Data Compression

Data Compression subject = Information Theory title = Data Compression Data Compression- in beginners terms Data Compression just sounds complicated. Dont be afraid, compression is our good friend for many reasons. It saves hard drive space. It makes data files to handle. It also cuts those immense file download times from the Internet.

Wouldnt it be nice if we could compress all files down to just a few bytes? There is a limit to how much you can compress a file. How random the file is, is the determining factor to how far it can be compressed. If the file is completely random and no pattern can be found, then the shortest representation of the file is the file it self. The actual proof that proves this is at the end of my paper. The key to compressing a file is to find some sort of exploitable pattern.

Most of this paper will be explaining those patterns that are commonly used. Null suppression is the most primitive form of data compression that I could find. Basically, it says that if you have different fields that data is in (possibly a spread sheet), and any of them have only zeros in them, then the program just eliminates the data and goes straight from the empty data set to the next. Only one step up from null suppression is Run Length Encoding. Run length encoding simply tells you how many of what you have in a row. It would change a set of binary data like {0011100001} into what the computer reads as (2)zeros, (3)ones, (4)zeros, 1.

As you can see, it works on the same basic idea of finding a series of 0s (null suppression) and 1s in this case too and abbreviating them. Once the whole idea of data compression caught on, more people started working on programs for it. From these people we got some new premises to work with. Substitutional encoding is a big one. It was invented jointly by two people: Abraham Lempel and Jakob Ziv.

Most compression algorithms (big word meaning roughly program) using substitutional encoding start with LZ for Lempel-Ziv. LZ-77 is a really neat compression in which the program starts off just copying the source file over to the new target file, but when it recognizes a phrase of data that it has previously written, it replaces the second set of data in the target file with directions on how to get to the first occurrence of it and copy it in the directions place. This is more commonly called a sliding-window compression because the focus of the program is always sliding all around the file. LZ-78 is the compression that most people have in their homes. Some of the more common ones are ZIP, LHA, ARJ, ZOO, and GZIP. The main idea behind LZ-78 is a dictionary.

Yet it works quite a bit like the LZ-77. For every phrase it comes across, it indexes the string by a number and writes it in a dictionary. When the program comes across the same string, it uses the associated number in the dictionary instead of the string. The dictionary is then written along side the compressed file to be used in decoding. There is a combined version of LZ-77 an LZ-78.

It is called LZFG. It only writes to the dictionary when it finds the repeated phrase, not on every phrase. Then instead of LZFG replacing the second set of data with directions on how to get to the first occurrence of it, the program puts in the number reference for the dictionarys translation. Not only is it faster, but it compresses better because of the fact that it doesnt have as big of a dictionary attached. Statistical encoding is another one of the new compression concepts.

It is an offshoot of the LZ family of compressors; It uses basically the same style as LZFG, but instead of assigning the numbers in order that the strings come out of the source file, statistical compressors do some research. It calculates the number of times each string is used and then ranks the string with the most number of uses at the top of the hash table. The string with the least is ranked at the bottom. (A hash table is where the rank is figured) The higher up a string is on this list, the smaller of a reference number it gets to minimize the total bit usage. This gives this compression just a slight edge on the others, but every little bit helps. (ha ha -bit- ) Beware! There are a few compression programs out there that claim wonderful compression ratios; ratios that beat the compression limit for that files randomness. These programs arent really compression programs.

They are OWS and WIC. Never compress anything with these. What they do is split up the file that you desired to compress and hide most of it on another part of your hard drive. OWS puts it in a specific spot on the physical hard drive disk. WIC puts the extra information in a hidden file called winfile.dll.

The real problems with these programs are that if you dont have the winfile.dll or the information on the certain spot on your drive, then the program wont put your file back together. My original intent with this project was to invent a new compression algorithm. I started with the idea that if you took the file in its pure binary form and laid it out in a matrix, there were certain rows and columns that you could add up to get an output that would be able to recreate the original matrix. I was close too. I had four different outputs that actually would be what would make up the compressed file that combined together to create one output for each bit. From this single output I could determine if the bit was 1 or 0.

It worked perfectly for matrixes of 1×1, 2×2, and 3×3. Except that with this small of a matrix, I wasnt compressing it at all. It was more of a coding system that took up more space than did the original file. I even found a way to shrink the size of the four outputs but it was not enough to even break even on bit count. When I got to the 4x4s I found an overlap.

An overlap is a term I made up for this algorithm. It means that I got the same single output for a 1 as I did a 0. When that happens, I cant figure out which it is: a 1 or 0. When you cant recreate the original file, data compression has failed. It becomes lossy. I needed a fifth original output.

If you want more information on how I thought the algorithm would have worked, please refer to my Inventors Log that I included. Its way too much to re-type here and it would serve no real purpose in this paper. If you were paying attention earlier, you would be saying, Why dont you find a pattern? Otherwise you cant compress it. You are treating it like a random file. I didnt find out that it was impossible to compress random data until about the time my algorithm was failing.

Because of my setbacks I started looking for an entirely new way to compress data, using a pattern of some sort. I got to thinking about all of the existing algorithms. I wanted to combine a hash table, statistical coder, and a run length coder. The only hard part that I would see in that would be trying to get the patent holders of each of those algorithms to allow me to combine them and actually modify them slightly. In its current algorithm, the statistical coder only accepts alpha-numeric phrases.

I would like to modify it to not read the characters that the binary code spells out, but the binary code it self. I dont know what form the output is aside from compressed, but for my purposes it wouldnt matter what the form the output is. I would program into the program all of the 32 combinations of 5 bits (2^5). Each of the combinations would be labeled in the program 1 through 32. I would then make a hash table of all of the 5 bit combinations.

This would give me an output which I would run through a run length coder. Since the entire algorithm is reliant on binary code and not on characters, it can be recursable, or it can compress further an already compressed file. LZs cant do that because once they convert a string into its dictionary/sliding window form, it ceases to be one of the characters that it compresses. Now that you are aquatinted with our friend, Data Compression, I hope he will be able to serve you better. Now you can download programs faster, save space, and who knows? Maybe you will invent the next new compression algorithm.

Until then, keep your mice happy and your monitors warm. Proof that random data is not compressible: Lets suppose the file to be compressed is 8 bits long (x works, but this is easier) and is random There are exactly 2^8 different possible 8 bit data strings. (2^x) To compress the file it must shrink it by at least one bit (2^x)-1 So there are at most 2^7 different compressed files 2^(x-1) Thus at least two source files compress down to the same file. Therefore The compression cannot be lossless. Bibliography Aronson, Jules Data Compression- a comparison of Methods Washington D.C.: Institute for Computer Science and Technology http://simr02.si.ehu.es/DOCS/mice/compression-faq/ part1/faq-doc-x.html x=Intro,8,9, and 10 http://www.epl.co.uk/genit18.htm http://www.sees.bangor.ac.uk/~gerry/sp summary.html http://Literacy.com//mkp/pages/3468/index.html.

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