码，尤其对纠正突发性的误码最有效。通常，n、k、t分别为204、188和8。11-74"EN300（Cable框图，其中包括了数据帧结构（Framingstructure、信道编码及调制。可以看到，使用了RS(204,编码。其中，RS(204,188)码定义如下。理论算法RS译码主要有时域译码和频域译码BM迭代算法或者欧式算（Euclid'sAlgorithBM迭代算法原理及以此算法为基础的RS译码器的FPGARS4步：第一步由接收到的码组计算伴随式；第二步求解关键方程；第三步计算出错误图样；最后由错误图样和接收码组计算出可能发送的码字。图11-75给出了RS译码器的一般步骤框图。RSΛ(x)，1966年伯利坎普（Berlekamp）提出了可以由伴随式计算错误位置多项式的迭代译码算法，这极大地加快了求解错误位置多项式的速度，该方法简单且易于实现，从而从工程上解决了RS译码的问题；1969年梅西算法就称为BM迭代译码算法。（1）Reed-Solomon码基本概念RSk（n,C=(Cn-1,…,C1,C0)，可用码字多项式表示为：同理，DFT的逆变换IDFT定义为：如果通过接收到的R求出伴随式S，能够解出关键方程，然后又解出(x)和(x)容易地恢复错误图样EChien搜索及Forney算法用于恢复过计算C=R-，就得到了发送码字。下面将介绍关键方程的求解。（3）BM及其改进算法求解关键方程1966年伯利坎普（Berlekamp）年梅西指出了该算法与序列的最短线性移位寄存器综合之间的关系，并进行了简化，因此，此译码算法就称为BM迭代译码算法。在VLSI设计中，RS解码时的关键方程求解比较复杂，主要有以下三种方法：Berlekamp-Massey（BM）算法、EuclideanPGZ(t>3)般认为BM算法涉及到有限inversRS(204,188译码器关键方程求解采用了改进的BM算法，算法迭代时无需求解有限域元素逆inversionles先详细介绍BM算法。3.RS(204,码器建模这里以具体的DVB标准中定义的RS(204,FPGA/VLSI模型。在DVB标准中，RS(204,码定义如下：在图11-82中，"Pow"模块表示生成根i的幂次i，"Exp"表示查表求i的幂，"Inv"用查找表求?(-i)的逆。程序说明本部分将给出RS(204,188)译码器的VerilogHDL程序代码，其中RS码的生成多项式g(x)为：8ForneyChien搜索等模块并行工作。在经过243个字节的固有延需额外的握手控制信号。者参阅。下面首先给出伴随式计算模块程序，如下所示。moduleSCalculate(clk,init,sc_done,r,s_out);parameter t=8, 纠错能3. N=204,//N-RS码长度4. m=8;//m-GF(2m)扩展域input clk,init;input[m-1:0] r;output[m-1:0] s_out;output sc_done; 9.10.reg[m-1:0]s[t*2:1],s_latched[t*2:1];11.wire[m-1:0]r_a[t*2-1:0];integer counter;always@(posedgeclk)begin:SC_BLOCKintegerj;if((init)||(counter==N))beginfor(j=1;j<=t*2;j=j+1)锁存上一帧数据的伴随式，开始新的计算s_latched[j]<=18.19.for(j=1;j<=t*2;j=j+1)20.s[j]<=r;21.counter<=1;22.end23.elseif(counter<=N-1)begin24.for(j=1;j<=t*2;j=j+1)25.s[j]<=r^r_a[j-1];26.counter<=counter+1;27.end28.end29./*下面是有限域的常数乘法器的例化*/30.ff_const_mulr_x_a0(.din(s[1]),.dout(r_a[0]));//a^031.ff_const_mulr_x_a1(.din(s[2]),.dout(r_a[1]));//a^132.ff_const_mulr_x_a2(.din(s[3]),.dout(r_a[2]));//a^233.ff_const_mulr_x_a3(.din(s[4]),.dout(r_a[3]));//a^334.ff_const_mulr_x_a4(.din(s[5]),.dout(r_a[4]));//a^435.ff_const_mulr_x_a5(.din(s[6]),.dout(r_a[5]));//a^536.ff_const_mulr_x_a6(.din(s[7]),.dout(r_a[6]));//a^637.ff_const_mulr_x_a7(.din(s[8]),.dout(r_a[7]));//a^738.ff_const_mulr_x_a8(.din(s[9]),.dout(r_a[8]));//a^839.ff_const_mulr_x_a9(.din(s[10]),.dout(r_a[9]));//a^940.ff_const_mulr_x_a10(.din(s[11]),.dout(r_a[10]));