Huffman compression is a lossless compression algorithm that is ideal for compressing text or program files. Huffman compression belongs to a family of algorithms with a variable codeword length.

That means that individual symbols characters in a text file for instance are replaced by bit sequences that have a distinct length. So symbols that occur a lot in a file are given a short sequence while others that are used seldom get a longer bit sequence. Since these are 6 characters, this text is 6 bytes or 48 bits long.

If these code words are used to compress the file, the compressed data look like this: This means that 11 bits are used instead of 48, a compression ratio of 4 to 1 for this particular file. This compression algorithm is mainly efficient in compressing text or program files. Images, like they are often used in prepress, are better handled by other compression algorithms. Huffman compression is mainly used in compression programs like pkZIP, lha, gz, zoo and arj. How Huffman compression works Huffman compression belongs to a family of algorithms with a variable codeword length.

A practical example will show you the principle: Suppose you want to compress the following piece of data: ACDABA Since these are 6 characters, this text is 6 bytes or 48 bits long. If these code words are used to compress the file, the compressed data look like this: This means that 11 bits are used instead of 48, a compression ratio of 4 to 1 for this particular file. Huffman encoding can be further optimized in two different ways: Adaptive Huffman code dynamically changes the codewords according to the change of probabilities of the symbols.

Extended Huffman compression can encode groups of symbols rather than single symbols. Advantages and disadvantages This compression algorithm is mainly efficient in compressing text or program files. Where is Huffman compression used Huffman compression is mainly used in compression programs like pkZIP, lha, gz, zoo and arj. Can we use dis algo for lossless image compression and dn send it on network?? What are the other algorithms of huffman that will apply in the text file compression?

Can this algorithm be used while sending data on network? Please reply. A cookie is used to collect visitor statistics.

Clark forklift steering cylinder removalThe adverts also use one. You are free to leave if you dislike their use. Got it.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I am not asking how Huffman coding is working, but instead, I want to know why it is good. I understand the ultimate purpose of Huffman coding is to give certain char a less bit number, so space is saved.

What I don't understand is that why the decision of number of bits for a char can be related to the char's frequency? Huffman Encoding Trees says. It is sometimes advantageous to use variable-length codes, in which different symbols may be represented by different numbers of bits. For example, Morse code does not use the same number of dots and dashes for each letter of the alphabet. In particular, E, the most frequent letter, is represented by a single dot.

So in Morse code, E can be represented by a single dot because it is the most frequent letter. But why? Why can it be a dot just because it is most frequent? If you assign less number or bits or shorter code words for most frequently used symbols you will be saving a lot of storage space.

Suppose you want to assign 26 unique codes to English alphabet and want to store an english novel only letters in term of these code you will require less memory if you assign short length codes to most frequently occurring characters. You might have observed that postal code and STD codes for important cities are usually shorter as they are used very often.

This is very fundamental concept in Information theory. Starts by combining the two least weight nodes into a tree which is assigned the sum of the two leaf node weights as the weight for its root node.

Do this until you get a single tree. For example consider below binary tree where E and T have high weights as very high occurrence. It is a prefix tree.

To get the Huffman code for any character, start from the node corresponding to the the character and backtrack till you get the root node. Indeed, an E could be, say, three dashes followed by two dots. When you make your own encoding, you get to decide. If your goal is to encode a certain text so that the result is as short as possible, you should choose short codes for the most frequent characters. The Huffman algorithm ensures that we get the optimal codes for a specific text.

If the frequency table is somehow wrong, the Huffman algorithm will still give you a valid encoding, but the encoded text would be longer than it could have been if you had used a correct frequency table. This is usually not a problem, because we usually create the frequency table based on the actual text that is to be encoded, so the frequency table will be "perfect" for the text that we are going to encode.

Given some set of documents for instance, encoding those documents as Huffman codes is the most space efficient way of encoding them, thus saving space. The statistics are important because the symbols with the highest probability frequency are given the shortest codes.

Thus the symbols most likely to be in your data use the least amount of bits in the encoding, making the coding efficient. The prefix code part is useful because it means that no code is the prefix of another.

This increases the inefficiency of transmitting data using morse as you need a special symbol pause to signify the end of transmission of one code. Compare that to Huffman codes where each code is unique, as soon as you discover the encoding for a symbol in the input, you know that that is the transmitted symbol because it is guaranteed not to be the prefix of some other symbol.

It's the dual effect of having the most frequent characters using the shortest bit sequences that gives you the savings. For a concrete example, let's say you have a piece of text that consists of e characters and of all other characters combined.

Now let's say we represent e as a single 1-bit and every other letter as a 0-bit followed by its original 8 bits a very primitive form of Huffman. You can see that half the characters have been expanded from 8 bits to 9, giving bits, or bytes. However, the e characters have been reduced from 8 bits to 1, meaning they take up bits, or bytes.Thanks for your time. What if we place the alphabets having higher frequency in the left and lower at the right?

