Lempel Ziv Welch

9 Key excerpts on "Lempel Ziv Welch"

• 

  eBook - PDF

  Image Processing and Analysis

  • Stan Birchfield(Author)
  • 2017(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  The process continues to the final subsequence of 1100, which is represented by (4,0) since it is 0 appended to dict [4], which itself is 0 appended to dict [2], which is the subsequence 11. If we assume that the dictionary has 16 entries, then each entry requires 5 bits (4 for the index, and 1 for the appended bit). Therefore, the original sequence of 48 bits has been trans-formed into a sequence of 5 # 15 5 75 bits, which might make it appear that Lempel-Ziv is not very good at compression. In practice, however, on longer input sequences the compres-sion ability of Lempel-Ziv is significant and—as mentioned above—approaches the entropy of the source. It is also important to keep in mind that there are many implementation details that are omitted from this simple example that can be used to further improve performance. 8.2.3 Lempel-Ziv-Welch Algorithm One variant of Lempel-Ziv is the Lempel-Ziv-Welch (LZW) algorithm, which also builds the dictionary on the fly as the data are compressed. The trick behind LZW is to notice that the bit appended to each dictionary entry is not needed. Therefore, a dictionary entry in LZW consists only of the index of the previous dictionary entry. The patented LZW algorithm is used by the GIF image file format but is not widely used anymore since GIF has largely been replaced by PNG. In fact, PNG stands for “PNG is not GIF” and was developed intentionally to avoid the patent restrictions † of LZW by reverting to the simpler version of Lempel-Ziv. † The patent has since expired. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 8.2 Lossless Compression 369 LZW encoding works as follows. An initial alphabet size is determined, and the diction-ary is initialized for each symbol of the alphabet.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Digital Image Processing and Analysis

  Image Enhancement, Restoration and Compression

  • Scott E Umbaugh(Author)
  • 2022(Publication Date)
  • CRC Press

    (Publisher)

  Standards for RLC have been defined by the International Telecommunications Union-Radio (ITU-R, previously CCIR). These standards, initially defined for use with FAX transmissions, have become popular for binary image compression. They use horizontal RLC, but postprocess the resulting RLC with a Huffman encoding scheme. Newer versions of this standard also utilize a 2-D technique where the current line is encoded based on a previous line. This additional processing helps to reduce the file size. These encoding methods provide compression ratios of about 15–20 for typical documents.

  8.2.4 Lempel–Ziv–Welch Coding

  The Lempel–Ziv–Welch (LZW) coding algorithm operates by encoding strings of data. For images, these strings of data correspond to sequences of pixel values. The algorithm creates a string table that contains the strings and their corresponding codes. The string table is updated as the file is read, with new codes being inserted whenever a new string is encountered. If a string is encountered that is already in the table, the corresponding code for that string is put into the compressed file.

  LZW coding uses code words with more bits than the original data. For example, with 8-bit image data, an LZW coding method could employ 10-bit words. The corresponding string table would then have 210  = 1,024 entries. This table consists of the original 256 entries, corresponding to the original 8-bit data, and allows 768 other entries for string codes. The string codes are assigned during the compression process, but the actual string table is not stored with the compressed data. During decompression, the information in the string table is extracted from the compressed data itself.

  For the GIF and TIFF image file formats, the LZW algorithm was specified, but there was some controversy over this since the algorithm was patented. However, the patent expired in 2003. Before 2003, since these image formats were widely used, other methods similar in nature to the LZW algorithm were developed to be used with these image file formats. Similar versions of this algorithm include the adaptive Lempel–Ziv, used in the UNIX compress function, and the Lempel–Ziv 77 algorithm, used in the UNIX gzip function. Note that the tar utility in most Linux distributions can use gzip via the -z flag, and the 7-Zip

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  The Essential Guide to Image Processing

  • Alan C. Bovik(Author)
  • 2009(Publication Date)
  • Academic Press

    (Publisher)

