Experiment No 1 Dce (Huffman Encoding)

 

EXPERIMENT NO. 1 NAME :Aditi Khot STD :TE EXTC A BATCH : A3 ROLL NO : 117A2051 AIM :

To Study Huffman Encoding Technique. 

CODE :

probabilities = [0.4 0.3 0.2 0.1];  % Normalise the probabilities  probabilities = probabilities/sum(probabilities); probabilities/sum(probabilities);  % For each probability...  for index  index = 1:length(probabilities)  for % ...create an empty codeword  codewords{index} = []  % Create a set containing only this codeword  set_contents{index} = index  % Store the probability associated with this set  set_probabilities(index) set_probabilities(inde x) = probabilities(index)  end  '-------------------------------------------------------------------------'); ) ;  disp('-------------------------------------------------------------------------' disp( disp('The disp( 'The sets of symbols and their probabilities are:' are:'))  for set_index  set_index = 1:length(set_probabilities)  for disp([num2str(set_probabilities(set_index)),' ', num2str(set_contents{set_index})])  end  % Keep going until all the sets have been merged into one  while length(set_contents) > 1  while length(set_contents) % Determine which sets have the t he lowest total probabilities  [temp, sorted_indices] = sort(set_probabilities) sort (set_probabilities)  % Get the set having the lowest probability  zero_set = set_contents{sorted_indices(1)}  % Get that probability zero_probability = set_probabilities(sorted_indices( set_probabilities(sorted_indices(1)) 1))  % For each codeword in the set...  for codeword_index for codeword_index = 1:length(zero_set)  % ...append a zero  codewords{zero_set(codeword_index)} = [codewords{zero_set(codeword_index)}, 0] end  % Get the set having the second lowest probability  one_set = set_contents{sorted_indices(2)}  % Get that probability one_probability = set_probabilities(sorted_indices(2)) set_probabilities(sorted_indices(2))  % For each codeword in the set...  for codeword_index  codeword_index = 1:length(one_set)  for % ...append a one  codewords{one_set(codeword_index)} codewords{one_set(codeword_in dex)} = [codewords{one_set(codeword_index)}, [codewords{one_set(codeword_index)}, 1] end 

 

disp('The symbols, their probabilities and the allocated bits are:'); disp('The are:');  % For each codeword...  for index for index = 1:length(codewords)  % ...display its bits  disp([num2str(index),'' ',num2str(probabilities(index)), disp([num2str(index), ,num2str(probabilities(index)),'' ',num2str(codewords{index})])  end  % Remove the two sets having the lowest probabilities...  set_contents(sorted_indices(1:2)) = []  % ...and merge them into a new set  set_contents{length(set_contents)+1} set_contents{length(set_contents)+ 1} = [zero_set, one_set]  % Remove the two lowest probabilities...  set_probabilities(sorted_indices(1:2)) set_probabilities(sorted_ indices(1:2)) = []  % ...and give their sum to the new set  set_probabilities(length(set_probabilities)+1) set_probabilities(length( set_probabilities)+1) = zero_probability + one_probability  disp('The disp( 'The sets and their probabilities are:' are:'))  for for set_index  set_index = 1:length(set_probabilities)  disp([num2str(set_probabilities(set_index)),' ', num2str(set_contents{set_index})])  end  end  '-------------------------------------------------------------------------'); ) ;  disp('-------------------------------------------------------------------------' disp( are:'); );  disp('The symbols, their probabilities and the allocated Huffman codewords are:' disp('The % For each codeword...  for index = 1:length(codewords)  for index % ...display its bits in reverse order  disp([num2str(index), ' ', num2str(probabilities(index)), num2str(probabilities(index)),'' ',num2str(codewords{index}(length(codewords{index}):-1:1))])  end  % Calculate the symbol entropy  entropy = sum(probabilities.*log2(1./probabilities)) sum(probabilities.*log2(1./probabilities))  % Calculate the average Huffman codeword length  av_length = 0  for for index  index = 1:length(codewords)  av_length = av_length + probabilities(index)*length(codewords{index})  end  disp(['The disp([ 'The symbol entropy is: ',num2str(entropy)])  'The average Huffman codeword length is: ',num2str(av_length)])  disp(['The disp([ 'The Huffman coding rate is: ',num2str(entropy/av_length)])  disp(['The disp([ OUTPUT :

