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

2. 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

3. Simple Example
Source A
Source B
Source statistics exploited in the encoder. Different statistics Different code.

4. Simple Example - Revisited
Source A
Source B
Different statistics Same code.
Source statistics exploited in the decoder.
“Lossless” compression with residual error rate.

5. Compression with Side Information
Source
A/B
Encoder
Decoder

6. Distributed Compression of Dependent Sources
Source X
Encoder X X
Joint
Decoder Y
Source Y
Encoder Y

7. Achievable Rates for Distributed Coding Example
Separate encoding and decoding of X and Y
Separate encoding and joint decoding of X and Y

8. General Dependent i.i.d. Sequences
[Slepian, Wolf, 1973]
Vanishing error probability for long sequences
No errors

9. Distributed Compression and Channel Coding
Source
X|Y
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

10. 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]

11. Compression by Turbo Coding
L bits in
L bits
Systematic Convolutional Encoder Rate
bits
bits
Systematic Convolutional Encoder Rate
Interleaver length L
L bits
[Aaron, Girod, DCC 2002]

12. Turbo Decoder SISO Decoder “Channel” probabilities calculations
Pchannel
bits in
SISO Decoder
Pa posteriori
“Channel” probabilities calculations
Pa priori
Pextrinsic
Deinterleaver length L
Interleaver length L
Decision
bits in
L bits out
“Channel” probabilities calculations
Pextrinsic
Pa priori
Deinterleaver length L
SISO Decoder
Pchannel
Pa posteriori
Interleaver length L
[Aaron, Girod, DCC 2002]

13. Results for Compression of Binary Sequences
X,Y dependent binary sequences with symmetric cross-over probabilities
Rate 4/5 constituent convolutional codes;
RX=0.5 bit per input bit
0.15 bit
[Aaron, Girod, DCC 2002]

14. 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)

15. Distributed Lossy Compression of Dependent Sources
Source X
Encoder X X’
Achievable rate region
Joint
Decoder Y’
Source Y
Encoder Y

16. Lossy Compression with Side Information
Source
Encoder
Decoder
[Wyner, Ziv, 1976]
[Zamir,1996]

17. Practical Wyner-Ziv Encoder and Decoder
Wyner-Ziv Decoder
Quantizer
Slepian-Wolf Encoder
Slepian-
Wolf
Decoder
Minimum Distortion
Reconstruction

18. Non-Connected Quantization Regions
Example: Non-connected intervals for scalar quantization
Decoder: Minimum mean-squared error reconstruction with side information x x

19. Quantizer Reconstruction Function

20. Finding Quantization Regions1 2 3 4
q = x

21. Lloyd Algorithm for Wyner-Ziv Quantizers
Choose initial quantizers
Find best reconstruction functions for current quantizers
Update rate measure for current quantizers
[Fleming, Zhao, Effros, unpublished]
[Rebollo-Monedero, Girod, DCC 2003]
Lagrangian cost for current quantizers, reconstructor and rate measure
Convergence
End Y N
Find best quantizers for current reconstruction and rate measure

22. Which Rate Measure? Wyner-Ziv Encoder Wyner-Ziv Decoder
Conditional entropy coder H(Q|Y)
[Rebollo-Monedero, Girod, DCC 2003]
Quantizer
Slepian-Wolf Encoder
Slepian-
Wolf
Decoder
Minimum Distortion
Reconstruction

23. 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

24. Quantizer w/ rate constraint H(Q) Quantizer w/ rate constraint H(Q|Y)
Example (cont.)
Quantizer w/ rate constraint H(Q) Quantizer w/ rate constraint H(Q|Y)
PSNR=37.4 dB H(Q)=1.87 bit H(Q|Y)=0.54 bit
PSNR=39 dB H(Q)=3.05 bit H(Q|Y)=0.54 bit

25. Quantizer w/ rate constraint H(Q) Quantizer w/ rate constraint H(Q|Y)
Example (cont.)
Quantizer w/ rate constraint H(Q) Quantizer w/ rate constraint H(Q|Y)
PSNR[dB]
PSNR[dB]
Rate [bit]
Rate [bit]

26. Wyner-Ziv Quantizers: Lessons Learnt
Typically no quantizer index reuse for rate constraint H(Q|Y) 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)

27. Sensor Networks [Pradhan, Ramchandran, DCC 2000]
Remote Sensor
Remote Sensor
Central Unit
Local Sensor
Side Information
Remote Sensor
Remote Sensor
[Pradhan, Ramchandran, DCC 2000]
[Kusuma, Doherty, Ramchandran, ICIP 2001]
[Pradhan, Kusuma, Ramchandran, SP Mag., 2002]
[Chou, Perovic, Ramchandran, Asilomar 2002]

28. Video Compression with Simple Encoder
Interframe Decoder
Scalar Quantizer
Turbo Encoder
Buffer
Video frame X
Intraframe Encoder
Turbo Decoder
Request bits
Slepian-Wolf Codec
Interpolation
Key frames
previous
next
Reconstruction X’ Y
[Aaron, Zhang, Girod, Asilomar 2002]
[Aaron, Rane, Zhang, Girod, DCC 2003]

29. Video Compression with Simple Encoder
Decoder Side information
After Wyner-Ziv Decoding
16-level quantization (~1 bpp)

30. Video Compression with Simple Encoder
Decoder Side information
After Wyner-Ziv Decoding
16-level quantization (~1 bpp)

31. Video Compression with Simple Encoder
Decoder Side information
After Wyner-Ziv Decoding
16-level quantization (~1 bpp)

32. Performance of Simple Wyner-Ziv Video Coder
7 dB

33. Light Field Acquisition

34. Compression of 280 Views of Buddha
~ 4dB
Data set: Buddha
Total number of views: 280
Image size: 512 x 512
Shape:
JBIG compression 0.11 bpp
Geometry:
Silhouette-based reconstruction
Experimental setup
Compress and transmit shape information for all the views
Half of the original views available at the decoder
Used for rendering the other half as side information Y
Wyner-Ziv coding of the remaining views X
Pixel-domain coding,
Only encode pixels within the object shape for each view

35. Reconstructed Views Wyner-Ziv JPEG-2000 Rate: 0.11 bpp Rate: 0.11 bpp
PSNR 39.9 dB
Rate: bpp
PSNR dB

36. Digitally Enhanced Analog Transmission
Channel
Wyner-
Ziv
Encoder
Digital
Channel
Decoder
Side
info
Forward error protection of the signal waveform
Information-theoretic bounds [Shamai, Verdu, Zamir,1998]
“Systematic lossy source-channel coding”

37. Forward Error Protection for MPEG Video Broadcasting
MPEG Encoder
MPEG Decoder with Error Concealment S S’
Wyner-Ziv Decoder A S*
Wyner-Ziv Encoder A
Error-Prone channel
Wyner-Ziv Decoder B
S**
Wyner-Ziv Encoder B
Graceful degradation without a layered signal representation

38. Error-resilient Video Transmission with Embedded Wyner-Ziv Codec
Carphone CIF, 50 30fps, 1 Mbps,
1% Random Macroblock loss
[Aaron, Rane, Rebollo-Monedero, Girod, ICIP 2003]

39. Wyner-Ziv Coding of Video: Why 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

40. The End