The solution given above provides a longer code for B than F in decimal which goes against the huffman rule. But as per the suggestion the vulnerability can be removed. Correct me if I am wrong. That was great tutorial on Huffman tree, i searched many other ones but this is the best. Keep it up sir. If the variable length code Huffman code is given for all the characters. Plus their frequency is also given except for one character. Now how to find the missing frequency range of that character?

Your email address will not be published. It is an algorithm which works with integer length codes. Huffman tree can be achieved by using compression technique. The data encoding schemes broadly categorized in two categories. The fixed length code can store maximumbits data.

**Text Compression with Huffman Coding**

Huffman C. Insert Q,z. The Q is initialized as a priority queue with the character C. Couple these nodes together to a new interior node.

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Construct a Huffman tree by using these nodes. Huffman Tree. Now the list contains only one element i.

Leave a Reply Cancel reply Your email address will not be published.Login Now. In applications where the alphabet size is large, pmax is generally quite small, and the amount of deviation from the entropy, especially in terms of a percentage of the rate, is quite small.

However, in cases where the alphabet is small and the probability of occurrence of the different letters is skewed, the value of pmax can be quite large and the Huffman code can become rather inefficient when compared to the entropy. To overcome this inefficiency we use adaptive Huffman coding, the same can be illustrated with the help of following example:. The entropy for this source is 0.

A Huffman code for this source is shown in Table below. The average length for this code is 1. The difference between the average code length and the entropy, or the redundancy, for this code is 0. Now for the source described in the above example, instead of generating a codeword for every symbol, we will generate a codeword for every two symbols. The extended alphabet, probability model, and Huffman code for this example are shown in Table below.

The average codeword length for this extended code is 1. However, each symbol in the extended alphabet corresponds to two symbols from the original alphabet.

Therefore, in terms of the original alphabet, the average codeword length is 1. Find answer to specific questions by searching them here.

It's the best way to discover useful content. Download our mobile app and study on-the-go. You'll get subjects, question papers, their solution, syllabus - All in one app. Login You must be logged in to read the answer. Go ahead and login, it'll take only a minute. Explain extended huffman coding. What is the advantage of extended Huffman coding? Follow via messages Follow via email Do not follow. Please log in to add an answer. Continue reading Find answer to specific questions by searching them here.

Find more. Engineering in your pocket Download our mobile app and study on-the-go.Huffman coding suffers from the fact that the uncompresser need have some knowledge of the probabilities of the characters in the compressed files. Not only can this add somewhat to the bits needed to encode the file, but, if this crucial piece of knowledge is unavailable, compressing the file requires two passes- one pass to find the frequency of each character and construct the huffman tree and a second pass to actually compress the file.

Expanding on the huffman algorithm, Faller and Gallagher, and later Knuth and Vitter, developed a way to perform the huffman algorithm as a one pass procedure. Sayood While the methods of each of these eminent gentlemen differ slightly, the discrepancies do not effect the basic "adaptive huffman" algorithm.

The differences between the two methods will be explored in greater depth later in this document.

### Adaptive Huffman Coding

The fact that the file is encoded dynamically has significant implications for the effectiveness of the tree as a encoder and decoder. Because the Huffman tree is constructed from the character counts of the file as a whole, it works effectively at a universal level. Adaptive Huffman coding also works at a universal level, but is far more effective than static huffman coding at a local level because the tree is constantly evolving.

How to fight jinnSay, for example, a file starts out with a series of a character that are not repeated again in the file. In static Huffman coding, that character will be low down on the tree because of its low overall count, thus taking lots of bits to encode.

In adaptive huffman coding, the character will be inserted at the highest leaf possible to be decoded, before eventually getting pushed down the tree by higher-frequecy characters. At the heart of the Adaptive Huffman algorithm is the sibling property which states "each node except the root has a sibling and the nodes can be listed in order of non-increasing weight with each node adjacent to its siblings" Data Compression Library To maintain this property, we will keep track of each nodes order and its weight where the order is simply used as a numbering system for the weights that increases left to right, top to bottom, and where the weight keeps track of the number of times the value contained in the node has occured so far in the file, with nodes that do not contain values like the root and other internal nodes having a weight equal to the sum of their two child nodes.

Nodes with higher orders will also have correspondingly higher weights. Below is a declaration of the struct Tree used for the adaptive hufman algorithm as well as an example tree.

Although you do not yet know how the tree was set up, it should be obvious that the weights are set up in an numbering structure similar to a heap and that the order is determined in reverse in-order. The ordering starts at because there are characters that can be represented with 8 bits and a maximum total of internal nodes equal towith an additional node granted for the NYT node, which will be dealt with later.

