These programs are a file compressor and decompressor based on the
Limpel-Ziv algorithm.

The compression algorithm builds a string translation table that maps
substrings from the input stream into fixed-length codes. These codes
are used by the decompression algorithm to rebuild the compressor's table
and reconstruct the original data stream. In it's simplest form, the
algorithm can be stated as:
"If k is in the table, then is in the table."

The following comments were paraphrased from the VMS LZCOMP program
sources. The algorithm is from the article "A Technique for High
Performance Data Compression" by Terry A. Welch which appeared in IEEE
Computer Volume 17, Number 6 (June 1984), pp 8-19.

Compress:
1) Initialize table to single character strings.
2) Read first character. Set (the prefix string) to that
character.
3) Read next character, k.
4) If at end of file, output code and exit.
5) If k is in the table, set to k; goto step 3.
6) Output code .
7) Put k into table.
8) Set to k. Goto step 3.

is a code which represents a string in the table. When a new
character k is read in, the table is searched for k. If this
combination is found, is set to the code for that combination and the
next character is read in. Otherwise, this combination is added to the
table, the code is written to the output stream and is set to k.

The decompression algorithm builds an identical table by parsing each
received code into a prefix string and extension character. The
extension character is pushed onto the stack and the prefix string
translated again until it is a single character. This completes the
decompression. The decompressed code is then output by popping the stack
and a new entry is made in the table.

The algorithm breaks when the input stream contains the sequence
kkk, where k is already in the compressor's table. This
sequence is handled in step 3 below.

Decompress:
1) Read first input code, assign to , k, oldcode and
finchar. Output k.
2) Read next code , assign to incode. If end of file, exit.
3) If not in table (kkk case),
a) Push finchar onto stack.
b) Set and incode to oldcode.
4) If in table,
a) Push .char onto stack.
b) Set to .code.
c) Goto step 4.
5) Set oldcode and finchar to , output finchar.
6) While characters on stack pop stack and output character.
7) Add k to table.
8) Set oldcode to incode.
9) Goto step 2.

The algorithm used here has one additional feature. The output codes are
variable length. They start at nine bits. Once the number of codes
exceeds the current code size, the number of bits in the code is
increased. When the table is completely full, a clear code is
transmitted for the decompressor and the table is reinitialized. This
program uses a maximum code size of 12 bits for a total of 4096 codes.

The decompressor realizes that the code size is changing when it's table
size reaches the maximum for the current code size. At this point, the
code size is increased. Remember that the decompressor's table is
identical to the compressor's table at any point in the original data
stream.

My sources of reference while implementing these programs were the
following:

Bernie Eiben, DEC
Unix (tm) COMPRESS program sources
VMS LZCOMP/LZDCMP program sources (Martin Minow, DEC)
ARC file archiver sources (Thom Henderson, System Enhancement
Associates)