//a^1041.ff_const_mulr_x_a11(.din(s[12]),.dout(r_a[11]));//a^1142.ff_const_mulr_x_a12(.din(s[13]),.dout(r_a[12]));//a^1243.ff_const_mulr_x_a13(.din(s[14]),.dout(r_a[13]));//a^1344.ff_const_mulr_x_a14(.din(s[15]),.dout(r_a[14]));//45.ff_const_mulr_x_a15(.din(s[16]),.dout(r_a[15]));//46.defparamr_x_a0.CONST=15'h4405,r_x_a1.CONST=15'h6202,47. r_x_a2.CONST=15'h7101,r_x_a3.CONST=15'h3880,48.r_x_a4.CONST=15'h1C40, r_x_a5.CONST=15'h0E20,49. r_x_a6.CONST=15'h4710, r_x_a7.CONST=15'h2388,50.r_x_a8.CONST=15'h11C4,51. r_x_a9.CONST=15'h48E2,r_x_a10.CONST=15'h2471,52. r_x_a11.CONST=15'h5238,53.r_x_a12.CONST=15'h691C,r_x_a13.CONST=15'h748E,54.r_x_a14.CONST=15'h3A47,55. r_x_a15.CONST=15'h1D23;56./*sc_done信号，指示后续电路进行新的计算*/reg sc_done;integershift_count;always@(posedgeclk)beginif(counter==N)beginsc_done<=1;shift_count<=1;endelsebeginsc_done<=0;if((0<shift_count)&&(shift_count<=t*2))beginshift_count<=shift_count+1;endelseshift_count<=0;end74.//移位输出伴随式reg[m-1:0]s_out;always@(shift_count)beginif((0<shift_count)&&(shift_count<=t*2))s_out=s_latched[shift_count];elses_out=0;83.84.endmodule对上面的程序有如下的说明。"init"信号是一个包（204）信号。因为RS码的b0=Sj0开始直到1511-7。即：因为整个译码器采用流水线结构，所以在伴随式计算完后，产生一个时钟周期有效的"sc_done"信号，用以启动后续电路进行新的计算。由于在BM算法中，用到了(x)和S(x)Sj串行输出。接下来，给出BM算法求错误位置多项式(x)的程序代码1. //*****************************************2. // 改进的BM算法3. //*****************************************moduleBMA(S,clk,kes_init,kes_done,Lmd0,Lmd1,Lmd2,Lmd3,Lmd4,Lmd5,Lmd6,Lmd7,Lmd8,L,s_out);parameter t=8,N=204, m=8;input clk,kes_init;input[m-1:0]S;output[m-1:0]L,Lmd0,Lmd1,Lmd2,Lmd3,Lmd4,Lmd5,Lmd6,Lmd7,Lmd8;output[m-1:0]s_out;output 12.reg [m-1:0]L;13.reg[m-1:0]B[t:0]; 即所求的错误多项式reg[m-1:0]T[t:0],gamma,delta,16.reg[m-1:0]SSR[t*2:1];wire[m-1:0]S_B[t:0]; //Productof(S*B)integer counter;19.reg[m-1:0] s_latched[t*2:1];reg comput,kes_done;always@(posedgeclk)begin:BM_BLOCKintegerj;if(kes_init)begin 初始化变量delta<=0;25.for(j=2;j<=t*2;j=j+1)26.SSR[j]<=0;27.SSR[1]<=S;counter<=0;endelseif(counter==t*2-1)begin31.delta<=((S_B[0]^S_B[1])^(S_B[2]^S_B[3]))^((S_B[4]^S_B[5])32. ^(S_B[6]^S_B[7]))^S_B[8]; 的值33.for(j=1;j<=t*2-1;j=j+1)34.SSR[j+1]<=SSR[j];35.SSR[1]<=S;for(j=1;j<=t*2;j=j+1) 锁存输入的伴随式序列s_latched[j]<=SSR[j];counter<=counter+1;endelseif(counter<=t*2)begin41.delta<=((S_B[0]^S_B[1])^(S_B[2]^S_B[3]))^((S_B[4]^S_B[5])42. ^(S_B[6]^S_B[7]))^S_B[8]; Δ43.for(j=1;j<=t*2-1;j=j+1)44.SSR[j+1]<=SSR[j];45.SSR[1]<=S;counter<=counter+1;endend49.