下面是使用matlab實現關于Raptor 碼解碼成功率的仿真代碼，并繪制成功率隨編碼符號數量變化的圖形示例。代碼中包含了 Raptor 碼的預編碼（使用稀疏矩陣乘法模擬）、LT 編碼、解碼過程，以及解碼成功率的計算和繪圖。
具體代碼如下：

% 參數設置
num_source_symbols = 100; % 源符號數量
min_num_encoded_symbols = 100; % 最小編碼符號數量
max_num_encoded_symbols = 200; % 最大編碼符號數量
step_num_encoded_symbols = 10; % 編碼符號數量步長
num_trials = 100; % 每個編碼符號數量下的試驗次數
degree_distribution = 'robust_soliton'; % 使用魯棒孤子分布% 預定義數組存儲結果
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% 生成隨機源符號source_symbols = randi([0, 1], num_source_symbols, 1);% Raptor碼預編碼（簡單示例，使用稀疏矩陣乘法）precoding_matrix = sprand(num_source_symbols, num_source_symbols, 0.1); % 稀疏矩陣示例precoded_symbols = mod(precoding_matrix * source_symbols, 2);% Raptor碼LT編碼部分[raptor_encoded_symbols, raptor_encoding_graph] = lt_encode(precoded_symbols, num_encoded_symbols, degree_distribution);% 假設接收端接收到足夠多的編碼包（這里不模擬丟包）received_raptor_symbols = raptor_encoded_symbols;% Raptor碼解碼raptor_decoded_symbols = raptor_decode(received_raptor_symbols, raptor_encoding_graph, precoding_matrix);% 檢查是否成功解碼if all(raptor_decoded_symbols == source_symbols)num_success = num_success + 1;endendsuccess_rates(idx) = num_success / num_trials;
end% 繪制解碼成功率隨編碼符號數量變化的圖形
figure;
plot(num_encoded_symbols_vec, success_rates, 'b-o');
xlabel('編碼符號數量');
ylabel('解碼成功率');
title('Raptor碼解碼成功率隨編碼符號數量的變化');
grid on;% LT碼編碼函數
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數組存儲每個編碼符號對應的源符號索引for i = 1:num_encoded_symbols% 根據度分布選擇度if strcmp(degree_distribution, 'robust_soliton')degree = robust_soliton_degree(num_source);elseerror('不支持的度分布函數');end% 隨機選擇源符號進行異或運算生成編碼符號selected_indices = randperm(num_source, degree);encoded_symbols(i) = mod(sum(source_symbols(selected_indices)), 2);encoding_graph{i} = selected_indices;end
end% Raptor碼解碼函數
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 = [];% 先進行LT碼部分的解碼[precoded_decoded_symbols, ~] = lt_decode(encoded_symbols, encoding_graph);% 再通過預編碼矩陣恢復原始源符號decoded_symbols = mod(precoding_matrix' * precoded_decoded_symbols, 2);
end% LT碼解碼函數
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); % 記錄每個編碼符號的度% 初始化每個編碼符號的度for i = 1:num_encodeddegree_count(i) = numel(encoding_graph{i});end% 迭代解碼while true% 尋找度為1的編碼符號degree_one_indices = find(degree_count == 1);if isempty(degree_one_indices)break;endfor k = degree_one_indices% 找到對應的源符號索引source_index = encoding_graph{k}(1);decoded_symbols(source_index) = encoded_symbols(k);known_indices = [known_indices; source_index];% 更新其他編碼符號的度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; % 統計異或操作次數endendencoded_symbols(k) = 0;degree_count(k) = 0;endend
end% 魯棒孤子度分布函數
function degree = robust_soliton_degree(num_symbols)c = 0.01; % 控制參數delta = 0.01; % 控制參數M = num_symbols;% 計算rho函數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% 計算mu函數mu = @(d) (rho(d) + tau(d)) / sum(rho(1:M) + tau(1:M));% 按照mu函數選擇度degree = randsample(1:M, 1, true, mu(1:M));
end