BCH和RS码的编译码程序

close all; clear all; %reed-solomon decoder simulation %by:yumi m=8; %number of bits each symbol n=2^m-1; %code length t=8; %error correction ability k=n-2*t; %information length pp = 301; %primitive polynomial msg = gf([1:k], m, pp); code = rsenc(msg, n, k); %code = gf(zeros(1, n), m, pp); alpha = gf(2, m, pp); zero = gf(0, m, pp); one = gf(1, m, pp); %reccode=zeros(1, n); %reccode(7) = 5; %reccode(5) = 2; %reccode(2) = 11; %generate integers between reccode=zeros(1, n); reccode(1:8)=255; %reccode(1)=255; %reccode(2)=2; %reccode(3)=3; %reccode(15)=72; %reccode(20)=57; %reccode(32)=135; %reccode(90)=172; %reccode(156)=145; %reccode(170)=74; %reccode(255)=255; reccode = gf(reccode, m, pp); reccode = code + reccode; %functional simulation of decoding %creating alpha array alpha_tb=gf(zeros(1, 2*t), m, pp); for i=1:2*t; alpha_tb(i)=alpha^i; end; %syndrome syndrome_o = gf(zeros(1, 2*t), m, pp); syndrome = gf(zeros(1, 2*t), m, pp); for i = 1:n, syndrome_o = syndrome_o.*alpha_tb +reccode(i); cat = 1; end; %reverse s(2t-1)...s(0) for i=1:2*t, syndrome(i)=syndrome_o(2*t+1-i); end; %ibma lamda = gf([1, zeros(1, t)], m, pp); lamda0 = gf([1, zeros(1, t)], m, pp); b = gf([0, 1, zeros(1, t)], m, pp); k = 0; gamma = one; delta = zero; syndrome_array1 = gf(zeros(1, t+1), m, pp); for r = 1:2*t, %step 1: r1 = 2*t-r+1; r2 = min(r1+t, 2*t); num = r2-r1+1; syndrome_array1(1:num) = syndrome(r1:r2); delta = syndrome_array1*lamda'; %step 2: lamda0 = lamda; lamda = gamma*lamda-delta*b(1:t+1); %step 3: if((delta ~= zero) && (k>=0)) b(2:2+t)=lamda0; gamma = delta; k=-k-1; else b(2:2+t) = b(1:t+1); gamma = gamma; k=k+1; end mini=1; end omega = gf(zeros(1, t), m, pp); syndrome_array2 = gf(zeros(1, t), m, pp); for i= 1:t, i1 = 2*t-i+1; syndrome_array2(1:i) = syndrome(i1: 2*t); omega(i) = syndrome_array2*lamda(1:t)'; end; %chien search algorithm and forney algorithm in paralle %seperate the even and the odd parts of lamda and omega even=floor(t/2)*2; if(even==t) odd=t-1; else odd=t; end %lamda_even=lamda(1:2:even+1); %lamda_odd=lamda(2:2:odd+1); %inverstable inverse_tb = gf(zeros(1, t+1), m, pp); for i=1:t+1, inverse_tb(i) = alpha^(-i+1); end; %inverse_omega=inverse_tb(1:t); %iteratively compute omega and lamda_v=gf(0, m, pp); lamda_ov=gf(0, m, pp); omega_v=gf(0, m, pp); accu_tb=gf(ones(1, t+1), m,pp); accu_tb1=gf(ones(1, t), m, pp); for i=1:n, root=alpha^(1-i); lamda_v=lamda*accu_tb'; lamda_ov=lamda(2:2:odd+1)*accu_tb(2:2:odd+1)'; omega_v=omega*accu_tb1'; accu_tb=accu_tb.*inverse_tb; accu_tb1=accu_tb1.*inverse_tb(1:t); if(lamda_v==zero) error(1,n-i+1)=1; ev=(omega_v/lamda_ov)*root; evv=ev.x; error(2, n-i+1)=double(evv); else error(1, n-i+1)=0; error(2, n-i+1)=0; end kk=1; end found = find(error(1,:)~=0) error(2, found)