function Turbo_Decoder

% 输入，信息位和校验位

t = [1 1 -1 1 1 -1 1 1 -1 1 1 1 -1 1 -1 -1];

U = [+0.213 -0.371 +0.139 +0.514 +0.539 -0.422 +1.533 +1.457 +0.323 +2.028 -0.414 +1.482 -1.701 -0.175 -0.862 -0.918];

C = [+0.364 0.000 +1.818 0.000 +0.388 0.000 +0.267 0.000 +1.103 0.000 +3.560 0.000 +0.893 0.000 -2.049 0.000];

C2= [ 0.000 -0.351 0.000 +1.646 0.000 -2.587 0.000 -1.678 0.000 -0.170 0.000 -1.003 0.000 -1.306 0.000 -0.492];

% 计算LLR(log-likelihood ratio)

% 认为信道为AWGN信道N(0,1.2)，即SNR = E/N0 = 1/(2*1.2^2)

sigma = 1.2;

Lu = log((1/sqrt(2*pi*sigma)*exp(-(U -1).^2/(2*sigma*sigma)))./(1/sqrt(2*pi*sigma)*exp(-(U +1).^2/(2*sigma*sigma))));

Lc = log((1/sqrt(2*pi*sigma)*exp(-(C -1).^2/(2*sigma*sigma)))./(1/sqrt(2*pi*sigma)*exp(-(C +1).^2/(2*sigma*sigma))));

Lc2 = log((1/sqrt(2*pi*sigma)*exp(-(C2-1).^2/(2*sigma*sigma)))./(1/sqrt(2*pi*sigma)*exp(-(C2+1).^2/(2*sigma*sigma))));

% 初始化外信息为0

Lu_ex = zeros(1,length(U));

% 循环迭代

for m =1:4

Lu1 = Lu + Lu_ex;

Lu_ex = Turbo_BCJR(Lu1,Lc,0);

%Lu_ex = Lu_new-Lu1;

Lu2 = Lu + Lu_ex;

Lu_est = Lu2;

Lu2 = Turbo_Interleaver(Lu2);

Lu_ex = Turbo_BCJR(Lu2,Lc2,0);

%Lu_ex = Lu_new-Lu2;

Lu_ex = Turbo_Interleaver(Lu_ex);

Lu_est = Lu_est + Lu_ex;

d = sign(Lu_est);

fprintf('Iteration %d, BER: %d\n',m,sum(abs(d-t))/2);

end

end

function [out] = Turbo_Interleaver(in)

out = reshape(reshape(in,4,4)',1,16);

end

function [Le] = Turbo_BCJR(Lu, Lc,end_s)

FRAME_LENGTH = length(Lu);

% 计算分支度量(bench metric),就是分别计算在时刻i各个输出的概率

m11 = (Lu+Lc)/2;

m10 = (Lu-Lc)/2;

% 计算前向状态度量(forawrd state metric):

alpha = zeros(1,(FRAME_LENGTH+2)*4);

alpha(1:4) = -1000*ones(1,4);

alpha(1) = 0;

for k=1:FRAME_LENGTH

m_t = alpha((k-1)*4+0+1) - m11(k-1+1);

m_b = alpha((k-1)*4+2+1) + m11(k-1+1);

alpha(k*4+0+1) = log(exp(m_t)+exp(m_b));

m_t = alpha((k-1)*4+0+1) + m11(k-1+1);

m_b = alpha((k-1)*4+2+1) - m11(k-1+1);

alpha(k*4+1+1) = log(exp(m_t)+exp(m_b));

m_t = alpha((k-1)*4+1+1) - m10(k-1+1);

m_b = alpha((k-1)*4+3+1) + m10(k-1+1);

alpha(k*4+2+1) = log(exp(m_t)+exp(m_b));

m_t = alpha((k-1)*4+1+1) + m10(k-1+1);

m_b = alpha((k-1)*4+3+1) - m10(k-1+1);

alpha(k*4+3+1) = log(exp(m_t)+exp(m_b));

end

% 计算后向状态度量(backward state metris)

beta = zeros(1,(FRAME_LENGTH+2)*4);

beta((FRAME_LENGTH)*4+0+1:(FRAME_LENGTH)*4+0+4) = -1000*ones(1,4);

beta((FRAME_LENGTH)*4+end_s+1) = 0;

for k=FRAME_LENGTH-1:-1:0

m_t = beta((k+1)*4+0+1) - m11(k+1);

m_b = beta((k+1)*4+1+1) + m11(k+1);

beta(k*4+0+1) = log(exp(m_t)+exp(m_b));

m_t = beta((k+1)*4+2+1) - m10(k+1);

m_b = beta((k+1)*4+3+1) + m10(k+1);

beta(k*4+1+1) = log(exp(m_t)+exp(m_b));

m_t = beta((k+1)*4+0+1) + m11(k+1);

m_b = beta((k+1)*4+1+1) - m11(k+1);

beta(k*4+2+1) = log(exp(m_t)+exp(m_b));

m_t = beta((k+1)*4+2+1) + m10(k+1);

m_b = beta((k+1)*4+3+1) - m10(k+1);

beta(k*4+3+1) = log(exp(m_t)+exp(m_b));

end

% 计算在输入Y(1:n)的情况下，状态i-1为u',状态i为u的联合概率

Lnew = zeros(1,length(FRAME_LENGTH));

for k = 1:FRAME_LENGTH

enumerator = 0;

denominator = 0;

t_d = alpha((k-1)*4+0+1) + beta(k*4+0+1) - m11(k-1+1);

denominator = denominator + exp(t_d);

t_e = alpha((k-1)*4+0+1) + beta(k*4+1+1) + m11(k-1+1);

enumerator = enumerator + exp(t_e);

t_d = alpha((k-1)*4+1+1) + beta(k*4+2+1) - m10(k-1+1);

denominator = denominator + exp(t_d);

t_e = alpha((k-1)*4+1+1) + beta(k*4+3+1) + m10(k-1+1);

enumerator = enumerator + exp(t_e);

t_d = alpha((k-1)*4+2+1) + beta(k*4+1+1) - m11(k-1+1);

denominator = denominator + exp(t_d);

t_e = alpha((k-1)*4+2+1) + beta(k*4+0+1) + m11(k-1+1);

enumerator = enumerator + exp(t_e);

t_d = alpha((k-1)*4+3+1) + beta(k*4+3+1) - m10(k-1+1);

denominator = denominator + exp(t_d);

t_e = alpha((k-1)*4+3+1) + beta(k*4+2+1) + m10(k-1+1);

enumerator = enumerator + exp(t_e);

Lnew(k) = log(enumerator/denominator);

end

Le = Lnew - Lu;

end

This license applies to everything in the package, except where otherwise noted.

This software is provided 'as-is', without any express or implied warranty. In no event will the authors be held liable for any damages arising from the use of this software.

Permission is granted to anyone to use this software for any purpose, including commercial applications, and to alter it and redistribute it freely, subject to the following restrictions:

1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.

2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.

3. This notice may not be removed or altered from any source distribution.

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Written by Benben Qiao 2008

参考： [1].

http://www.feiyilin.com/bcjr.html