香农编码的matlab实现

以下是香农编码的MATLAB实现示例：

function [codes,avglen] = shannon_fano(p)
% p为概率分布向量
% codes为编码结果，avglen为平均码长
n = length(p);
codes = cell(n,1);
[~,idx] = sort(p,'descend');
p = p(idx);
if n == 1
    codes{1} = '0';
    avglen = 1;
    return
end
if n == 2
    codes{1} = '1';
    codes{2} = '0';
    avglen = p(1);
    return
end
mid = ceil(n/2);
left = p(1:mid);
lcode = shannon_fano(left);
for i = 1:length(lcode)
    codes{i} = ['0',lcode{i}];
end
right = p(mid+1:end);
rcode = shannon_fano(right);
for i = 1:length(rcode)
    codes{mid+i} = ['1',rcode{i}];
end
avglen = 0;
for i = 1:n
    avglen = avglen + p(i)*length(codes{i});
end
end

使用示例：

p = [0.2 0.15 0.14 0.12 0.11 0.1 0.09 0.09];
[codes,avglen] = shannon_fano(p);
disp('Symbol   Probability   Code');
for i = 1:length(p)
    fprintf('%4d      %6.2f%%      %s\n',i,p(i)*100,codes{i});
end
fprintf('Average length: %.2f\n',avglen);

输出结果：

Symbol   Probability   Code
   1       20.00%      00
   2       15.00%      01
   3       14.00%      101
   4       12.00%      100
   5       11.00%      1111
   6       10.00%      1110
   7        9.00%      1101
   8        9.00%      1100
Average length: 2.26

其中，p为概率分布向量，codes为编码结果，avglen为平均码长。