%bch decoder using Berlekamp-Massey and Chien search
%standard bch decoder simulation
%by: yumi
%10/21/2005
close all; clear all;
m=12;
n=2^m-1;
t=2;
k=2^m-1-m*t;
simplified = 1;
%the constants used in the algorithm
alpha = gf(2, m);
zero = gf(0, m);
one = gf(1, m);
%since all zero is always a codeword, only have to specify the error
%code = zeros(1, n);
code=gf(zeros(1, n), 1);
code(1)=gf(1, 1);
code(2)=gf(1, 1);
codev = code.x;
reccode=gf(codev, m);
%creating alpha array
%note that syndrome should be in the order [s3, s2, s1, s0]
alpha_tb=gf(zeros(1, 2*t), m);
for i=1:2*t,
alpha_tb(i)=alpha^(2*t-i+1);
end;
%syndrome generation
syndrome=gf(zeros(1, 2*t), m);
for i=1:n,
syndrome=syndrome.*alpha_tb+reccode(i);
end;
%imba
lambda = gf([1, zeros(1, t)], m);
lambda0= lambda;
b=gf([0, 1, zeros(1, t)], m);
b2 = gf([0, 0, 1, zeros(1, t)], m);
k=0;
gamma = one;
delta = zero;
syndrome_array = gf(zeros(1, t+1), m);
if(simplified == 1)
for r=1:t,
r1 = 2*t-2*r+2;
r2 = min(r1+t, 2*t);
num = r2-r1+1;
syndrome_array(1: num) = syndrome(r1:r2);
delta = syndrome_array*lambda';
lambda0 = lambda;
lambda = gamma*lambda-delta*b2(2:t+2);
if((delta~= zero) && (k>=0))
b2(3)=zero;
b2(4:3+t) = lambda0(1:t);
gamma = delta;
k = -k;
else
b2(3:3+t) = b2(1:t+1);
gamma = gamma;
k=k+2;
end
joke=1;
end
else
for r=1:2*t,
r1 = 2*t-r+1;
r2 = min(r1+t, 2*t);
num = r2-r1+1;
syndrome_array(1:num) = syndrome(r1:r2);
delta = syndrome_array*lambda';
lambda0 = lambda;
lambda = gamma*lambda-delta*b(1:t+1);
if((delta ~= zero) && (k>=0))
b(2:2+t)=lambda0;
gamma = delta;
k=-k-1;
else
b(2:2+t) = b(1:t+1);
gamma = gamma;
k=k+1;
end
joke=1;
end
end
%inverstable
inverse_tb = gf(zeros(1, t+1), m);
for i=1:t+1,
inverse_tb(i) = alpha^(-i+1);
end;
%chien's search
lambda_v = zero;
accu_tb=gf(ones(1, t+1), m);
for i=1:n,
lambda_v=lambda*accu_tb';
accu_tb = accu_tb.*inverse_tb;
if(lambda_v==zero)
error(1,n-i+1)=1;
else
error(1,n-i+1)=0;
end
end
found = find(error(1,:)~=0)
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