  A popular lossless universal coding scheme is a dictionary-based coding method developed by Ziv and Lempel in 1977 [ 17 ] and known as Lempel-Ziv-77 (LZ77) coding. One year later, Ziv and Lempel presented an alternate dictionary-based method known as LZ78. Dictionary-based coders dynamically build a coding table (called dictionary) of variable-length symbol strings as they occur in the input data. As the coding table is constructed, fixed-length binary codewords are assigned to the variable-length input symbol strings by indexing into the coding table. In Lempel-Ziv (LZ) coding, the decoder can also dynamically reconstruct the coding table and the input sequence as the code bits are received without any significant decoding delays. Although LZ codes do not explicitly make use of the source probability distribution, they asymptotically approach the source entropy rate for very long sequences [ 5 ]. Because of their adaptive nature, dictionary-based codes are ineffective for short input sequences since these codes initially result in a lot of bits being output. Short input sequences can thus result in data expansion instead of compression. There are several variations of LZ coding. They mainly differ in how the dictionary is implemented, initialized, updated, and searched. Variants of the LZ77 algorithm have been used in many other applications and provided the basis for the development of many popular compression programs such as gzip, winzip, pkzip, and the public-domain Portable Network Graphics (PNG) image compression format. One popular LZ coding algorithm is known as the LZW algorithm, a variant of the LZ78 algorithm developed by Welch [ 18 ]. This is the algorithm used for implementing the compress command in the UNIX operating system. The LZW procedure is also incorporated in the popular CompuServe GIF image format, where GIF stands for Graphics Interchange Format

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Mathematical Tools in Signal Processing with C++ and Java Simulations

  • Willi-Hans Steeb(Author)
  • 2005(Publication Date)
  • WSPC

    (Publisher)

  This method uses a sliding window method while compressing. The data that is within the range of the window is what is active in the algorithm. LZSS was im- plemented by Storer and Szymanski. It addressed the problem of inefficient use of space in the token, as well as how comparisons are done. The LZ78 method drops all of the things that made the previous methods slow and cumbersome. Mainly, instead of having file buffers, which require several file pointers inside the file, LZ78 simply breaks input into phases to be processed. In this way it moves sequentially through the file. Like LZ77 and LZ78, LZW is a dictionary (also called codebook or string table) based compression algorithm and does not perform any analysis of the input text. The addition of T. Welch in 1984 is an initialisation of the dictionary to the standard 256 ASCII characters, represented by the codes 0 - 255. By having this preestablished starting point, even the smaller files were able 13.2. LZW COMPRESSION 209 to be compressed, as more of the code was able to be represented by the dictionary entries. Larger files would have slight gain in the efficiency of their encoding. LZW is widely known for its application in GIF and in the V.42 communi- cation standard. The idea behind the LZW algorithm is simple but there are implementation details that one needs to take care of. The Lempel, Ziv and Welch compression relies on reoccurrence of bytes sequences (strings) in its input. It maintains a table mapping input strings to their associated output codes. The table initially contains mappings for all possible strings of length one. Input is taken one byte at a time to find the longest initial string present in the table. The code for that string is output and then the string is extended with one more input byte, b. A new entry is added to the table mapping the extended string to the next unused code (obtained by incrementing a counter).

