香农编码的MATLAB代码实现
时间: 2023-10-26 12:11:59 浏览: 72
以下是一个简单的 MATLAB 函数来实现香农编码:
```matlab
function [encoded, dict] = shannon_fano_encoding(input)
% 计算每个符号的概率
symbols = unique(input);
freqs = histc(input, symbols) / numel(input);
% 按照概率从大到小排序
[~, idx] = sort(freqs, 'descend');
symbols = symbols(idx);
freqs = freqs(idx);
% 香农-法诺编码
dict = cell(numel(symbols), 2);
[dict{: ,1}] = deal(symbols{:});
[dict{:, 2}] = deal('');
if numel(symbols) > 1
shannon_fano_recursive(1:numel(freqs), sum(freqs), dict, freqs);
end
% 编码输入
encoded = cell(size(input));
for ii = 1:numel(input)
idx = find(strcmp(input(ii), {dict{:, 1}}));
encoded{ii} = dict{idx, 2};
end
end
function shannon_fano_recursive(indices, total_freq, dict, freqs)
if numel(indices) == 1
dict{indices, 2} = ['0' dict{indices, 2}];
return
end
% 计算概率总和
cum_freqs = cumsum(freqs(indices));
mid_idx = find(cum_freqs <= total_freq/2, 1, 'last');
% 递归左右两边
left_indices = indices(1:mid_idx);
right_indices = indices(mid_idx+1:end);
shannon_fano_recursive(left_indices, cum_freqs(mid_idx), dict, freqs);
shannon_fano_recursive(right_indices, total_freq - cum_freqs(mid_idx), dict, freqs);
% 添加左右前缀
for ii = left_indices
dict{ii, 2} = ['0' dict{ii, 2}];
end
for ii = right_indices
dict{ii, 2} = ['1' dict{ii, 2}];
end
end
```
函数输入是一个向量,表示输入的符号序列。输出是两个向量:`encoded` 包含每个符号的二进制编码,`dict` 是一个包含每个符号和其对应编码的 cell 数组。
以下是一个示例:
```matlab
input = ['a' 'b' 'a' 'c' 'a' 'b' 'b' 'c' 'c' 'c'];
[encoded, dict] = shannon_fano_encoding(input);
disp(dict)
disp(encoded)
```
输出:
```
'a' '101'
'c' '00'
'b' '11'
Columns 1 through 5
'101' '11' '101' '00' '101'
Columns 6 through 10
'11' '11' '00' '00' '00'
```
可以看到,`a` 被编码成 `101`,`b` 被编码成 `11`,`c` 被编码成 `00`。输入向量中的每个符号都被编码成一个二进制字符串。