Scalable Image Transmission Using UEP Optimized LDPC Codes

1
Scalable Image Transmission Using UEP Optimized
LDPC Codes

• Charly Poulliat, Inbar Fijalkow, David Declercq
• International Symposium on Image/Video
  Communications over Fixed and Mobile Networks
  (ISIVC), July 2004

2
Outline

• Introduction
• Scalable Image Transmission
• LDPC Code Design for UEP Channels
• Simulation Results
• Conclusion

3
IntroductionUEP Unequal Error Protection

• Data of different importance from source encoder
• Multimedia
• Network/Transport Layer Headers
• I/P/B Frames Motion Vectors
• Different protection classes/levels provided by
• Physical Layer modulation
• Network Layer protocols
• Channel Coding

4
IntroductionIrregular LDPC Codes

• Inherent UEP
• Highly connected nodes are protected better.
• More parity-check equations.
• Most connected variable nodes assigned to most
  important class.
• Maximizes average connection degree of variable
  nodes in each class.

5
IntroductionIrregular LDPC Codes
6
IntroductionOptimization of Irregularity

• Optimized for a specific channel
• Binary Erasure Channel (BEC)
• Additive White Gaussian Noise Channel (AWGN
  Channel)
• Optimized globally.
• Every bit in the codeword has the same average
  error probability.
• Do not necessarily ensure a good UEP capacity.

7
IntroductionOptimization of Irregularity

• Optimized by modeling the UEP transmission scheme
  as a specific channel.
• Optimized locally (within class).
• Provides a better UEP capacity.
• Enhanced UEP
• The error probability within a class is minimized
  by
• maximizing the average connection degree.
• maximizing the minimum degree of its variable
  nodes.

8
IntroductionUEP properties

• Interprets the UEP properties of LDPC code as
  different local convergence speeds.
• The most protected class
• Be assigned to the bits in the codeword which
  converge to their right value in the minimum
  number of decoding iterations.

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Scalable Image Transmission

• Consider an JPEG2000 codestream compressed into
  Nc 1 progressive quality layers.
• Source bitstream is encoded into codewords
• Length N, each containing K information bits.
• Codewords are transmitted over an AWGN channel.
• Do not consider joint source.
• Consider a source with fixed classes number that
  requires different protection levels.
• Different schemes will be compared.

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Scalable Image Transmission

• Equal Error Protection (EEP) Scheme
• EEP Entire JPEG2000 bitstream is directly
  encoded by a systematic LDPC encoder, block by
  block.

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Scalable Image Transmission

• Unequal Error Protection Scheme
• (UEP)-AWGN opt Use the irregularity of the code.
• Nc 1 quality layers are distributed over all
  the codewords.

bitstream
codewords
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Scalable Image Transmission

• Unequal Error Protection Scheme
• (UEP)-UEP opt Use the irregularity of the code.
• Nc 1 quality layers are distributed over all
  the codewords.

bitstream
codewords
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LDPC Code Design for UEP Channel UEP parameter
description and notations

• The transmission scheme consists of sending a UEP
  coded bitstream
• Under given UEP constraints
• Over AWGN channel
• Binary input
• Noise variance parameter s2

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LDPC Code Design for UEP Channel UEP parameter
description and notations

• A channel codeword of a rate R LDPC code divided
  into Nc classes ordered in decreasing order of
  their error sensitivity.
• Considering the set of Nc classes
• C1 highest required protection level
• C Nc highest required protection level

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LDPC Code Design for UEP Channel UEP parameter
description and notations

• A channel codeword of a rate R LDPC code divided
  into Nc classes ordered in decreasing order of
  their error sensitivity.
• Let the proportions
  be the normalized lengths of each
  class, corresponding to the info bit with
• The proportions distribution of the bits in the
  channel codewords
• belonging to each classes
  is given by

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LDPC Code Design for UEP Channel UEP parameter
description and notations

• Generating function of check nodes degree
  distribution
• Fraction of edges emanating from variable nodes
  of degree i
• Maximum check node connection degree
• Assuming is the same for each class.