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Communication Systems

  • Simon Haykin, Michael Moher(Authors)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  matter to the decoder. Any one of them will produce the same output sequence. (Some more advanced algorithms use the first occurrence as it may be represented by fewer bits in general.) The decoding algorithm is much simpler than the encoding algorithm, as the decoder knows exactly where to look in the decoded stream (search buffer) to find the matching string. The decoder starts with an empty (all zeros) search buffer, then: • For each codeword received, the decoder reads the string from the search buffer of the indicated position and length and appends it to the right-hand end of the search buffer. • The next character is then appended to the search buffer, • The search buffer is then slid to the right so the pointer occurs immediately after the last known symbol and the process is repeated. From the example described here, we note that, in contrast to Huffman coding, the Lempel–Ziv algorithm uses fixed length codes to represent a variable number of source symbols. If errors occur in the transmission of a data sequence that has been encoded with the Lempel–Ziv algorithm, the decoding is susceptible to error propagation. For short sequences of characters, the matching strings found in the search buffer are unlikely to be very long. In this case, the output of the Lempel–Ziv algorithm may be a ‘‘compressed’’ sequence, which is longer than the input sequence. The Lempel–Ziv algorithm only achieves its true advantage when processing long strings of data, for example, large files. For a long time, Huffman coding was unchallenged as the algorithm of choice for lossless data compression. Then, the Lempel–Ziv algorithm took over almost completely from the Huffman algorithm and became the standard algorithm for file compression. In recent years, more advanced data compression algorithms have been developed building upon the ideas of Huffman, Lempel, and Ziv.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Elements of Multimedia

  • Sreeparna Banerjee(Author)
  • 2019(Publication Date)
  • Chapman and Hall/CRC

    (Publisher)

  One finds that three characters are matched and the (offset, length) = (12,3). Hence, the final compressed output is given by, [ABB………………….DERR, (4,5), FEE, (12,3) …]

  Decompression: A sliding window of identical size is required. A look-ahead window is not required. Decompress data into the sliding window when (offset, length) is detected. The decompressor points to the position of offset and begins to copy the specified number of symbols and to shift0 them into the same sliding window.

  Restrictions of the algorithm: To keep the runtime and buffering capacity in an acceptable range, the addressing must be limited to a certain maximum value. Contents exceeding this range will not be considered for coding and will not be covered by the size of the addressing pointer.

  Compression efficiency of the algorithm: The achievable compression rate depends only on repeating sequences. Other types of redundancy like an unequal probability distribution of the set of symbols cannot be reduced. For that reason, the compression of a pure LZ77 implementation is relatively low.

  A significantly better compression rate can be achieved by combining LZ77 with an additional entropy coding algorithm, for example, the Huffman or Shannon-Fano coding. The widespread deflate compression method (e.g., for GZIP or ZIP) uses Huffman codes.

  7.3.6.4      LZW Algorithm

  The LZW compression method was derived from LZ78 by Jacob Ziv and Abraham Lempel and later invented by Terry A. Welch in 1984 who had published his considerations in the article “A Technique for High-Performance Data Compression.” LZW is an important part of a variety of data formats. Graphic formats like gif, tiff (optional), and Postscript use LZW for entropy coding.

  LZW is a dictionary-based algorithm that contains any byte sequence already coded. The compressed data exceptionally consist of indices to this dictionary. Before starting, the dictionary is preset with entries for the 256 single byte symbols. Any entry following represents sequences larger than one byte. The algorithm presented by Terry Welch defines mechanisms to create the dictionary and to ensure that it will be identical for both the encoding and decoding process.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  The Communications Handbook

  • Jerry D. Gibson(Author)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  The dictionary can be static or adaptive. Most of the adaptive schemes have been inspired by two papers by Ziv and Lempel in 1977 and 1978 [Bell, Cleary, and Witten, 1990]. The 1977 algorithm and its derivatives use a portion of the already encoded string as the dictionary. For example, consider the encoding of the string abra , where the underlined portion of the string has already been encoded. The string abra could then be encoded by simply sending the pair (7,4), where the first number is the location of the previous occurrence of the string relative to the current position and the second number is the length of the match. How far back we search for a match depends on the size of a prespecified window and may include all of the history. The 1978 algorithm actually builds a dictionary of all strings encountered. Each new entry in the dictionary is a previous entry followed by a letter from the source alphabet. The dictionary is seeded with the letters of the source alphabet. As the coding progresses, the entries in the dictionary will consist of longer and longer strings. The most popular derivative of the 1978 algorithm is the LZW algorithm, a variant of which is used in the UNIX compress command, as well as the GIF image compression format, and the V.42-bis compression standard. We now describe the LZW algorithm. The LZW algorithm starts with a dictionary containing all of the letters of the alphabet [Bell, Cleary, and Witten, 1990]. Accumulate the output of the source in a string s as long as the string s is in the dictionary. If the addition of another letter α from the source output creates a string s ∗ α that is not in the dictionary, send the index in the dictionary for s , add the string s ∗ α to the dictionary, and start a new string that begins with the letter α . The easiest way to describe the LZW algorithm is through an example.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Multimedia Computing

