RiBM.m

%BCH decoder using RiBM and Chien search
close all; clear all;

%parameter
m=5;
n=2^m-1;
t=1;
k=2^m-1-m*t;

%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=gf(zeros(1, n), 1);

%error injection, location
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;

%%%%%%%%%%%%%%%%%%%%%%%%%%%
%RiBM algorithm
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%init
max = 3*t+1;
k = 0;
gamma = one;
theta = gf(zeros(1, max), m);           %3*t+1
delta = gf(zeros(1, max+1), m);         %3*t+2
theta(1:2*t) = syndrome;                %2*t
delta(1:2*t) = syndrome;
theta(max) = one;
delta(max) = one;

for r=1:2*t,            
    delta_o = delta;            
        
    %step1
    delta(1:max) = gamma*delta(2:max+1)-delta(1)*theta;

    %step2
    if((delta_o(1) ~= zero) && (k>=0))
        theta = delta_o(2:max+1);
        gamma = delta_o(1);
        k=-k-1;
    else
        theta = theta;
        gamma = gamma;
        k=k+1;
    end          
end

%lambda
lambda = delta(t+1:2*t+1);

%inverstable
inverse_tb = gf(zeros(1, t+1), m);
for i=1:t+1,
    inverse_tb(i) = alpha^(-i+1);
end;

%%%%%%%%%%%%%%%%%%%%%%%%%%%
%chien's search
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%note: no fail detection
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)