LZW compression algorithm

Lempel–Ziv–Welch compression algorithm

Student: Coordinator: Vlad Alexandru Alexandr u Pasca Cristian !ihaescu

Dr. Dr. ng.

Lempel–Ziv–Welch "LZW# is a universal lossless data compression algorithm created $% A$raham Lempel& 'aco$ Ziv& and (err% Welch. t )as pu$lished $% Welch in *+,- as an improved implementation o the LZ/, algorithm pu$lished $% Lempel and Ziv in *+/,. (he algorithm is simple to implement& and has the potential or ver% high throughput in hard)are implementations. (he $asic plan complements the $asic plan or 0u1man coding. 2ather than maintain a ta$le o varia$le3length code)ords or 4xed3length patterns in the input& )e maintain a ta$le o 4xed3length code)ords or varia$le3length patterns in the input. A surprising added eature o the method is that& $% contrast )ith 0u1man encoding& )e do not have to encode the ta$le. (he program )or5s in the ollo)ing )a% : it encodes se6uences o ,3 $it data as 4xed3length *73$it codes. (he codes rom 8 to 799 represent *3 character se6uences consisting o the corresponding ,3$it character& and the codes 79 through -8+9 are created in a dictionar% or se6uences encountered in the data as it is encoded. At each stage in compression& input $%tes are gathered into a se6uence until the next character )ould ma5e a se6uence or )hich there is no code %et in the dictionar%. (he code or the se6uence ")ithout that character# is added to the output& and a ne) code "or the se6uence )ith that character# is added to the dictionar%. 0ere is a high level vie) o the encoding algorithm : *. nitiali;e the dictionar% to contain all strings o length one. 7. mit the dictionar% index or W to output and remove W rom the input. -. Add W ollo)ed $% the next s%m$ol in the input to the dictionar%. 9. ?o to Step 7.   (he decoding algorithm )or5s $% reading a value rom the encoded input and outputting the corresponding string rom the initiali;ed dictionar%. At the same time it o$tains the next value rom the input& and adds to the dictionar% the concatenation o the string @ust output and the 4rst character o the string o$tained $% decoding the next input value. (he decoder then proceeds to the next input value ")hich )as alread% read in as the next value in the previous pass# and repeats the process until there is no more input& at )hich point the 4nal input value is decoded )ithout an% more additions to the dictionar%. 0ere is a high level vie) o the decoding algorithm :

*. 7. =. -.

Write the current string val. 2ead a code)ord x rom the input. Set s to the value associated )ith x in the s%m$ol ta$le. Associate the next unasssigned code)ord value to val B c in the s%m$ol ta$le& )here c is the 4rst character o s. 9. Set the current string val to s. LZW compression example. (he 4gure $elo) gives details o the operation o LZW compression or the example input ABRACADABRABRABRA.
 (he input is */ ASC characters o / $its each or a total o **+ $its the output is *7 code)ords o , $its each or a total o + $itsEa compression ratio o ,7 percent even or this tin% example. And the expansion :

Uses: LZW compression $ecame the 4rst )idel% used universal data compression method on computers. A large >nglish text 4le can t%picall% $e compressed via LZW to a$out hal its original si;e. LZW )as used in the pu$lic3domain program compress& )hich $ecame a more or less standard utilit% in Fnix s%stems circa *+,. t has since disappeared rom man% distri$utions& $oth $ecause it inringed the LZW patent and $ecause g;ip produced $etter compression ratios using the LZ//3$ased D> algorithm.