Wyner-Ziv Coding of Video - Towards Practical Distributed Coding -

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Wyner-Ziv Coding of Video - Towards Practical
Distributed Coding -
Bernd Girod Information Systems
Laboratory Stanford University
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Outline

• Distributed lossless compression (Slepian-Wolf
  coding)
• Simple examples
• Slepian-Wolf Theorem
• Slepian-Wolf coding vs. systematic channel coding
• Turbo codes for compression
• Lossy compression with side information
  (Wyner-Ziv coding)
• Wyner-Ziv Theorem
• Optimal quantizer design with Lloyd algorithm
• Application to video coding
• Low complexity video coding
• Error-resilient video transmission

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Simple Example
Source A
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Simple Example - Revisited
Source A
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Compression with Side Information
Source A/B
Encoder
Decoder
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Distributed Compression of Dependent Sources
Source X
Encoder X
X
Joint Decoder
Y
Source Y
Encoder Y
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Achievable Rates for Distributed Coding Example
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General Dependent i.i.d. Sequences
Slepian, Wolf, 1973
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Distributed Compression and Channel Coding
Source XY
Encoder
Decoder
P

• Idea
• Interpret Y as a noisy version of X with
  channel errors D
• Encoder generates parity bits P to protect
  against errors D
• Decoder concatenates Y and P and performs
  error-correcting decoding

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Practical Slepian-Wolf Encoding

• Coset codes Pradhan and Ramchandran, 1999
• Trellis codes Wang and Orchard, 2001
• Turbo codes
• Garcia-Frias and Zhao, 2001
• Bajcsy and Mitran, 2001
• Aaron and Girod, 2002
• LDPC codes Liveris, Xiong, and Georghiades,
  2002

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Compression by Turbo Coding
L bits in
L bits
Systematic Convolutional Encoder Rate
Systematic Convolutional EncoderRate
L bits
Aaron, Girod, DCC 2002
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Turbo Decoder
Pchannel
SISO Decoder
Pa posteriori
Pextrinsic
Pa priori
L bits out
Pextrinsic
Pa priori
SISO Decoder
Pchannel
Pa posteriori
Aaron, Girod, DCC 2002
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Results for Compression of Binary Sequences

• X,Y dependent binary sequences with symmetric
  cross-over probabilities
• Rate 4/5 constituent convolutional codes
• RX0.5 bit per input bit

Aaron, Girod, DCC 2002
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Channel Coding vs. Slepian-Wolf Coding

• Systematic Channel Coding
• Systematic bits and parity bits subject to
  bit-errors
• Mostly memoryless BSC channel
• Low bit-error rate of channel
• Rate savings relative to systematic bits

• Slepian-Wolf Coding
• No bit errors in parity bits
• General statistics incl. memory
• Whole range of error probabilities
• Rate savings relative to parity bits
• Might have to compete with conventional
  compression (e.g., arithmetic coding)

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Distributed Lossy Compression of Dependent Sources
Source X
Encoder X
X
Joint Decoder
Y
Source Y
Encoder Y
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Lossy Compression with Side Information
Source
Encoder
Decoder
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Practical Wyner-Ziv Encoder and Decoder
Wyner-Ziv Decoder
Wyner-Ziv Encoder
Slepian- Wolf Decoder
Minimum Distortion Reconstruction
Slepian-Wolf Encoder
Quantizer
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Non-Connected Quantization Regions

• Example Non-connected intervals for scalar
  quantization
• Decoder Minimum mean-squared error
  reconstruction with side information

x
x
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Quantizer Reconstruction Function
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Finding Quantization Regions
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Lloyd Algorithm for Wyner-Ziv Quantizers
Choose initial quantizers
Find best reconstruction functions for current
quantizers

• Fleming, Zhao, Effros, unpublished
• Rebollo-Monedero, Girod, DCC 2003

Lagrangian cost for current quantizers,
reconstructor and rate measure
N
Find best quantizers for current reconstruction
and rate measure
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Which Rate Measure?
Wyner-Ziv Decoder
Wyner-Ziv Encoder
Slepian- Wolf Decoder
Slepian-Wolf Encoder
Minimum Distortion Reconstruction
Quantizer
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Example
Data set Video sequence Carphone, 100 luminance
frames, QCIF

• X pixel values in even frames
• Y motion-compensated interpolation from two
  adjacent odd frames

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Example (cont.)
Quantizer w/ rate constraint H(Q)
Quantizer w/ rate constraint H(QY)
PSNR39 dBH(Q)3.05 bit H(QY)0.54
bit
PSNR37.4 dBH(Q)1.87 bit H(QY)0.54 bit
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Example (cont.)
Quantizer w/ rate constraint H(Q) Quantizer w/
rate constraint H(QY)
PSNRdB
PSNRdB
Rate bit
Rate bit
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Wyner-Ziv Quantizers Lessons Learnt

• Typically no quantizer index reuse for rate
  constraint H(QY) and high rates Slepian-Wolf
  code provides more efficient many-to-one mapping
  in very high dimensional space.
• Uniform quantizers close to minimum m.s.e., when
  combined with efficient Slepian-Wolf code
• Quantizer index reuse required for rate
  constraint H(Q) and for fixed-length coding
• Important to decouple dimension of quantizer
  (i.e. scalar) and Slepian-Wolf code (very large)

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Sensor Networks
Local Sensor
Central Unit
Side Information
Pradhan, Ramchandran, DCC 2000 Kusuma,
Doherty, Ramchandran, ICIP 2001 Pradhan,
Kusuma, Ramchandran, SP Mag., 2002 Chou,
Perovic, Ramchandran, Asilomar 2002
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Video Compression with Simple Encoder
Aaron, Zhang, Girod, Asilomar 2002 Aaron,
Rane, Zhang, Girod, DCC 2003
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Video Compression with Simple Encoder
After Wyner-Ziv Decoding
Decoder Side information
16-level quantization (1 bpp)
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Video Compression with Simple Encoder
After Wyner-Ziv Decoding
Decoder Side information
16-level quantization (1 bpp)
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Video Compression with Simple Encoder
After Wyner-Ziv Decoding
Decoder Side information
16-level quantization (1 bpp)
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Performance of Simple Wyner-Ziv Video Coder
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Light Field Acquisition
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Compression of 280 Views of Buddha
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Reconstructed Views
Wyner-Ziv
JPEG-2000
Rate 0.11 bpp PSNR 39.9 dB
Rate 0.11 bpp PSNR 37.4 dB
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Digitally Enhanced Analog Transmission
Analog Channel

• Forward error protection of the signal waveform
• Information-theoretic bounds Shamai, Verdu,
  Zamir,1998
• Systematic lossy source-channel coding

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Forward Error Protection for MPEG Video
Broadcasting
MPEG Encoder
MPEG Decoder with Error Concealment
S
S
Error-Prone channel

• Graceful degradation without a layered signal
  representation

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Error-resilient Video Transmissionwith Embedded
Wyner-Ziv Codec
Carphone CIF, 50 frames _at_ 30fps, 1 Mbps, 1
Random Macroblock loss
Aaron, Rane, Rebollo-Monedero, Girod, ICIP 2003
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Wyner-Ziv Coding of VideoWhy Should We Care?

• Chance to reinvent compression from scratch
• Entropy coding
• Quantization
• Signal transforms
• Adaptive coding
• Rate control
• . . .
• Enables new compression applications
• Very low complexity encoders
• Error-resilient transmission of signal waveforms
• Digitally enhanced analog transmission
• Unequal error protection without layered coding
• . . .

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The End