//S(x)*B(x)50.FF_MulS_x_B0(.B(SSR[1]),.A(B[0]),.P(S_B[0]));51.FF_MulS_x_B1(.B(SSR[2]),.A(B[1]),.P(S_B[1]));52.FF_MulS_x_B2(.B(SSR[3]),.A(B[2]),.P(S_B[2]));53.FF_MulS_x_B3(.B(SSR[4]),.A(B[3]),.P(S_B[3]));54.FF_MulS_x_B4(.B(SSR[5]),.A(B[4]),.P(S_B[4]));55.FF_MulS_x_B5(.B(SSR[6]),.A(B[5]),.P(S_B[5]));56.FF_MulS_x_B6(.B(SSR[7]),.A(B[6]),.P(S_B[6]));57.FF_MulS_x_B7(.B(SSR[8]),.A(B[7]),.P(S_B[7]));58.FF_MulS_x_B8(.B(SSR[9]),.A(B[8]),.P(S_B[8]));59.wire[m-1:0]gamma_B[t:0]; //Productofγ*B(x)wire[m-1:0]delta_T[t-1:0]; //ProductofΔ*T(x)always@(negedgeclk)begin:LABLEintegerj;if(kes_init)beginfor(j=1;j<=t;j=j+1)begin66.B[j]<=0;T[j]<=0;67.end68.B[0]<=1;T[0]<=1;69.L<=0; k<=0; gamma<=1;endelseif(comput)beginB[0]<=gamma_B[0]; B(x)73.for(j=0;j<t;j=j+1)74.B[j+1]<=gamma_B[j+1]^delta_T[j];75.76.if((delta)&&((L<<1)<=k))begin //Condition77.for(j=0;j<=t;j=j+1)78.T[j]<=B[j]; //T[x]=B[x]79.L<=k+1-L;gamma<=delta; //γ=Δendelsebeginfor(j=0;j<t;j=j+1)begin84.T[j+1]<=T[j]; //T[x]=x*T[x];85.end86.T[0]<=0;87.end88.k<=k+1;endend//γ*B(x)FF_Mulgamma_x_B0(.A(gamma),.B(B[0]),.P(gamma_B[0]));FF_Mulgamma_x_B1(.A(gamma),.B(B[1]),.P(gamma_B[1]));FF_Mulgamma_x_B2(.A(gamma),.B(B[2]),.P(gamma_B[2]));FF_Mulgamma_x_B3(.A(gamma),.B(B[3]),.P(gamma_B[3]));FF_Mulgamma_x_B4(.A(gamma),.B(B[4]),.P(gamma_B[4]));FF_Mulgamma_x_B5(.A(gamma),.B(B[5]),.P(gamma_B[5]));FF_Mulgamma_x_B6(.A(gamma),.B(B[6]),.P(gamma_B[6]));FF_Mulgamma_x_B7(.A(gamma),.B(B[7]),.P(gamma_B[7]));FF_Mulgamma_x_B8(.A(gamma),.B(B[8]),.P(gamma_B[8]));101.//Δ*T(x)FF_Muldelta_x_T0(.A(delta),.B(T[0]),.P(delta_T[0]));FF_Muldelta_x_T1(.A(delta),.B(T[1]),.P(delta_T[1]));FF_Muldelta_x_T2(.A(delta),.B(T[2]),.P(delta_T[2]));FF_Muldelta_x_T3(.A(delta),.B(T[3]),.P(delta_T[3]));FF_Muldelta_x_T4(.A(delta),.B(T[4]),.P(delta_T[4]));FF_Muldelta_x_T5(.A(delta),.B(T[5]),.P(delta_T[5]));FF_Muldelta_x_T6(.A(delta),.B(T[6]),.P(delta_T[6]));FF_Muldelta_x_T7(.A(delta),.B(T[7]),.P(delta_T[7]));111.always@(counter)beginif((0<counter)&&(counter<=t*2))comput=1;elsecomput=0;118.integershift_count;always@(posedgeclk)beginif(counter==t*2-1)beginkes_done<=1;shift_