  • Gerald Friedland, Ramesh Jain(Authors)
  • 2014(Publication Date)
  • Cambridge University Press

    (Publisher)

  If it reaches the maximum number of entries, the algorithm continues with the current dictionary under the hope that the output file does not become too long. If it determines that the out-put length has passed a threshold, it recompresses the data by creating an additional dic-tionary. The Unix compress tool uses LZC. However, the LZC is patented, so users must pay a license fee. LZW, a common LZ78 variant, does not store the following symbol explicitly but as the first symbol of the following token. The dictionary starts with all possible input symbols as first entries. This leads to a more compact code and lets users define the input symbols (which can vary in bit length). The popular Graphics Interchange Format (GIF) uses the LZW variant. Although initially popular, enthusiasm for LZ78 dampened, mostly because parts of it were patent protected in the United States. The patent for the LZW algo-rithm was strictly enforced and led to the creation of the patent-free PNG image format. As mentioned earlier, the RLE algorithm is most useful when characters repeat often, and Huffman compression is most useful when you can build a nonuniformly distributed probability model of the underlying data. The LZ algorithms are especially useful with text-like data – that is, data where strings of limited but variable lengths repeat themselves. Typical compression ratios are (original:compressed) 2:1 to 5:1 or more for text files. In contrast to RLE and Huffman, LZ algorithms need a certain input file size to amortize. Compressing a file with just a few bits, such as our example from the beginning of the chapter, won’t yield a very good compression result. The Unix program “tar,” for example, therefore concatenates all files into one large archive and then invokes “gzip” on the entire archive. Arithmetic Coding Arithmetic encoding approaches seek to overcome Huffman encoding’s limitations – namely, that messages can only be encoded using an integer number of bits per symbol.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Bioinformatics Programming in Python

  A Practical Course for Beginners

  • Ruediger-Marcus Flaig(Author)
  • 2011(Publication Date)
  • Wiley-Blackwell

    (Publisher)

  This is not really a serious drawback as pictures are generally not in the gigabyte range, and more efficient compression agorithms actually pose a security threat. A file may be hand-crafted in such a way that an algorithm such as LZW, described below, creates a terabyte monstrosity when being unpacked – a common trick of hackers to blow up test programs for incoming email (mailbomb). It will also be noted that, even though the algorithm performs no modification of the data unless at least a minimum of benefit can be achieved, still the addition of a few “meta” bytes to the compressed file is inevitable to store necessary information, so there may be files that actually increase in size. This is a general problem of compression algorithms. There cannot be any algorithm that will be able to reduce the size of every file. This can be argued for mathematically, but plain logic suffices. If there were such an algorithm, its output files could be compressed over and over again, until every primary file is compressed to the size of one byte. Obviously, this is nonsense. A compression algorithm uses regularities to reduce file size. With completely chaotic data, no compression is possible, and vice versa. As has been pointed out during the SETI project, ideally compressed data show no regularities whatsoever. 16.3 The LZW compression algorithm 16.3.1 History. In 1978, Jacob Ziv and Abraham Lempel developed the LZ78 compression algorithm (US Patent 7 4,464,650), which was improved by Terry Welch, who published it in 1984. The improved algorithm 8 has since been known as the LZW algorithm and has gained widespread acceptance, as it is straightforward and does not require any statistical voodoo

  Sign up to read

  Learn more about book