Lecture Notes on Data Compression | COP 3530, Study notes of Data Structures and Algorithms

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Data Compression

• Reduce the size of data.
  • Reduces storage space and hence storage cost.
    • Compression ratio = original data size/compressed data size
      • Reduces time to retrieve and transmit data.

Lossless And Lossy Compression

• compressedData = compress(originalData) • decompressedData = decompress(compressedData) • When originalData = decompressedData, the

compression is lossless.

• When originalData != decompressedData, the

compression is lossy.

Text Compression

• Lossless compression is essential.^ •Popular text compressors such aszip and Unix’s compress are basedon the LZW (Lempel-Ziv-Welch)method.

LZW Compression

• Character sequences in the original text are

replaced by codes that are dynamicallydetermined.

• The code table is not encoded into the

compressed text, because it may bereconstructed from the compressed text duringdecompression.

LZW Compression

code^ key

0 a

1 b

• Original text = abababbabaabbabbaabba • Compression is done by scanning the original text

from left to right.

• Find longest prefix p for which there is a code in the

code table.

• Represent p by its code pCode and assign the next

available code number to pc, where c is the nextcharacter in the text that is to be compressed.

LZW Compression

code^ key

0 a

1 b

(^2) ab

• Original text = abababbabaabbabbaabba • p = a • pCode = 0 • c = b • Represent a by 0 and enter ab into the code table. • Compressed text = 0

LZW Compression

code^ key

0 a

1 b

(^2) ab

(^3) ba

(^4) aba

• Original text =

abababbabaabbabbaabba

• Compressed text = 01 • p = ab • pCode = 2 • c = a • Represent ab by 2 and enter aba into the code table. • Compressed text = 012

LZW Compression

code^ key

0 a

1 b

(^2) ab

(^3) ba

(^4) aba

(^5) abb

• Original text =

abababbabaabbabbaabba

• Compressed text = 012 • p = ab • pCode = 2 • c = b • Represent ab by 2 and enter abb into the code table. • Compressed text = 0122

LZW Compression

• Original text =

abababbabaabbabbaabba

• Compressed text = 01223

code^ key

0 a

1 b

(^2) ab

(^3) ba

• p = ba • pCode = 3 • c = a • Represent ba by 3 and enter baa into the code table. • Compressed text = 012233

(^4) aba

(^6) bab

(^7) baa

abb

LZW Compression

• Original text =

abababbabaabbabbaabba

• Compressed text = 012233

code^ key

0 a

1 b

(^2) ab

(^3) ba

• p = abb • pCode = 5 • c = a • Represent abb by 5 and enter abba into the code

table.

• Compressed text = 0122335

(^4) aba

(^6) bab

(^7) baa

(^8) abba

abb

LZW Compression

code • Original text = abababbabaabbabbaabba • Compressed text = 01223358

key

0 a

1 b

(^2) ab

(^3) ba

• p = abba • pCode = 8 • c = null • Represent abba by 8. • Compressed text = 012233588

(^4) aba

(^6) bab

(^7) baa

(^8) abba

(^9) abbaa

abb

Code Table Representation

• Dictionary.
  • Pairs are (key, element) = (key,code). – Operations are : get(key) and put(key, code)
    • Limit number of codes to 2

• Use a hash table. code^ key^ – Convert variable length keys into fixed length keys.^ – Each key has the form pc, where the string p is a key thatis already in the table.^ – Replace pc with (pCode)c.

0 a

1 b

(^2) ab

(^3) ba

(^4) aba

(^6) bab

(^7) baa

(^8) abba

(^9) abbaa

abb

LZW Decompression

code^ key

0 a

1 b

• Original text = abababbabaabbabbaabba • Compressed text = 012233588 • Convert codes to text from left to right. • 0 represents a. • Decompressed text = a • pCode = 0 and p = a. • p = a followed by next text character (c) is entered

into the code table.

LZW Decompression

code^ key

0 a

1 b

(^2) ab

• Original text = abababbabaabbabbaabba • Compressed text = 012233588 • 1 represents b. • Decompressed text = ab • pCode = 1 and p = b. • lastP = a followed by first character of p is entered

into the code table.