count<=1;endelsebeginkes_done<=0;if((0<shift_count)&&(shift_count<=t*2))beginshift_count<=shift_count+1;endelseshift_count<=0;end134.reg[m-1:0]s_out;always@(shift_count)beginif((0<shift_count)&&(shift_count<=t*2))s_out=s_latched[t*2-shift_count+1];elses_out=0;142.assignLmd0=B[0];assignLmd1=B[1];assignLmd2=B[2];assignLmd3=B[3];assignLmd4=B[4];assignLmd5=B[5];assignLmd6=B[6];assignLmd7=B[7];assignLmd8=B[8];endmodule关于改进的BM算法，对程序说明如下。^的计算公式：为了在求出值后，能马上用于计算(k+1)，程序中用到了反相时钟，即在时钟上升沿计算，在时钟下降沿计算(k+1)。模块也是串行输出伴随式序列，以便后面的卷积求和。下面的程序代码完成了Forney算法，包括错误计算多项式(x)的计算。1. //******************************************2. //计算：Eiα^i*Ω(α^-i)/Λ`(α^-i)3. //******************************************moduleerror_valuator(clk,init,s,Lmd0,Lmd1,Lmd2,Lmd3,Lmd4,Lmd5,Lmd6,Lmd7,Lmd8,ErrorValue);parameter t=8,N=204, m=8;input clk,init;input[m-1:0]s,Lmd0,Lmd1,Lmd2,Lmd3,Lmd4,Lmd5,Lmd6,Lmd7,Lmd8;output[m-1:0]ErrorValue;11.12./*计算：Ω(x)=Λ(x)*S(x)(modx^2t)*/reg[m-1:0]OmegaC[t*2-1:0],SyndromeSR[t+1:1],LmdC[t:0];wire[m-1:0]sLmdC[t:0];integer counter1;always@(posedgeclk)begin:OMEGA_COEEFICIENTintegerj;if(init)begin19.for(j=2j<=t+1j=j+1)//加载伴随式序列(12t)SyndromeSR[j]<=0;SyndromeSR[1]<=s;//Λ(x)的系数LmdC[0]<=Lmd0;LmdC[1]<=Lmd1;LmdC[2]<=Lmd2;LmdC[3]<=Lmd3;LmdC[4]<=Lmd4;LmdC[5]<=Lmd5;LmdC[6]<=Lmd6;LmdC[7]<=Lmd7;LmdC[8]<=Lmd8;for(j=0j<=t*2-1j=j+1) //OmegaC[j]寄存器OmegaC[j]<=0;counter1<=1;endelseif((0<counter1)&&(counter1<=t*2))begin31.for(j=1;j<=t;j=j+1)SyndromeSR[j+1]<=SyndromeSR[j];SyndromeSR[1]<=s;34.for(j=0;j<t*2-1;j=j+1)OmegaC[j]<=OmegaC[j+1];OmegaC[t*2-1]<=(sLmdC[0]^sLmdC[1])^(sLmdC[2]^sLmdC[3])^(sLmdC[4]^sLmdC[5])^(sLmdC[6]^sLmdC[7])^sLmdC[8];counter1<=counter1+1;endelsecounter1<=0;endFF_Muls_x_Lmdc0(.A(SyndromeSR[1]),.B(LmdC[0]),.P(sLmdC[0]));44.FF_Muls_x_Lmdc1(.A(SyndromeSR[2]),.B(LmdC[1]),.P(sLmdC[1]));45.FF_Muls_x_Lmdc2(.A(SyndromeSR[3]),.B(LmdC[2]),.P(sLmdC[2]));46.FF_Muls_x_Lmdc3(.A(SyndromeSR[4]),.B(LmdC[3]),.P(sLmdC[3]));47.FF_Muls_x_Lmdc4(.A(SyndromeSR[5]),.B(LmdC[4]),.P(sLmdC[4]));48.FF_Muls_x_Lmdc5(.A(SyndromeSR[6]),.B(LmdC[5]),.P(sLmdC[5]));49.FF_Muls_x_Lmdc6(.A(SyndromeSR[7]),.B(LmdC[6]),.P(sLmdC[6]));50.FF_Muls_x_Lmdc7(.A(SyndromeSR[8]),.B(LmdC[7]),.P(sLmdC[7]));51.FF_Muls_x_Lmdc8(.A(SyndromeSR[9]),.B(LmdC[8]),.P(sLmdC[8]));52.53.regComput_Err; //Ω(a^-i)计算的控制信号54.always@(counter1)begin55.if(counter1==(t*2+1))Comput_Err=1;else Comput_Err=0;58.59.