费诺编码matlab代码

以下是一个简单的 MATLAB 实现费诺编码的代码：

function [codebook, avglen] = fano(p)
% FANO  Fano codebook for a given probability mass function.
%   Given a probability mass function p, return a Fano codebook.
%   The codebook is represented as a cell array of strings, where
%   codebook{i} is the binary codeword for the symbol with probability
%   p(i). Also return the average codeword length.

n = length(p);
codebook = cell(n, 1);
avglen = 0;

% Sort the symbols in decreasing order of probability.
[sp, si] = sort(p, 'descend');

% Divide the symbols into two groups, each with roughly equal probability.
q = cumsum(sp);
k = find(q >= 0.5, 1);

% Recursively generate the codebook for each group.
if k > 1
    [codebook1, avlen1] = fano(sp(1:k-1));
    for i = 1:k-1
        codebook{i} = ['0' codebook1{i}];
    end
    avglen = avglen + (q(k-1) - 0) * avlen1;
end
if k < n
    [codebook2, avlen2] = fano(sp(k:n));
    for i = k:n
        codebook{si(i)} = ['1' codebook2{i-k+1}];
    end
    avglen = avglen + (q(n) - q(k-1)) * avlen2;
end
end

在这个实现中，我们首先将符号按概率从大到小排序，然后将它们分成两组，每组的概率尽量相等。然后，我们递归地生成每个组的编码，并将它们合并成整个代码本。在合并过程中，我们使用每个组的概率加权平均编码长度来计算平均编码长度。注意，这个实现中没有使用符号的频率来计算编码长度，而是使用每个组的概率加权平均。