Recursively Indexed Quantization of Memoryless Sources

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Recursively Indexed Quantization of Memoryless
Sources

• Author Khalid Sayood, member IEEE
• Sangsin Na, member IEEE
• IEEE Transactions of Information theory Vol. 38,
  No. 5, Sep. 92
• Reporter ChiaHsing Lee, 8817586
• NCTU CSIE

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Outline

• Source coding scheme
• Recursive indexing scheme
• Recursive index quantizer
• Analysis of rate and distortion
• Conclusion

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Source coding scheme

• Encoder of source coding
• Complexity of binary encoder
• More input alphabets(y), more operations needed.
• Reduce alphabets size may introduce distortion of
  quantization

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Recursive indexing scheme

• An modulo operation
• Given 2 sets
• ,
• such that
• if i mK R
• In inverse,

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Recursively indexed quantizer

• Definition
• Given
• Quantizer of size K, step size , and are
  the smallest and largest output levels

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Recursively indexed quantizer

• Q(x)
• Nearest output level, Q(x)
• If
• , where
• If , and
• , where
• If , and

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Quantize and recursively index

• y be the output levels of , i.e
• ,
• if
• if

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Analysis of distortion

• Distortion of quantizer
• Granular error
• applied to source with
• Overload error
• no

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Analysis of rate

• Rate is determined by binary encoder
• Fixed-to-fixed length
• Another mapping relation
• Fixed-to-variable length
• Such like huffman coding or arithmetic coding

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Analysis of rate

• Fixed-to-fixed length
• Let be the number of symbols to represent
  level j
• , j1, 2, ..(N-1),

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Rate of recursively indexed quantizer

• Fixed-to-variable length

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Numerical Result

• RD curve for various size of Laplacian source

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Numerical Result
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Conclusion

• Advantage
• Avoid overload distortion
• Reduce distortion
• Reduce the input of binary encoder
• Reduce encoder complexity
• Need not modified original encoder