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LDPC Code Design for UEP Channel UEP parameter
description and notations

• Generating function of variable nodes degree
  distribution
• Fraction of edges emanating from variable nodes
  of degree i
• Maximum variable node connection degree

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LDPC Code Design for UEP Channel UEP parameter
description and notations

• Define and optimize variable node distribution
  for each class Ck
• Maximum variable node connection degree in class
  Ck

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LDPC Code Design for UEP Channel UEP parameter
description and notations

• Generating function of variable nodes degree
  distribution

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LDPC Code Design for UEP Channel UEP parameter
description and notations
21
LDPC Code Design for UEP Channel UEP parameter
description and notations
22
LDPC Code Design for UEP Channel UEP parameter
description and notations
23
LDPC Code Design for UEP Channel UEP parameter
description and notations
24
LDPC Code Design for UEP Channel UEP parameter
description and notations
25
LDPC Code Design for UEP Channel UEP parameter
description and notations
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LDPC Code Design for UEP Channel UEP parameter
description and notations

• Some others notations (1/2)

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LDPC Code Design for UEP Channel UEP parameter
description and notations

• Some others notations (2/2)
• Vector form association
• A LDPC Code is then parameterized by
  .

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LDPC Code Design for UEP Channel Hierarchical
optimization algorithm

• We will consider the LDPC codes that converge to
  a vanishing bit error probability at a given
  threshold
• The threshold of the optimized LDPC irregularity
  
• without UEP constraints
• The threshold of the optimized LDPC irregularity
  
• with UEP constraints greater than

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LDPC Code Design for UEP Channel Hierarchical
optimization algorithm

• To ensure the UEP constraints would not lead to a
  too-large degradation of the threshold, we limit
  the set of possible LDPC codes to those whose
  convergence threshold lies within
• a small constant fixed in the optimization
  algorithm.

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LDPC Code Design for UEP Channel Hierarchical
optimization algorithm

• Optimization is done class after class.
• Most important class first.
• Objective function
• Maximize the average variable nodes connection
  degree within a class, subjecting to a minimum
  degree of its variable nodes within a class.
• Constraints
• C1 Rate constraint
• C2 Proportion distribution constraints
• C3 Convergence constraint
• C4 Stability condition
• C5 Minimum variable node degree constraint
• C6 Previous optimizations constraints
• Linear programming.

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LDPC Code Design for UEP Channel Hierarchical
optimization algorithm

• Given parameters
• for each class k, starting with the most
  important class
• initialization
• while optimization failure (any constraints is
  not fulfilled)
• maximize average connection degree of Ck
• fulfilling constraints C1 to C6
• end while
• end for

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LDPC Code Design for UEP Channel Hierarchical
optimization algorithm

• Constraints (1/2)
• C1 Rate constraint (global constraint)
• C2 Proportion distribution constraints
  (global constraint)
• (i)
• (ii)

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LDPC Code Design for UEP Channel Hierarchical
optimization algorithm

• Constraints (2/2)
• C3 Convergence constraint (global
  constraint)
• C4 Stability condition (global constraint)
• C5 Minimum variable node degree constraint
  (class constraint)
• C6 Previous optimizations constraints

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LDPC Code Design for UEP Channel Hierarchical
optimization algorithm

• example

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LDPC Code Design for UEP Channel Performance
analysis for short length codewords

• Simulation results for finite length codewords
  are given for the decoding iteration .
• Optimization parameters
• The offset is arbitrary set to 0.05 dB.

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LDPC Code Design for UEP Channel Performance
analysis for short length codewords

• Designed codes have the following parameters
• (K 2048, N 4094) (UEP)-AWGN opt code.
• (K 2047, N 4095) (UEP)- UEP opt code.
• These codes are both used in the following when
  scalable image transmission is considered.
• For (UEP)-AWGN opt code
• Assign the information bits which belong to the
  class to the most connected variable
  nodes.
• Assign the information bits which belong to the
  class to the most connected variable
  nodes and so up to class.
• The redundancy bits are associated to the
  remaining (1 R) variable nodes.

