Data Compression. Reduces storage space and hence storage cost. Compression ratio = original data size /


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1 Dt Compression Reduce the size of dt. Reduces storge spce nd hence storge cost. Compression rtio = originl dt size / compressed dt size Reduces time to trnsmit nd retrieve dt. Reduces the storge requirement. (prticulrly useful in emedded systems, network ridges, routers etc.) Adpted from Shni s Dt Structures nd Applictions slides.
2 Lossless And Lossy Compression compresseddt = compress(originldt) decompresseddt = decompress(compresseddt) When originldt = decompresseddt, the compression is lossless. When originldt!= decompresseddt, the compression is lossy.
3 Lossless And Lossy Compression Lossy compressors generlly otin much higher compression rtios thn do lossless compressors. Sy vs.. Lossless compression is essentil in pplictions such s text file compression. Lossy compression is cceptle in mny imging pplictions. In video trnsmission, slight loss in the trnsmitted video is not noticed y the humn eye.
4 Text Compression Lossless compression is essentil. Populr text compressors such s zip nd Unix s compress re sed on the LZW (LempelZivWelch) method.
5 LZW Compression Chrcter sequences in the originl text re replced y s tht re dynmiclly determined. The tle is not end into the compressed text, ecuse it my e reconstructed from the compressed text during decompression.
6 LZW Compression Assume the letters in the text re limited to {, }. In prctice, the lphet my e the 56 chrcter ASCII set. The chrcters in the lphet re ssigned numers eginning t. The initil tle is:
7 LZW Compression Originl text = Compression is done y scnning the originl text from left to right. Find longest prefix p for which there is in the tle. Represent p y its pcode nd ssign the next ville numer to pc, where c is the next chrcter in the text tht is to e compressed.
8 LZW Compression Originl text = p = pcode = c = Represent y nd enter into the tle. Compressed text =
9 LZW Compression Originl text = Compressed text = p = pcode = c = Represent y nd enter into the tle. Compressed text =
10 LZW Compression Originl text = Compressed text = p = pcode = c = Represent y nd enter into the tle. Compressed text =
11 LZW Compression 5 Originl text = Compressed text = p = pcode = c = Represent y nd enter into the tle. Compressed text =
12 LZW Compression 5 6 Originl text = Compressed text = p = pcode = c = Represent y nd enter into the tle. Compressed text =
13 LZW Compression Originl text = Compressed text = p = pcode = c = Represent y nd enter into the tle. Compressed text =
14 LZW Compression Originl text = Compressed text = p = pcode = 5 c = Represent y 5 nd enter into the tle. Compressed text = 5
15 LZW Compression Originl text = Compressed text = 5 p = pcode = 8 c = Represent y 8 nd enter into the tle. Compressed text = 58
16 LZW Compression Originl text = Compressed text = 58 p = pcode = 8 c = null Represent y 8. Compressed text = 588
17 Code Tle Representtion Dictionry. Pirs re (, element) = (,). Opertions re : get() nd put(, ) Limit numer of s to. Use hsh tle. Convert vrile length s into fixed length s. Ech hs the form pc, where the string p is tht is lredy in the tle. Replce pc with (pcode)c.
18 Code Tle Representtion
19 Implementtion of LZW lgorithm void Compress() {// LempelZivWelch compressor. ChinHshTle<element, long> h(d); element e; for (int i = ; i < lph; i++) {// initilize e. = i; e. = i; h.insert(e); } int used = lph; // s used // input nd compress unsigned chr c; in.get(c); long p = c; // prefix
20 Implementtion of LZW lgorithm if (!in.eof()) {// file length is > do {// process rest of file in.get(c); if (in.eof()) rek; // finished long k = (p << ByteSize) + c; // see if for k in dictionry if (h.serch(k, e)) p = e.; // yes else {// k not in tle output(p); if (used < s) // crete new {e. = used++; e. = (p << ByteSize) c; h.insert(e);} p = c;} } while (true); output(p); if (sttus) {c = LeftOver << excess; out.put(c);} } out.close(); in.close(); }
21 LZW Decompression Originl text = Compressed text = 588 Convert s to text from left to right. represents. Decompressed text = pcode = nd p =. p = followed y next text chrcter (c) is entered into the tle.
22 LZW Decompression Originl text = Compressed text = 588 represents. Decompressed text = pcode = nd p =. lstp = followed y first chrcter of p is entered into the tle.
23 LZW Decompression Originl text = Compressed text = 588 represents. Decompressed text = pcode = nd p =. lstp = followed y first chrcter of p is entered into the tle.
24 LZW Decompression Originl text = Compressed text = 588 represents Decompressed text =. pcode = nd p =. lstp = followed y first chrcter of p is entered into the tle.
25 LZW Decompression 5 Originl text = Compressed text = 588 represents Decompressed text =. pcode = nd p =. lstp = followed y first chrcter of p is entered into the tle.
26 LZW Decompression 5 6 Originl text = Compressed text = 588 represents Decompressed text =. pcode = nd p =. lstp = followed y first chrcter of p is entered into the tle.
27 LZW Decompression Originl text = Compressed text = represents Decompressed text =. pcode = 5 nd p =. lstp = followed y first chrcter of p is entered into the tle.
28 LZW Decompression Originl text = Compressed text = represents??? When is not in the tle, its is lstp followed y first chrcter of lstp. lstp = So 8 represents.
29 LZW Decompression Originl text = Compressed text = represents Decompressed text =. pcode = 8 nd p =. lstp = followed y first chrcter of p is entered into the tle.
30 Code Tle Representtion Dictionry. Pirs re (, element) = (, wht the represents) = (, Key). Opertions re : get() nd put(, ) Keys re integers,,, Use D rry Tle. Tle[] = Key. Ech hs the form pc, where the string p is tht is lredy in the tle. Replce pc with (pcode)c.
31 Compression. Time Complexity O(n) expected time, where n is the length of the text tht is eing compressed. Decompression. O(n) time, where n is the length of the decompressed text.
Data Compression. Lossless And Lossy Compression. Text Compression. Lossless And Lossy Compression. Lossless compression is essential.
Dt Compression Lossless And Lossy Compression Reduce the size of dt. ƒ Reduces storge spce nd hence storge cost. Compression rtio = originl dt size/compressed dt size ƒ Reduces time to retrieve nd trnsmit
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