//Ω(a^-i)，i203~060.reg[m-1:0]OmegaIR[t*2-1:0],OmegaA;61.wire[m-1:0]aOmegaIR[t*2-1:1],a52OmegaC[t*2-1:1];62.always@(posedgeclk)begin:OMEGA_ALPHA63.integerj;64.if(Comput_Err)begin65.for(j=1j<=t*2-1j=j+1) //OmegaIR[j]迭代寄存器66.OmegaIR[j]<=a52OmegaC[j];67.OmegaIR[0]<=OmegaC[0];68.end69.elsebegin //Ω(a^-i)70.for(j=1;j<=t*2-1;j=j+1)71.OmegaIR[j]<=aOmegaIR[j];72.OmegaIR[0]<=OmegaIR[0];73.end74.end75.ff_const_mula1_x_OmegaIR1(.din(OmegaIR[1]),76..dout(aOmegaIR[1]));//a^1*Ω177.ff_const_mula2_x_OmegaIR2(.din(OmegaIR[2]),78..dout(aOmegaIR[2]));//a^2*Ω279.ff_const_mula3_x_OmegaIR3(.din(OmegaIR[3]),80. .dout(aOmegaIR[3])); //a^3*Ω381.82.483.84.585.86.687.88.789.90.891.92.993.94.

ff_const_mula4_x_OmegaIR4(.din(OmegaIR[4]),.dout(aOmegaIR[4])); //a^4*Ωff_const_mula5_x_OmegaIR5(.din(OmegaIR[5]),.dout(aOmegaIR[5])); //a^5*Ωff_const_mula6_x_OmegaIR6(.din(OmegaIR[6]),.dout(aOmegaIR[6])); //a^6*Ωff_const_mula7_x_OmegaIR7(.din(OmegaIR[7]),.dout(aOmegaIR[7])); //a^7*Ωff_const_mula8_x_OmegaIR8(.din(OmegaIR[8]),.dout(aOmegaIR[8])); //a^8*Ωff_const_mula9_x_OmegaIR9(.din(OmegaIR[9]),.dout(aOmegaIR[9])); //a^9*Ωff_const_mula10_x_OmegaIR10(.din(OmegaIR[10]),.dout(aOmegaIR[10])); //a^10*Ω1095.ff_const_mula11_x_OmegaIR11(.din(OmegaIR[11]),96. .dout(aOmegaIR[11])); //a^11*Ω1197.ff_const_mula12_x_OmegaIR12(.din(OmegaIR[12]),98. .dout(aOmegaIR[12])); //a^12*Ω1299.ff_const_mula13_x_OmegaIR13(.din(OmegaIR[13]),100..dout(aOmegaIR[13]));//a^13*Ω13101.ff_const_mula14_x_OmegaIR14(.din(OmegaIR[14]),102..dout(aOmegaIR[14]));//a^14*Ω14103.ff_const_mula15_x_OmegaIR15(.din(OmegaIR[15]),104..dout(aOmegaIR[15]));//a^15*Ω15defparama1_x_OmegaIR1.CONST=15'h6202,a2_x_OmegaIR2.CONST=15'h7101,107.,a3_x_OmegaIR3.CONST=15'h3880,a4_x_OmegaIR4.CONST=15'h1C40108.a5_x_OmegaIR5.CONST=15'h0E20,a6_x_OmegaIR6.CONST=15'h4710,109.a7_x_OmegaIR7.CONST=15'h2388,a8_x_OmegaIR8.CONST=15'h11C4,110.a9_x_OmegaIR9.CONST=15'h48E2,a10_x_OmegaIR10.CONST=15'h2471,a11_x_OmegaIR11.CONST=15'h5238,a12_x_OmegaIR12.CONST=15'h691C,a13_x_OmegaIR13.CONST=15'h748E,a14_x_OmegaIR14.CONST=15'h3A47,a15_x_OmegaIR15.CONST=15'h1D23;114.115.ff_const_mula52_x_OmegaC1(.din(OmegaC[1]),116. .dout(a52OmegaC[1])); //a^52*Ω1117.ff_const_mul118.