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下面是使用matlab实现关于Raptor 码解码成功率的仿真代码，并绘制成功率随编码符号数量变化的图形示例。代码中包含了 Raptor 码的预编码（使用稀疏矩阵乘法模拟）、LT 编码、解码过程，以及解码成功率的计算和绘图。
具体代码如下：

% 参数设置
num_source_symbols = 100; % 源符号数量
min_num_encoded_symbols = 100; % 最小编码符号数量
max_num_encoded_symbols = 200; % 最大编码符号数量
step_num_encoded_symbols = 10; % 编码符号数量步长
num_trials = 100; % 每个编码符号数量下的试验次数
degree_distribution = 'robust_soliton'; % 使用鲁棒孤子分布% 预定义数组存储结果
success_rates = zeros((max_num_encoded_symbols - min_num_encoded_symbols) / step_num_encoded_symbols + 1, 1);
num_encoded_symbols_vec = min_num_encoded_symbols:step_num_encoded_symbols:max_num_encoded_symbols;for idx = 1:length(num_encoded_symbols_vec)num_encoded_symbols = num_encoded_symbols_vec(idx);num_success = 0;for trial = 1:num_trials% 生成随机源符号source_symbols = randi([0, 1], num_source_symbols, 1);% Raptor码预编码（简单示例，使用稀疏矩阵乘法）precoding_matrix = sprand(num_source_symbols, num_source_symbols, 0.1); % 稀疏矩阵示例precoded_symbols = mod(precoding_matrix * source_symbols, 2);% Raptor码LT编码部分[raptor_encoded_symbols, raptor_encoding_graph] = lt_encode(precoded_symbols, num_encoded_symbols, degree_distribution);% 假设接收端接收到足够多的编码包（这里不模拟丢包）received_raptor_symbols = raptor_encoded_symbols;% Raptor码解码raptor_decoded_symbols = raptor_decode(received_raptor_symbols, raptor_encoding_graph, precoding_matrix);% 检查是否成功解码if all(raptor_decoded_symbols == source_symbols)num_success = num_success + 1;endendsuccess_rates(idx) = num_success / num_trials;
end% 绘制解码成功率随编码符号数量变化的图形
figure;
plot(num_encoded_symbols_vec, success_rates, 'b-o');
xlabel('编码符号数量');
ylabel('解码成功率');
title('Raptor码解码成功率随编码符号数量的变化');
grid on;% LT码编码函数
function [encoded_symbols, encoding_graph] = lt_encode(source_symbols, num_encoded_symbols, degree_distribution)num_source = size(source_symbols, 1);encoded_symbols = zeros(num_encoded_symbols, 1);encoding_graph = cell(num_encoded_symbols, 1); % 使用cell数组存储每个编码符号对应的源符号索引for i = 1:num_encoded_symbols% 根据度分布选择度if strcmp(degree_distribution, 'robust_soliton')degree = robust_soliton_degree(num_source);elseerror('不支持的度分布函数');end% 随机选择源符号进行异或运算生成编码符号selected_indices = randperm(num_source, degree);encoded_symbols(i) = mod(sum(source_symbols(selected_indices)), 2);encoding_graph{i} = selected_indices;end
end% Raptor码解码函数
function decoded_symbols = raptor_decode(encoded_symbols, encoding_graph, precoding_matrix)num_encoded = numel(encoded_symbols);num_source = size(precoding_matrix, 1);precoded_decoded_symbols = zeros(num_source, 1);known_indices = [];% 先进行LT码部分的解码[precoded_decoded_symbols, ~] = lt_decode(encoded_symbols, encoding_graph);% 再通过预编码矩阵恢复原始源符号decoded_symbols = mod(precoding_matrix' * precoded_decoded_symbols, 2);
end% LT码解码函数
function [decoded_symbols, decoding_complexity] = lt_decode(encoded_symbols, encoding_graph)num_encoded = numel(encoded_symbols);num_source = 0;for i = 1:num_encodednum_source = max(num_source, max(encoding_graph{i}));enddecoded_symbols = zeros(num_source, 1);known_indices = [];decoding_complexity = 0;degree_count = zeros(num_encoded, 1); % 记录每个编码符号的度% 初始化每个编码符号的度for i = 1:num_encodeddegree_count(i) = numel(encoding_graph{i});end% 迭代解码while true% 寻找度为1的编码符号degree_one_indices = find(degree_count == 1);if isempty(degree_one_indices)break;endfor k = degree_one_indices% 找到对应的源符号索引source_index = encoding_graph{k}(1);decoded_symbols(source_index) = encoded_symbols(k);known_indices = [known_indices; source_index];% 更新其他编码符号的度for j = 1:num_encodedif any(ismember(encoding_graph{j}, source_index))degree_count(j) = degree_count(j) - 1;encoding_graph{j}(ismember(encoding_graph{j}, source_index)) = [];decoding_complexity = decoding_complexity + 1; % 统计异或操作次数endendencoded_symbols(k) = 0;degree_count(k) = 0;endend
end% 鲁棒孤子度分布函数
function degree = robust_soliton_degree(num_symbols)c = 0.01; % 控制参数delta = 0.01; % 控制参数M = num_symbols;% 计算rho函数rho = @(d) 1 / (d * (d + 1));tau = @(d) zeros(size(d));for d = 1:Mif d <= floor(M^(1/3))tau(d) = 1 / (d * M^(1/3));elseif d <= Mtau(d) = 1 / (d * (d - 1));endend% 计算mu函数mu = @(d) (rho(d) + tau(d)) / sum(rho(1:M) + tau(1:M));% 按照mu函数选择度degree = randsample(1:M, 1, true, mu(1:M));
end