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Data Compression Michael J. Watts mike.watts.nz

Data Compression Michael J. Watts http://mike.watts.net.nz. Lecture Outline. What is compression? Huffman encoding Lempel-Ziv encoding Fraunhofer compression JPEG compression. What is Compression?. Reduction of the length of symbols used to represent data Symbols can be anything

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Data Compression Michael J. Watts mike.watts.nz

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  1. Data Compression Michael J. Watts http://mike.watts.net.nz

  2. Lecture Outline • What is compression? • Huffman encoding • Lempel-Ziv encoding • Fraunhofer compression • JPEG compression

  3. What is Compression? • Reduction of the length of symbols used to represent data • Symbols can be anything • Based on redundancy • Information theory • Lossless vs lossy • Degree of compression depends on amount of redundancy • Random data compression?

  4. What is Compression? • Represent symbols with codewords • One symbol == one codeword • Length of codeword < length of symbol • Many algorithms exist • Huffman • Lempel-Ziv • Fraunhofer

  5. Huffman Encoding • Based on probability (frequency) of symbols • Assign codewords as bits • Builds a binary tree based on probability • Frequent / high probability symbols at the top • Infrequent / low probability symbols lower down • Branches labelled with 0 and 1 • Frequent symbols get short bit strings • Infrequent symbols get longer bit strings

  6. Huffman Encoding • Algorithm • Arrange symbols in order of decreasing probability • Combine two symbols with lowest probability • Assign a new name, add their probabilities • Rebuild the list • Combine the next two lowest symbols • Repeat until there is one symbol, with probability of one • Build a binary tree • Form codewords by tracing down the tree to the symbol

  7. Huffman Encoding • Decompression is the opposite of compression • Follow bit sequence to a terminal node • Needs to see the entire data set • Must know symbol probabilities • Also combined with other techniques • MP3 encoding

  8. Lempel-Ziv • Dictionary based encoder • Lossless • Replaces phrases with tokens • Tokens smaller than the phrases • Converts input stream to compressed output stream • Doesn't need to see entire data set • Dictionary is built as it moves through the stream

  9. Lempel-Ziv • Separates input stream into tokens • Each token represents the shortest phrase that has not been seen • Tokens are numbered • Tokens contain other tokens • Compression is inefficient at the start • Better later • Larger dictionary

  10. Fraunhofer / MP3 Encoding • Lossy algorithm • Compression of audio data • Perceptual encoding • Psycho-acoustic model • Throws out what can't be heard • Frequency bands • Masking effects • Output is further compressed • Uses Huffman encoding

  11. MP3 Encoding • Only usable on audio • Part of the MPEG standard • DVDs • Rather widely used by itself

  12. JPEG Compression • Joint Photographic Experts Group • Used to compress images • Compresses groups of pixels • Uses a Discrete Cosine Transformation • DCT • Quantises the results of the DCT • Lossy! • Further compression is applied

  13. Summary • Compression is an application of information theory • Encodes long strings as shorter strings • All schemes depend on redundant / repetitive data • Common gotchas • A compression algorithm cannot compress its own output • Cannot easily compress completely random data • No / little redundancy

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