assignment no 6 huffmancoding

8/12/2019 Assignment No 6 HuffmanCoding

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Assignment # 6 1

Assignment # 6

Huffman coding

Saad Iftikhar 039

Munhal Imran

Muhammad Hassan Zia 029Moeez Aslam

Hamza Hashmi

junaid Afzal Swatti

Ali Tausif 061

Armaghan Ahmed

Zohair Fakhar

Mohsin Altaf

Instructor:

Sir Qasim Umer Khan


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Assignment # 6 2

AbstractIn this assignment we have implemented

the Huffman entropy encoding algorithm for data

compression. The results obtained after extensive

testing with different sets showed acceptable results

and confirmed the notion that more similar the data

set the better is compression achieved by Huffman

compression algorithm.

I. INTRODUCTIONncomputer science andinformation theory,Huffman

coding is anentropy encodingalgorithm used forlossless

data compression.The term refers to the use of avariable-

length code table for encoding a source symbol (such as a

character in a file) where the variable-length code table has

been derived in a particular way based on the estimated

probability of occurrence for each possible value of the source

symbol. Huffman coding uses a specific method for choosing

the representation for each symbol, resulting in aprefix

code (sometimes called "prefix-free codes", that is, the bit

string representing some particular symbol is never a prefix of

the bit string representing any other symbol) that expresses the

most common source symbols using shorter strings of bits

than are used for less common source symbols

II. ASSIGNMENTIn this assignment we were required to implement

the Huffman algorithm in matlab.

III. PERFORMANCE

following are the matlab codes:CODE:

Class of Huffman code:

%-----huffman coding-------------%%%%----- version 1--------------%%%%%- data structure (classes)---%%%%%%------18-12-2013------------%%%

%%

classdef huffman % data structurevalues that the node has in it

propertiesleftNode = []rightNode = []probabilitycode = [];symbolhuffy % will store the huufman

code just for checkend

end%%%%%%%%%%%--------------%%%%%%%%%%%%%%

Code for probability finding of data:%- calculating frequency of elements--%%%%%--- Saad Iftikhar-------%%%%%%%%%%%%%%---- 17 december 2013----%%%%%%%%%%

%% calculate how many same numbers occurfunction[data_unique,data_freq]=frequency(data);clc;% data=[22 33 55 66 11 22 33 44 66];data_unique=unique(data); % thisfunction creates asorted ascending orderarray% with only unique elements no twoelements are repereated

fori=1:length(data_unique)data_unique1(i)= sum(data ==

data_unique(i));% this array has the correspondingfrequency of the data% in the unique arrayenddata_unique=data_unique;data_freq=data_unique1;

data_freq=data_freq/sum(data_freq);end%%%%%%%%%%%------------%%%%%%%%%%%%%%

Conversion of data from binary indecimal:%--- calculating frequency of elementsbinary version-------------%%%%%%%--- 20-21 december 2013---%%%%%%

%% convert the data to decimalfunction[convData]=dataConv(data,M);

Huffman Coding implementation in Matlab

I
http://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Information_theoryhttp://en.wikipedia.org/wiki/Entropy_encodinghttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Lossless_data_compressionhttp://en.wikipedia.org/wiki/Lossless_data_compressionhttp://en.wikipedia.org/wiki/Variable-length_codehttp://en.wikipedia.org/wiki/Variable-length_codehttp://en.wikipedia.org/wiki/Prefix_codehttp://en.wikipedia.org/wiki/Prefix_codehttp://en.wikipedia.org/wiki/Prefix_codehttp://en.wikipedia.org/wiki/Prefix_codehttp://en.wikipedia.org/wiki/Variable-length_codehttp://en.wikipedia.org/wiki/Variable-length_codehttp://en.wikipedia.org/wiki/Lossless_data_compressionhttp://en.wikipedia.org/wiki/Lossless_data_compressionhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Entropy_encodinghttp://en.wikipedia.org/wiki/Information_theoryhttp://en.wikipedia.org/wiki/Computer_science


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Assignment # 6 3

%%% always comes a whole no not afraction% M=8;k=log2(M);convData=[];

remainder=mod(length(data),k);

% this function here will check if thedata is exactly divisable by k or elsewill append 0 bits ;

if(remainder~=0)append=k-remainder;else

append=0;end

data=[zeros(1,append) data];fordataLength=1:k:length(data)

string=num2str(data(dataLength:dataLength+k-1));

decimal=bin2dec(string);convData=[convData decimal];

end%%%%%%%%%%%------------%%%%%%%%%%%%%%

Main code of Huffman:%%%%% main code of huffman coding algousing classes-------%%%%%%%%%%-- Saad Iftikhar 18-12-2013-%%%%%%%%---creating binary tree-----%%%%%%

%%%---huffman code using classes---%%%%%% functioncodedData=sourceHuffman(information,M);clc;

clear symbol;clear codeHuff;clear codeBits;clear arrr;%% initializingglobal symbol; % global variable willhave the the symbolsglobal codeHuff; % global variable will

have the the symbols huffman codesglobal codeBits;% global variable willhave the the symbols related length ofhuffman codesdecodeData=[];symbol=[];codeHuff=[];codeBits=[];

M=4;

information=[0 0 1 0 1 0 0 0 0 1];% information=randint(1,3000);convdata=dataConv(information,M); % thisfunction her will convert our% from binary format to decimal as restof our program is written for% decimal[data,prob]=frequency(convdata);

%% Empty Array of Object Huffmanarray = huffman.empty(length(prob),0);array_final =huffman.empty(length(prob),0);

