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For text files, the delay is short because the table isn't
very long. For programs, however, the delay is quite
noticeable because all 256 possible byte values are usually
used.
Trees are an excellent tool to understanding the theory
behind Huffman squeezing. Oddly enough, ARC doesn't use this
concept to any advantage at all.
ARC VERSION 2.20 PAGE - 35
Lempel-Zev-Welch(3), or LZW compression is used to
'crunch' files. It is really quite amazing since it almost
always is chosen as the most efficient compressor and can be
performed 'on the fly' without first having to analyze a
files contents. It takes advantage of the fact that certain
sequences of bytes occur more often than others in typical
data files.
For example, in an ascii listing of a BASIC program,
the BASIC keywords, INPUT, GOTO, GOSUB and others occur with
abundance. In this document, words like "ARC", "compress",
"squeeze", or characters sequences like ". " or ", " occur
quite often. If we could replace these character sequences
with shorter codes, we would end up with a shorter output
file. When you enter a line of BASIC code, the BASIC
interpreter does just that by looking to see if any of
keywords in the line occur in its keyword table. ARC does
something similar, but prepares the keyword table from
scratch for each file it crunches.
The LZW algorithm reads the input file sequentially and
remembers sequences of characters that have occurred
previously in the file and replaces subsequent occurrences
with shorter codes. It prepares a 'string table' as it goes
through the file which is used to generate the codes. Again,
we could think of the string table as a tree, but this time
it is a much more complicated tree since each node can have
as many as 256 branches!
Lets take a simplified example.
Suppose that the alphabet consisted only of the letters
a,b, and c and our file is "abababacababaa".
We start by assigning a code to each letter in our
alphabet. Thus a=1 b=2 and c=3.
The first character we encounter is an "a". It is in
the string table, so we save the "a" as a prefix string and
get another character which we call the extension. The next
character is a "b", so we now have the sequence "ab", which
is not in the string table. Whenever the current
prefix+extension string we have in memory is not in the
string table, we do three things. We send the code for the
prefix to the output file, add the prefix+extension string
to our string table, and make the extension the new prefix.
Thus we code out a "1" and set the prefix equal to "2", the
code for "b" and add "ab" to the string table as code 4.
____________________
3. Welch, Terry A., "A TECHNIQUE FOR HIGH PERFORMANCE DATA
COMPRESSION", IEEE COMPUTER, June 1984.
ARC VERSION 2.20 PAGE - 36
We now have "b" as the prefix, and read in the next
character from the input file as our new extension. The next
character is an "a". "ba" is not in the string table, so we
code out the "b", add "ba"=5 to the string table, and make
"a" the new prefix.
Now is when it starts to get interesting. We now have
"a" as the prefix and read in "b" as the next extension.
This time "ab" is in the string table, so we make the code
for "ab" the new prefix and get another extension. The next
character is an "a", "aba" is not in the string table so we
send the prefix code "ab"=4 to the output file and add
"aba"=6 to our string table. Next time we encounter the
sequence "aba", we'll only have to send one code in the
place of three characters!
The prefix is now "a". We get the next character "b".
"ab" is in the string table, so we make "ab"=4 the prefix
and get another character. This time its an "a". "aba" is
also in the string table, so we we make "aba"=6 our prefix
and get another extension. This time its a "c", so we code