>> kunalhuffman  codewords = [] [1x2 double] [1x3 double] [1x3 double] set_contents = [1] set_probabilities = 0.4000

 

codewords = [] [] [1x3 double] [1x3 double] set_contents = [1] [2] set_probabilities = 0.4000 0.3000 codewords = [] [] [] [1x3 double] set_contents = [1] [2] [3] set_probabilities = 0.4000 0.3000 0.2000 codewords = [] [] [] [] set_contents = [1] [2] [3] [4] set_probabilities = 0.4000 0.3000 0.2000 0.1000 The sets of symbols and their probabilities are: 0.4 1 0.3 2 0.2 3 0.1 4 temp = 0.1000 0.2000 0.3000 0.4000 sorted_indices = 4 3 2 1 zero_set = 4 zero_probability = 0.1000 codewords = [] [] [] [0] one_set = 3 one_probability = 0.2000 codewords = [] [] [1] [0] The symbols, their probabilities and the allocated bits are: 1 0.4 2 0.3 3 0.2 1 4 0.1 0 set_contents = [1] [2] set_contents = [1] [2] [1x2 double] set_probabilities =

 

0.4000 0.3000 set_probabilities = 0.4000 0.3000 0.3000 The sets and their probabilities are: 0.4 1 0.3 2 0.3 4 3 temp = 0.3000 0.3000 0.4000 sorted_indices = 2 3 1 zero_set = 2 zero_probability = 0.3000 codewords = [] [0] [1] [0] one_set = 4 3 one_probability = 0.3000 codewords = [] [0] [1] [1x2 double] codewords = [] [0] [1x2 double] [1x2 double] The symbols, their probabilities and the allocated bits are: 1 0.4 2 0.3 0 3 4

0.2 1 1 0.1 0 1

set_contents = [1]

set_contents = [1] [1x3 double] set_probabilities = 0.4000

set_probabilities = 0.4000 0.6000

 

  The sets and their probabilities are: 0.4 1 0.6 2 4 3 temp = 0.4000 0.6000 sorted_indices = 1 2 zero_set = 1 zero_probability = 0.4000 codewords = [0] [0] [1x2 double] [1x2 double] one_set = 2 4 3 one_probability = 0.6000 codewords = Columns 1 through 3 [0] [1x2 double] [1x2 double] Column 4 [1x2 double] codewords = Columns 1 through 3 [0] [1x2 double] [1x2 double] Column 4 [1x3 double] codewords = Columns 1 through 3 [0] [1x2 double] [1x3 double] Column 4 [1x3 double] The symbols, their probabilities and the allocated bits are: 1 0.4 0 2 0.3 0 1

 

3 4

0.2 1 1 1 0.1 0 1 1

set_contents = Empty cell array: 1-by-0 set_contents = [1x4 double] set_probabilities = Empty matrix: 1-by-0 set_probabilities = 1.0000 The sets and their probabilities are: 1 1 2 4 3 ------------------------------------------------------------------------The symbols, their probabilities and the allocated Huffman codewords are: 1 0.4 2 0.3 3 0.2 4 0.1

0 1 0 1 1 1 1 1 0

entropy = 1.8464 av_length = 0 av_length = 0.4000 av_length = 1.0000 av_length = 1.6000 av_length = 1.9000

The symbol entropy is : 1.8464 The average Huffman codeword length is : 1.9 The Huffman coding coding rate is : 0.97181 >>

 

  CONCLUSION : Huffman encoding is a compression technique that uses variable length encoding where

variable length codes are assigned to all the characters depending on how frequently they occur in the given text. Here we have successfully implemented Huffman code in Matlab and also performed dry run to check whether the answer obtained is correct.