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In [[computer science]] and [[information theory]], '''Tunstall coding''' is a form of [[entropy coding]] used for [[lossless data compression]].
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== History ==
 
Tunstall coding was the subject of Brian Parker Tunstall's PhD thesis in 1967, while at Georgia Institute of Technology. The subject of that thesis was "Synthesis of noiseless compression codes" <ref>{{cite book|last=Tunstall, Brian Parker|first=|title=Synthesis of noiseless compression codes|accessdate=2013-01-20|date=12,1967|publisher=[[Georgia Institute of Technology]]}}</ref>
 
Its design is a precursor to [[Lempel-Ziv]].
 
== Properties ==
 
Unlike [[variable-length code]]s, which include [[Huffman coding|Huffman]] and [[Lempel–Ziv|Lempel–Ziv coding]],
Tunstall coding is a [[code]] which maps source symbols to a fixed number of bits.<ref>http://www.rle.mit.edu/rgallager/documents/notes1.pdf, Study of Tunstall's algorithm at [[MIT]]</ref>
 
Unlike [[Typical set|typical set encoding]], Tunstall coding parses a stochastic source with codewords of variable length.
 
It can be shown<ref>[http://ipg.epfl.ch/lib/exe/fetch.php?media=en:courses:2013-2014:itc:tunstall.pdf], Study of Tunstall's algorithm from [[EPFL]]'s Information Theory department</ref>
that, for a large enough dictionary, the number of bits per source letter can be infinitely close to <math>H(U)</math>, the [[Entropy (information theory)|entropy]] of the source.
 
== Algorithm ==
 
The algorithm requires as input an input alphabet <math>\mathcal{U}</math>, along with a distribution of probabilities for each word input.
It also requires an arbitrary constant <math>C</math>, which is an upper bound to the size of the dictionary that it will compute.
The dictionary in question, <math>D</math>, is constructed as a tree of probabilities, in which each edge is associated to a letter from the input alphabet.
The algorithm goes like this:
 
   D := tree of <math>|\mathcal{U}|</math> leaves, one for each letter in <math>\mathcal{U}</math>.
  While <math>|D| < C</math>:
    Convert most probable leaf to tree with <math>|\mathcal{U}|</math> leaves.
 
== Example ==
 
Let's imagine that we wish to encode the string "hello, world".
Let's further assume (somewhat unrealistically) that the input alphabet <math>\mathcal{U}</math>
contains only characters from the string "hello, world" — that is, 'h', 'e', 'l', ',', ' ', 'w', 'o', 'r', 'd'.
We can therefore compute the probability of each character based on its statistical appearance in the input string.
For instance, the letter L appears thrice in a string of 12 characters: its probability is <math>3 \over 12</math>.
 
We initialize the tree, starting with a tree of <math>|\mathcal{U}|=9</math> leaves. Each word is therefore directly associated to a letter of the alphabet.
The 9 words that we thus obtain can be encoded into a fixed-sized output of <math>\lceil \log_2(9) \rceil = 4</math> bits.
 
[[File:Tunstall-1.png|Tunstall "hello, world" example — one iteration]]
 
We then take the leaf of highest probability (here, <math>w_1</math>), and convert it to yet another tree of <math>|\mathcal{U}|=9</math> leaves, one for each character.
We re-compute the probabilities of those leaves. For instance, the sequence of two letters L happens once.
Given that there are three occurrences of letters followed by an L, the resulting probability is <math>{1 \over 3} \cdot {3 \over 12} = {1 \over 12}</math>.
 
We obtain 17 words, which can each be encoded into a fixed-sized output of <math>\lceil \log_2(17) \rceil = 5</math> bits.
 
[[File:Tunstall-2.png|Tunstall "hello, world" example — two iterations]]
 
Note that we could iterate further, increasing the number of words by <math>|\mathcal{U}|-1=8</math> every time.
 
