how to get average length of third order extension huffman codewords in matlab

To calculate the average length of third order extension Huffman codewords in MATLAB, you can follow these steps:

1. Generate the Huffman codebook for your input data using the 'huffmandict' function. For the third order extension, you may need a modified version of the 'huffmandict' function that takes into account the third-order dependency between symbols. Example:

   main.m
   % Code to generate Huffman codebook
   symbols = unique(input_data); % Replace input_data with your actual input data
   probabilities = calculate_probabilities(input_data); % Replace calculate_probabilities with the function that calculates the probability of each symbol
   codebook = huffmandict(symbols, probabilities);
   315 chars
   5 lines

2. Calculate the length of each codeword in the codebook. Example:

   main.m
   % Code to calculate codeword lengths
   codeword_lengths = cellfun(@length, codebook(:, 2));
   90 chars
   3 lines

3. Calculate the average length of the codewords. Example:

   main.m
   % Code to calculate average codeword length
   average_length = sum(probabilities .* codeword_lengths);
   101 chars
   3 lines

Remember to replace 'input_data' with your actual input data and 'calculate_probabilities' with the function that calculates the probability of each symbol.

Please note that the third order extension refers to considering the third-order dependency between symbols. Implementing this extension would require modifying the 'huffmandict' function to generate the codebook using the appropriate probability calculations.