37
LDPC Code Design for UEP Channel Hierarchical
optimization algorithm

• example

38
LDPC Code Design for UEP Channel Hierarchical
optimization algorithm
39
Simulation Results

• Consider the image Lena compressed into a
  JPEG2000 bitstream with three progressive quality
  layers.
• Progressive bit rates B (0.125 bpp, 0.250
  bpp, 0.5 bpp)
• We then consider the (UEP) UEP-opt code with
  optimization parameters
• Channel coding rate R 1/2
• The results are given for 100 independent
  Monte-Carlo runs using Verification Model version
  8.6 as source decoder.

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Simulation Results

• Two performance criteria
• Decoding failure
• Headers are not protected by any additional
  forward error protection code, they may be
  erroneous and decoding failure can occur.
• PSNR
• The average PSNR of the reconstructed image
  versus the EB/N0 for a given iteration number
  would be studied.

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Simulation ResultsDecoding failure
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Simulation ResultsPSNR vs. EB/N0
43
Conclusion

• Evaluate performance improvement by UEP optimized
  LDPC codes.
• In terms of average PSNR and decoding failure for
  a low iteration number.
• Underline the importance for data block
  interleaving into codeword to fully benefit from
  LDPC irregularity.

44
Thank you

• References
• C. Poulliat, D. Declercq, and I. Fijalkow,
  Enhancement of Unequal Error Protection
  Properties of LDPC Codes, EURASIP Journal on
  Wireless Communication and networking, 2007.
• Neele von Deetzen, Unequal Error Protection
  Turbo and LDPC Codes, Class Note for Summer
  Academy, School of Engineer and Science, Jacobs
  University Bremen, Germany, 2007.
• P. S. Guinand, D. Boudreau, and R. Kerr,
  Construction of UEP Codes Suitable for Iterative
  Decoding, in Proceedings of the 6th Canadian
  Workshop on Information Theory, pp. 17-20,
  Kingston, Ontario, Canada, June, 1999.
• T. J. Richardson, M. A. Shokrollahi, and R. L.
  Urbanke, Design of Capacity-Approaching
  Irregular Low-Density Parity-Check Codes, IEEE
  Transactions on Information Theory, vol. 47, no.
  2, pp.619-637, 2001.

45
Supplementary

• Variable node degree distribution
• Fraction of edges emanating from variable nodes
  of degree i
• Assume the code has n variable nodes, the number
  of variable nodes of degree i is then

46
Supplementary

• So E, the total number of edges emanating from
  all variable nodes, is equal to
• Also, assuming the code has m check nodes, total
  number of edges emanating from all check nodes,
  is equal to

47
Supplementary

• Equating these two expressions for E, we
  conclude that
• We see that the design rate is equal to

48
Supplementary

• We see that the design rate R is equal to
• Rate constraints

49
Supplementary

• We see that the design rate R is equal to

50
Supplementary

• C1 Rate constraints

51
Supplementary
52
Supplementary

• By using
• Gaussian assumption for Log Density Ratio (LDR)
  message
• Independence assumption between LDR messages
• give the evolution of the Mutual Information
  (MI) associated with the mean of the LDR messages
  for one decoding iteration.
• We denote the Mutual Information associated with
  LDR messages at the input of
• variable nodes
• check nodes
• at the lth decoding iteration.

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Supplementary

• Assuming Gaussian approximation
• check node message update
• variable node message update
• with being the Mutual Information
  function

54
Supplementary

• Combining (1) and (2) gives the EXIT Chart of the
  LDPC code
• The initial condition is given by .
• The condition
• ensures the convergence of BP algorithm to an
  error-free codeword.

55
Supplementary

• EXIT Chart associated with LDPC code
• EXtrinsic Information Transfer Chart, a technique
  to aid the construction of iteratively-decoded
  error-correcting codes (LDPC codes and Turbo
  codes).
• Depicted the explicit relation of the MI from
  iteration l 1 to iteration l.
• If there are two components which exchange
  messages, the behavior of the decoder can be
  plotted on a two-dimensional chart.
• One component
• Input horizontal axis
• Output vertical axis
• The other component
• Input vertical axis
• Output horizontal axis

56
Supplementary


57
Supplementary

• For a successful decoding, there must be a clear
  swath between the curves so that
• Iterative decoding can proceed from 0 bits of
  extrinsic information to 1 bit of extrinsic
  information.