Data Compression

‘Data Compression’ just sounds complicated. Don’t 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. Wouldn’t 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 0’s (null suppression) and 1’s in this case too and abbreviating

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 dictionary’s translation.
Not only is it faster, but it compresses better because of the fact that it
doesn’t 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 file’s randomness. These programs