== Limitations ==
 
Tunstall coding requires the algorithm to know, prior to the parsing operation, what the distribution of probabilities for each letter of the alphabet is.
This issue is shared with [[Huffman coding]].
 
Its requiring a fixed-length block output makes it lesser than [[Lempel-Ziv]], which has a similar dictionary-based design, but with a variable-sized block output.
 
== References ==
{{reflist}}
 
{{Compression methods}}
 
[[Category:Lossless compression algorithms]]

Latest revision as of 12:41, 9 December 2014

The brand name itself is currently enough explanation for this model to be described in this best speed belt sander overview. You basically flip the lever, slip the old belt off and slip the new 1 on. Tracking is pretty very good and not as touchy as on my old Pc. As opposed to my Computer belt sander, this a single doesn't have a tendency to tip to either side. It is also extremely steady at the beginning and finish of a board when half of the belt is not in get in touch with with the wood. A quantity of diverse models are obtainable to fit your woodworking style. Was hunting for a top quality belt sander and came across the Metabo.



It also attributes an auto-tracking belt design and style which guarantees the sand belt stays on the device when in use. The Jet Open Sand Belt/Disc Sander is a very effective belt sander that is a mixture of disc and belt sander. The device is set on an open steel stand, and each belt and disc sanders run on a centrally balanced and totally encased induction motor. The sander belt rotates at 2500 SFPM and can be adjusted to operate vertically as nicely as horizontally. This belt sander functions effectively.

Soft flooring woods, like pine and cedar, sand promptly, but there is also a higher risk of damaging the wood when using a energy sander. An oscillating sander can have a square, rectangular, circular or triangular sanding pad, and it can be electric or powered by compressed air. When you can effortlessly ruin a piece of wood by making use of a belt or disc sander incorrectly, the similar is not accurate with an oscillating sander.

Wider sanding belt can cover a wider surface area and as a result will take much less time to do a particular task. Another model is the stationary sander where the material is moved rather of the sander itself. Some residence belt sanders employed in properties may also show this feature. This function as effectively as a lot of other folks is critical when picking out a sander. Guitar makers and those that like to tinker with furnishings items generally have one particular or two belt sanders. The "mighty" belt comes on assist again.

On the other hand, if you use a belt sander for lots of projects, or plan to use it for a major job such as a entire residence complete of hardwood flooring that wants rejuvenating�a loud, noisy sander could be a disadvantage. For those who have virtually any queries relating to where by and tips on how to utilize http://www.bestoscillatingtoolreviews.com/best-angle-grinder-reviews/, you possibly can email us with our web site. Just after taking a look at five important capabilities of each and every belt sander, the Makita does score a few much more points than the Porter Cable. When powered on, the drum sander quickly grinds away the old finish.

Most of the time, sanders are used for finishing function such as final smoothing of a piece of wood or metal bodywork just before placing the finish on. But, there are also those times when it really is important to do some main operate with a sander when you want to take material off. Belt sanders are made for rapidly cutting, not for fine finishing. The belt moves at a fairly high rate of speed, for the very same cause. While there are larger belt sanders on the market, the 3 inch by Who Tends to make The Very best 4.five Angle Grinder 21 inch size is the most frequent.

You just flip the lever, slip the old belt off and slip the new one particular on. Tracking is incredibly great and not as touchy as on my old Computer. In contrast to my Pc belt sander, this one particular does not have a tendency to tip to either side. It is also pretty steady at the beginning and end of a board when half of the belt is not in speak to with the wood. A number of distinct models are offered to match your woodworking style. Was seeking for a excellent belt sander and came across the Metabo.

You can also sand and shape a lot of sorts of materials on the 1 inch wide belt surface, such as metal, wood, plastics and composites. Chisels, knives and other tools sharpen up nicely on the 42 inch extended Aluminum Oxide belt that comes with the unit, and you can change and track belts in about 30 seconds. This�closed coat aluminum oxide belt uses�a "X" weight 65/35 polyester/cotton backing with a resin bond program.

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