*Ω2a52_x_OmegaC2(.din(OmegaC[2]),.dout(a52OmegaC[2]));//a^104119.ff_const_mula52_x_OmegaC3(.din(OmegaC[3]),120..dout(a52OmegaC[3]));//a^156*Ω3121.ff_const_mula52_x_OmegaC4(.din(OmegaC[4]),122..dout(a52OmegaC[4]));//a^208*Ω4123.ff_const_mula52_x_OmegaC5(.din(OmegaC[5]),124..dout(a52OmegaC[5]));//a^260*Ω5125.ff_const_mula52_x_OmegaC6(.din(OmegaC[6]),126..dout(a52OmegaC[6]));//a^312*Ω6127.ff_const_mula52_x_OmegaC7(.din(OmegaC[7]),128..dout(a52OmegaC[7]));//a^364*Ω7129.ff_const_mul130.*Ω8a52_x_OmegaC8(.din(OmegaC[8]),.dout(a52OmegaC[8]));//a^416131.ff_const_mula52_x_OmegaC9(.din(OmegaC[9]),132..dout(a52OmegaC[9]));//a^468*Ω9133.ff_const_mula52_x_OmegaC10(.din(OmegaC[10]),134..dout(a52OmegaC[10]));//a^520*Ω10135.ff_const_mula52_x_OmegaC11(.din(OmegaC[11]),136..dout(a52OmegaC[11]));//a^572*Ω11137.ff_const_mula52_x_OmegaC12(.din(OmegaC[12]),138..dout(a52OmegaC[12]));//a^624*Ω12139.ff_const_mula52_x_OmegaC13(.din(OmegaC[13]),140..dout(a52OmegaC[13]));//a^676*Ω13141.ff_const_mula52_x_OmegaC14(.din(OmegaC[14]),142..dout(a52OmegaC[14]));//a^728*Ω14143.ff_const_mula52_x_OmegaC15(.din(OmegaC[15]),144..dout(a52OmegaC[15]));//a^780*Ω15145.defparam146.a52_x_OmegaC1.CONST=15'h6D41,a52_x_OmegaC2.CONST=15'h0D84,147.a52_x_OmegaC3.CONST=15'h1BB9,a52_x_OmegaC4.CONST=15'h1F55,148.a52_x_OmegaC5.CONST=15'h0E20,a52_x_OmegaC6.CONST=15'h6B6A,149.a52_x_OmegaC7.CONST=15'h3C6C,a52_x_OmegaC8.CONST=15'h3CDD,150.a52_x_OmegaC9.CONST=15'h14FA,a52_x_OmegaC10.CONST=15'h2471,151.a52_x_OmegaC11.CONST=15'h535B,a52_x_OmegaC12.CONST=15'h39E3,a52_x_OmegaC13.CONST=15'h7DE6, a52_x_OmegaC14.CONST=15'h10A7,a52_x_OmegaC15.CONST=15'h1D23;154.155./*计算：Λ'(α^-i)*/156.reg[m-1:0]DifLmdIR[3:0],DifLmdA;157.wire[m-1:0]aDifLmdIR[3:1],a52LmdC[3:1];always@(posedgeclk)beginif(Comput_Err)begin //Λ'(x)的系数DifLmdIR[0]<=LmdC[1]; DifLmdIR[1]<=a52LmdC[1];DifLmdIR[2]<=a52LmdC[2];DifLmdIR[3]<=a52LmdC[3];endelsebegin //Λ'(α^-i)DifLmdIR[1]<=aDifLmdIR[1];DifLmdIR[2]<=aDifLmdIR[2];DifLmdIR[3]<=aDifLmdIR[3];endendff_const_mula2_x_DifLmdIR1(.din(DifLmdIR[1]),.dout(aDifLmdIR[1])); //a^2*Ω1ff_const_mula4_x_DifLmdIR2(.din(DifLmdIR[2]),.dout(aDifLmdIR[2])); //a^4*Ω1ff_const_mula6_x_DifLmdIR3(.din(DifLmdIR[3]),.dout(aDifLmdIR[3])); //a^6*Ω1175.defparam176.a2_x_DifLmdIR1.CONST=15'h7101, a4_x_DifLmdIR2.CONST=15'h1C40,177.a6_x_DifLmdIR3.CONST=15'h4710;178.179.ff_const_mula52_x_LmdC3(.din(LmdC[3]),180..dout(a52LmdC[1]));//a^104*Ω1181.ff_const_mula52_x_LmdC5(.din(LmdC[5]),182..dout(a52LmdC[2]));//a^208*Ω2183.ff_const_mula52_x_LmdC7(.din(LmdC[7]),184. .dout(a52LmdC[3])); //a^312*Ω3defparama52_x_LmdC3.CONST=15'h0D84,a52_x_LmdC5.CONST=15'h1F55,a52_x_LmdC7.CONST=15'h6B6A;188./*α^ii*/reg[m-1:0]ExpIndex;always@(posedgeclk)beginif(Comput_Err)ExpIndex<=N-1;else ExpIndex<=ExpIndex-1;195.always@(posedgeclk)beginOmegaA<=(OmegaIR[0]^OmegaIR[1])^(OmegaIR[2]^OmegaIR[3])^(OmegaIR[4]^OmegaIR[5])^(OmegaIR[6]^OmegaIR[7])^(OmegaIR[8]^OmegaIR[9])^(OmegaIR[10]^OmegaIR[11])^(OmegaIR[12]^OmegaIR[13])^(OmegaIR[14]^OmegaIR[15]);DifLmdA<=DifLmdIR[0]^DifLmdIR[1]^DifLmdIR[2]^DifLmdIR[3];203.204.//计算：α^i*Ω(α^-i)wire[m-1:0]AlphaPower,OmegaAlpha;FF_Mul_ROmega_x_AlphaPower(.clk(clk),.A(OmegaA),.B(AlphaPower),.P(OmegaAlpha));211.//计算Ei=α^i*Ω(α^-i)/Λ'(α^-i)-i)wire[m-1:0]InvDifLmdA;FF_Mul_ROmegaAlpha_x_InvDifC(.clk(clk),.A(OmegaAlpha),.B(InvDifLmdA),.P(ErrorValue));//InversionofΛ'(α^-i)rom_inv DifC_Inv(.clock(clk),.address(DifLmdA),.q(InvDifLmdA));//查表求α^i的幂rom_powerlpha_Power(.clock(clk),.address(ExpIndex),.q(AlphaPower));223.224.endmodule对程序说明如下：下面的VerilogHDL代码实现了Chien搜索功能。1. //******************************************2. // Chien搜索模块3. //******************************************4.moduleChienSearch(clk,init,5.Lmd0,Lmd1,Lmd2,Lmd3,Lmd4,Lmd5,Lmd6,Lmd7,Lmd8,6.Err_Indicator);7.8.9.

Lmd8;

parameter t=8,N=204,m=8,Delay_Length=18;input clk,init;input[m-1:0] Lmd0,Lmd1,Lmd2,Lmd3,Lmd4,Lmd5,Lmd6,Lmd7,output Err_Indicator;reg Err_Indicator;reg[m-1:0] LmdIR[t:0]; //迭代寄存wire[m-1:0] LmdIR_a[t:1],a52Lmd[t:1];always@(posedgeclk)begin:CHEIN_SEARCHintegerj;if(init)beginfor(j=1;j<=t;j=j+1)LmdIR[j]<=a52Lmd[j];LmdIR[0]<=Lmd0;endelsebeginfor(j=1;j<=t;j=j+1)LmdIR[j]<=LmdIR_a[j];LmdIR[0]<=LmdIR[0];endendff_const_mulLmdIR_x_a1(.din(LmdIR[1]),.dout(LmdIR_a[1]));//LmdIR1*a^1ff_const_mulLmdIR_x_a2(.din(LmdIR[2]),.dout(LmdIR_a[2]));//LmdIR2*a^2ff_const_mulLmdIR_x_a3(.din(LmdIR[3]),.dout(LmdIR_a[3]));//LmdIR3*a^3ff_const_mulLmdIR_x_a4(.din(LmdIR[4]),.dout(LmdIR_a[4]));//LmdIR4*a^