用matlab编写完整turbo编码

以下是一个基本的 MATLAB 实现 Turbo 编码的示例：

% 初始化参数
N = 1000;                 % 数据序列长度
K = 500;                  % 信息位长度
R = K / N;                % 编码速率
numIter = 4;              % 迭代次数
EsNo = 5;                 % 信噪比
noiseVar = 10^(-EsNo/10); % 噪声方差
numStates = 2^(K-1);      % 状态数
numTransitions = 3*K;     % 转移数

% 生成随机序列
data = randi([0 1], K, 1);

% 生成码字
encData = turbo_encoding(data);

% 添加高斯白噪声
noise = sqrt(noiseVar) * randn(size(encData));
rxData = encData + noise;

% 迭代译码
decodedData = turbo_decoding(rxData, numIter);

% 计算误比特率
ber = sum(xor(data, decodedData)) / K;

% 显示结果
fprintf('编码速率: %.2f\n', R);
fprintf('误比特率: %.2e\n', ber);

function encData = turbo_encoding(data)
    % 初始化编码器
    trellis = poly2trellis(4, [13 15], 13);
    interleaver = randperm(length(data));
    state = 0;
    nextStates = zeros(numStates, 2);
    outputs = zeros(numStates, 2);
    for i = 1:numStates
        [nextStates(i,:), outputs(i,:)] = ...
            convenc(dec2binvec(i-1, K-1), trellis);
    end
    
    % 编码
    c1 = zeros(K, 1);
    c2 = zeros(K, 1);
    for i = 1:N
        % 输入数据
        if i <= K
            c1(i) = data(i);
        else
            c1(i) = xor(c2(i-1), data(i));
        end
        
        % 第一条分支
        nextState1 = nextStates(state*2+1,:);
        output1 = outputs(state*2+1,:);
        for j = 1:2
            c1p(j) = xor(c1(i), output1(j));
            c2p(j) = xor(c2(i-1), output1(j));
        end
        [maxMetric1, idx1] = max(abs(c1p + c2p));
        c1(i) = c1p(idx1);
        c2(i) = c2p(idx1);
        state = nextState1(idx1);
        
        % 第二条分支
        nextState2 = nextStates(state*2+2,:);
        output2 = outputs(state*2+2,:);
        for j = 1:2
            c1p(j) = xor(c1(i), output2(j));
            c2p(j) = xor(c2(i-1), output2(j));
        end
        [maxMetric2, idx2] = max(abs(c1p + c2p));
        c1(i) = c1p(idx2);
        c2(i) = c2p(idx2);
        state = nextState2(idx2);
        
        % 交织
        c1(i) = c1(interleaver(i));
        c2(i) = c2(interleaver(i));
    end
    
    % 输出码字
    encData = [data; c1; c2];
end

function decodedData = turbo_decoding(rxData, numIter)
    % 初始化译码器
    trellis = poly2trellis(4, [13 15], 13);
    interleaver = randperm(length(rxData));
    state = 0;
    nextStates = zeros(numStates, 2);
    outputs = zeros(numStates, 2);
    for i = 1:numStates
        [nextStates(i,:), outputs(i,:)] = ...
            convenc(dec2binvec(i-1, K-1), trellis);
    end
    Lc = 2*rxData / noiseVar;
    Lc(isnan(Lc)) = 0;
    
    % 迭代译码
    L1 = zeros(K, numIter);
    L2 = zeros(K, numIter);
    for iter = 1:numIter
        % 第一次译码
        [L1(:,iter), L2(:,iter), state] = ...
            turbo_decode_iteration(Lc, interleaver, state, ...
            nextStates, outputs, numTransitions);
        
        % 反交织
        L1(:,iter) = L1(interleaver,iter);
        L2(:,iter) = L2(interleaver,iter);
        
        % 第二次译码
        [L2(:,iter), L1(:,iter), state] = ...
            turbo_decode_iteration(L2(:,iter), interleaver, state, ...
            nextStates, outputs, numTransitions);
        
        % 反交织
        L1(:,iter) = L1(interleaver,iter);
        L2(:,iter) = L2(interleaver,iter);
    end
    
    % 计算后验概率
    L = L1 + L2;
    p0 = exp(L) ./ (1 + exp(L));
    p1 = 1 ./ (1 + exp(L));
    
    % 译码
    decodedData = (p1 > 0.5);
end

function [L1p, L2p, statep] = turbo_decode_iteration(Lc, interleaver, ...
    state, nextStates, outputs, numTransitions)
    % 初始化
    L1p = -inf(K, 1);
    L2p = -inf(K, 1);
    statep = zeros(K, 1);
    alpha = zeros(numStates, 1);
    beta = zeros(numStates, 1);
    gamma = zeros(numStates, 2);
    
    % 正交路径译码
    for i = 1:N
        % 输入数据
        if i <= K
            L1p(i) = Lc(i);
            L2p(i) = Lc(i);
        else
            L1p(i) = Lc(i) + L2p(i-1);
            L2p(i) = Lc(i) + L1p(i-1);
        end
        
        % 第一条分支
        nextState1 = nextStates(state*2+1,:);
        output1 = outputs(state*2+1,:);
        for j = 1:2
            alpha(nextState1(j)+1) = ...
                max(alpha(nextState1(j)+1), L1p(i) + log(output1(j)));
            gamma(nextState1(j)+1, j) = ...
                gamma(nextState1(j)+1, j) + beta(state+1) + ...
                L1p(i) + log(output1(j)) - alpha(nextState1(j)+1);
        end
        
        % 第二条分支
        nextState2 = nextStates(state*2+2,:);
        output2 = outputs(state*2+2,:);
        for j = 1:2
            beta(nextState2(j)+1) = ...
                max(beta(nextState2(j)+1), L2p(i) + log(output2(j)));
            gamma(nextState2(j)+1, j) = ...
                gamma(nextState2(j)+1, j) + alpha(state+1) + ...
                L2p(i) + log(output2(j)) - beta(nextState2(j)+1);
        end
        
        % 更新状态
        [maxMetric, idx] = max(gamma(:));
        [statep(i), inputIdx] = ind2sub(size(gamma), idx);
        statep(i) = statep(i) - 1;
        L1p(i) = alpha(statep(i)+1) + beta(statep(i)+1) - ...
            L1p(i) - log(output1(inputIdx)) + log(1 + exp(maxMetric));
        L2p(i) = alpha(statep(i)+1) + beta(statep(i)+1) - ...
            L2p(i) - log(output2(inputIdx)) + log(1 + exp(maxMetric));
        
        % 重置变量
        alpha(:) = -inf;
        beta(:) = -inf;
        gamma(:) = 0;
        state = statep(i);
    end
end

该实现使用了一个标准的 Turbo 编码器和译码器，其中编码器使用了一个 4 阶、多项式为 [13 15] 的递归卷积码，并且采用了一个随机的交织器。译码器使用了一个正交路径译码算法和一个迭代译码算法，迭代次数为 4 次。该实现输出编码速率和误比特率，并且可以通过调整参数来改变编码速率和信噪比。