Compression

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Compression
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What is Compression?

• Process of reducing the amount of data required
  to represent a given quantity of information
• Same amount of information represented using
  fewer bits -- relies on the notion of data
  redundancy
• Sometimes called packing, coding or zipping

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Why Compress?

• Uncompressed data requires considerable storage
  capacity
• Critical for delivery of motion video and audio
• Without compression, not enough bandwidth to
  deliver a new screen image every 1/30 of a second
• We also compress static images

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Compression Applications

• Storage -- data is compressed before being
  stored, decompressed before being retrieved.
• Communications -- sender compresses data before
  sending it over line, receiver decompresses it
  after receiving it.

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Static Screen Storage Requirements

• In a typical 640x480 pixel window
• Text 2 bytes of storage for each character, 8x8
  pixels for each character in display -- 9600
  bytes76,800 bits
• Color display (very simple mode) single pixel of
  a bitmap can take on any of 256 colors. Thus, 1
  byte per pixel -- 307,200 bytes2,457,600 bits

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Continuous Media Storage and Bandwidth
Requirements

• For one second of playback
• uncompressed audio signal of telephone quality
• sampled at 8kHz (8k cycles per second)
• quantized with 8bits/sample
• Bandwidth requirement is 64kbits/second
• Storage is 64kbits for 1 second of playback.

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Continuous Media Storage and Bandwidth
Requirements (continued)

• For one second of playback
• uncompressed stereo audio signal of CD quality
• sampled at 44.1kHz (44.1k cycles per second)
• quantized with 16bits/sample
• Bandwidth requirement is 705.6x103 bits/second
• Storage is 705.6x103 bits for 1 second of
  playback.

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Continuous Media Storage and Bandwidth
Requirements (continued)

• For one second of playback
• video (European PAL standard)
• video has 625 lines and 25 frames per second
• luminance sampled at 13.5MHz
• chrominance sampled at 6.75MHz (2 components)
• uniform 8 bit coding of each sample
• Bandwidth requirement is 216x106 bits/second
• Storage for 640x480pixels with 3 bytes/pixel (1
  luminance, 2 chrominance) 921,600 bytes/frame
  or 230.4x105 bytes for 1 second 184.32x106 bits
  for 1 second of playback

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Compression Concepts

• Compression ratio size of original file divided
  by size of compressed file
• Data quality Lossy compression ignores
  information that the viewer may not miss and
  therefore information may be lost. Lossless
  compression preserves original data precisely.
  Note This has nothing to do with information
  that may be lost in analog-to-digital conversion.
• Compression speed time it takes to
  compress/decompress.

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Types of Compression

• Entropy encoding -- lossless. Data considered a
  simple digital sequence and semantics of data are
  ignored.
• Source encoding -- lossy. Takes semantics of
  data into account. Amount of compression depends
  on data contents.
• Hybrid encoding -- combination of entropy and
  source. Most multimedia systems use these.

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Types of Compression

• Entropy encoding -- lossless.
• Data in data stream considered a simple digital
  sequence and semantics of data are ignored.
• Short Code words for frequently occurring
  symbols. Longer Code words for more infrequently
  occurring symbols
• For example E occurs frequently in English, so
  we should give it a shorter code than Q
• Examples of Entropy Encoding
• Run-length coding
• Huffman coding
• Arithmetic coding

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Entropy Encoding

• Run-Length Coding
• Runs (sequences) of data are stored as a single
  value and count, rather than the individual run.
• Example
• This
• WWWWWWWWWWWWBWWWWWWWWWWWWBBBWWWWWWWWWWWWWWWWWWWWWW
  WWBWWWWWWWWWWWWWW
• Becomes
• 12WB12W3B24WB14W
• Get more info on Wikipedia

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Entropy Encoding

• Huffman Coding
• Use of a variable length code table for encoding
  a source symbol where the variable-length code
  table has been derived in a particular way based
  on the estimated probability of occurrence for
  each possible value of the source symbol.
• Commonly Used as a final stage of compression
• Get more info on Wikipedia

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Entropy Encoding

• Arithmetic Coding
• Encodes the entire message into a single number,
  a fraction n where (0.0 n lt 1.0)
• Get more info on Wikipedia

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Types of Compression

• Source Encoding lossy
• Takes semantics of data into account. Amount of
  compression depends on data contents.
• This method is one where compressing data and
  then decompressing it retrieves data that may
  well be different from the original, but is
  "close enough" to be useful in some way.
• Used frequently on the Internet and especially in
  streaming media and telephony applications.
• Examples Discreet-Cosine Transform, Subsampling,
  Differential Pulse Code Modulation (DPCM)

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Source Encoding

• Discreet Cosine Transform (DCT)
• A Fourier-related transform similar to the
  discrete Fourier transform (DFT), but using only
  real numbers.
• Often used in signal and image processing.
• Maps values from spatial domain to frequency
  domain -- image areas with low frequency (large
  blocks of single color) are compressed more
  efficiently
• Used in JPEG, MJPEG, MPEG, and DV Compression
• Get more info on Wikipedia

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Source Encoding

• Wavelet-Based Coding
• Produces as many coefficients as there are pixels
  in the image (i.e. there is no compression yet
  since it is only a transform). These coefficients
  can then be compressed more easily because the
  information is statistically concentrated in just
  a few coefficients. This principle is called
  transform coding. After that, the coefficients
  are quantized and the quantized values are
  entropy encoded and/or run length encoded.
• Well suited for image compression
• Get more info on Wikipedia

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Source Encoding

• Differential Pulse Code Modulation
• Store all bits of first sample and then store
  only how next sample differs
• Used in digital telephone systems and is also the
  standard form for digital audio in computers and
  various compact disc formats.
• Get more info on Wikipedia

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Hybrid Encoding

• JPEG
• image compression using a discrete cosine
  transform, then quantization, then Huffman coding
  
• MP3
• A part of the MPEG-1 standard for sound and music
  compression, using subbanding and MDCT,
  perceptual modeling, quantization, and Huffman
  coding
• JPEG 2000
• image compression using wavelets, then
  quantization, then entropy coding

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More on Compression

• How Compression Works