For this assignment, the numbering is only important in that the ordering should remain positive. More advanced versions of the program may use mathematical prinicples to prove how many bits are needed and thereby decrease the number of bits needed to recognize a character. This algorithm is called adaptive huffman coding because the tree is adaptive- it is created simultaneously with either the compressed or uncompressed file as it reads in the other.

The tree is dynamic and changes after the reading of every character. Both the compresser and decompresser use the same method to construct the tree and therefore can decode what the other has written. The tree is manipulated as the file is read to maintain the following properties: Each node has a sibling Node's with higher weights have higher orders On each level, the node farthest to the right will have the highest order although there might be other nodes with equal weight Leaf nodes contain character values, except the Not Yet Transmitted NYT node which is the node whereat all new characters are added Internal nodes contain weights equal to the sum of their children's weights All nodes of the same weight will be in consecutive order.

Now to get into the nitty-gritty of the actual manipulation. When a character is read in from a file, the tree is first checked to see if it already contains that character. If it doesn't, the NYT node spawns two new nodes. The node to its right is a new node containing the character and the new left node is the new NYT node.

If the character is already in the tree, you simply update the weight of that particular tree node. In some cases, when the node is not the highest-ordered node in its weight class, you will need to swap this node so that it fulfills the property that nodes with higher weight have higher orders. To do this, before you update the node's weight, search the tree for all nodes of equal weight and swap the soon-to-be updated value with the highest ordered node of equal weight.

Finally update the weight. However in both cases for inserting values, weights are changed for a leaf and this change will effect all nodes above it. Therefore, after you insert a node, you must check the parent above the node following the same procedure you followed when updating already seen values.

Check to see whether the node in question is the highest order node in its weight class prior to updating.A file contains the following characters with the frequencies as shown. If Huffman Coding is used for data compression, determine. To write Huffman Code for any character, traverse the Huffman Tree from root node to the leaf node of that character.

Watch this Video Lecture.

### Difference Between Huffman Coding and Shannon Fano Coding

Get more notes and other study material of Design and Analysis of Algorithms. It is used for the lossless compression of data. It uses variable length encoding. It assigns variable length code to all the characters.

The code length of a character depends on how frequently it occurs in the given text. The character which occurs most frequently gets the smallest code. The character which occurs least frequently gets the largest code. It is also known as Huffman Encoding. This is to prevent the ambiguities while decoding. It ensures that the code assigned to any character is not a prefix of the code assigned to any other character.

Huffman Coding or Huffman Encoding is a Greedy Algorithm that is used for the lossless compression of data. Huffman Coding Example and Time Complexity. Huffman Tree Construction Steps. Akshay Singhal. Publisher Name. Any of the above two conventions may be followed. But follow the same convention at the time of decoding that is adopted at the time of encoding.In computer science and information theorya Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression.

The process of finding or using such a code proceeds by means of Huffman codingan algorithm developed by David A. Huffman while he was a Sc. The output from Huffman's algorithm can be viewed as a variable-length code table for encoding a source symbol such as a character in a file.

## Adaptive Huffman coding

The algorithm derives this table from the estimated probability or frequency of occurrence weight for each possible value of the source symbol. As in other entropy encoding methods, more common symbols are generally represented using fewer bits than less common symbols. Huffman's method can be efficiently implemented, finding a code in time linear to the number of input weights if these weights are sorted.

InDavid A.

Spwm codeHuffman and his MIT information theory classmates were given the choice of a term paper or a final exam. The professor, Robert M. Fanoassigned a term paper on the problem of finding the most efficient binary code.

Huffman, unable to prove any codes were the most efficient, was about to give up and start studying for the final when he hit upon the idea of using a frequency-sorted binary tree and quickly proved this method the most efficient.

In doing so, Huffman outdid Fano, who had worked with information theory inventor Claude Shannon to develop a similar code. Building the tree from the bottom up guaranteed optimality, unlike the top-down approach of Shannonâ€”Fano coding.

Huffman coding uses a specific method for choosing the representation for each symbol, resulting in a prefix 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. Huffman coding is such a widespread method for creating prefix codes that the term "Huffman code" is widely used as a synonym for "prefix code" even when such a code is not produced by Huffman's algorithm.

We give an example of the result of Huffman coding for a code with five characters and given weights. We will not verify that it minimizes L over all codes, but we will compute L and compare it to the Shannon entropy H of the given set of weights; the result is nearly optimal. For any code that is biuniquemeaning that the code is uniquely decodeablethe sum of the probability budgets across all symbols is always less than or equal to one.

In this example, the sum is strictly equal to one; as a result, the code is termed a complete code. If this is not the case, one can always derive an equivalent code by adding extra symbols with associated null probabilitiesto make the code complete while keeping it biunique.

As defined by Shannonthe information content h in bits of each symbol a i with non-null probability is.

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