%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（1n-i+1）=1;
????else
????????error（1n-i+1）=0;
????end
end

found?=?find（error（1:）~=0）
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?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????3201??2005-12-12?22:02??rs.m

?????文件???????2549??2005-12-12?22:01??bch.m

?????文件?????352521??2008-04-11?21:21??BCH（31，16）、CRC-32與交織碼級聯的實現及分析.pdf

-----------?---------??----------?-----??----

???????????????358489????????????????????4