%% Assign Initial saving all theprobabilities of the numbers in the% probability property of theclass/structure alspfori=1:length(data)

array(i).probability = prob(i);

array(i).symbol = data(i);array_final(i).probability =prob(i);

array_final(i).symbol = data(i);end% here creating a temperary aaray to dothe sorting the algo we are using% is the bubleSort algo for ascendingordertemparray = array;%

%% Creating the Binary Tree for k =

1:size(temparray,2)-1 % size(a,2) givessize of the columns% binary tree is where a node/ parent hastwo children and lower% probability one is on left and higherone is on right% here to create a binary tree we have totraverse for the no of nodes -1% here we take size of the colums as sizeis always given as 2 dim vectorfork = 1:size(temparray,2)-1% % First Sort the temp array ussebuble sort%

fori=1:size(temparray,2)for j = 1:size(temparray,2)-1

% buble Sort algorithmif (temparray(j).probability

> temparray(j+1).probability)tempnode = temparray(j);

% this is the swaping operationtemparray(j) =

temparray(j+1);temparray(j+1) =

tempnode;


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Assignment # 6 4

endend

end

%% % now we have to Create a new node%

newnode = huffman; % a node of the

class of huffman

% Add the probailities here we arecreating the tree lowest two

% probability nodes are added intoone single node

newnode.probability =temparray(1).probability +temparray(2).probability;% new node has the sum of previous twoprobabilities% % now assign the left lowest probabilyone as 0 and higher probabilty oen

% as 1temparray(1).code = [0];temparray(2).code = [1];

%% % Attach Children Nodes to the newnode the parent node created

newnode.leftNode = temparray(1);newnode.rightNode = temparray(2);

%% % remove the previous two nodes andreplace by parent nodes just like% in C++ we would remove the pointerand of children nodes and replace% by pointer of father node%

temparray =temparray(3:size(temparray,2)); % fisttwo nodes are gone%% now appending the new parent node%

temparray = [newnode temparray];%end % end the looping and hence binarytree created%%rootNode = temparray(1); % the root

node is always the first nodele_code = []; % that will be the finalcode huffman%% % Looping though the tree% % See recursive function loop.m%final_data=[]; % variable definitionlater usedcheck=huffman;

f=traverse(rootNode,le_code); % here wewill traverse the tree and generatehuffman tree

% here is the loop for detectingreplacing the data with its huffman code

forcodeLength=1:length(convdata)forinner=1:length(symbol)

if(convdata(codeLength)==symbol(inner))level=sum(codeBits(1:inner-1))+1;final_data=[final_data

codeHuff(level:level+codeBits(inner)-1)];elseendend

end% codedData=final_data%%%%%%%%%%%----------------%%%%%%%%%%%%%%

Traversal code for code generation:%%%%%----------- function for traversalof the binary tree-------%%%%%%%%%%---- 20-12-2013------------%%%%%%%%--algorithm for traversing the treewhole to get the code-----%%%%%%%

functionf = traverse(tempNode,codec)

global symbol; % these are the global

variables to store our array code anddata as in recursive functions they arecontinously over writtenglobalcodeHuff;globalcodeBits;

if ~isempty(tempNode) % if we have thenext root or notcodec = [codec tempNode.code]; % appendwith the previous node

if~isempty(tempNode.symbol)% disp(tempNode.symbol);tempNode.huffy=[codec];% disp(codec);symbol=[symbol tempNode.symbol];codeHuff=[codeHuff codec];codeBits=[codeBits length(codec)];

end

traverse(tempNode.leftNode,codec);traverse(tempNode.rightNode,codec);


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Assignment # 6 5

endf=codec;end%%%%%%%%%-------------%%%%%%%%%%%%%%

Code for decoding of Huffman:

%---Huffman decoding algorithm---------%

%%%%%------- Saad Iftikhar----%%%%%%%%%%%-- 21-12-2013------------------------%

%% functiondecodedData=decodeHuffman(data,M,rootNode)

%lets traverse data and create thedecoded string using the structures

function [realdata,olright] =dHuffman(tempNode,data,M)%% traversing the tree and when we reacha leaf we assign the leaf nodes value tothe data vectordecoded=[]; % definig variablesrealdata=[];i=1;k=1;centerNode=tempNode; % variable of classhuffamnwhile(klength(data)) % if data is

over this is the leafrealdata=[realdata

centerNode.symbol];flag=1;k=i+1;break

endend

end%% here we convert the data from decimalback to binary formatbinaryReal=dec2bin(realdata,log2(M));binaryReal1=binaryReal';binaryRealFinal=binaryReal1(:);

binaryRealFinal=binaryRealFinal';forloop=1:length(binaryRealFinal)olright(loop)=str2double(binaryRealFinal(loop));end

end%%%%%%%%%%%------%%%%%%%%%%%%%%


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Assignment # 6 6

Results:

Information is the original data its size is 21 bits long. final_data is the Huffmancompressed data its size is greatly reduced to 10 as M=8 ,k=3 in this case quitesimilar data


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Assignment # 6 7

Now in this window it is shown that final data Huffman encoded data when sent to the decoding functions return the original

data and the sum(ol==information) returns 21 which means all 21 bits of original data and decoded data are a match.

IV. CONCLUSIONNow the implementation of the Huffman lossless entropy

encoding compression algorithm has confirmed the notion that

when data has many similar elements in it this compression

reduces the length of a code and hence increases the entropyno of useful information sent per bits.

assignment no 6 huffmancoding

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