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Compression with Side Information using Turbo Codes

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Title: Compression with Side Information using Turbo Codes


1
Compression with Side Information usingTurbo
Codes
Anne Aaron and Bernd Girod Information Systems
Laboratory Stanford University Data Compression
Conference April 3, 2002
2
Overview
  • Introduction
  • Turbo Coder and Decoder
  • Compression of Binary Sequences
  • Extension to Continuous-valued Sequences
  • Joint Source-Channel Coding
  • Conclusion

Compression with Side Information Using Turbo
Codes
April 3, 2002
3
Distributed Source Coding
Compression with Side Information Using Turbo
Codes
April 3, 2002
4
Research Problem
  • Motivation
  • Slepian-Wolf theorem It is possible to compress
    statistically dependent signals in a distributed
    manner to the same rate as with a system where
    the signals are compressed jointly.
  • Objective
  • Design practical codes which achieve compression
    close to the Slepian-Wolf bound

Compression with Side Information Using Turbo
Codes
April 3, 2002
5
Asymmetric Scenario Compression with Side
Information
  • Compression techniques to send at rate close to
    H(Y) are well known
  • Can perform some type of switching for more
    symmetric rates

Compression with Side Information Using Turbo
Codes
April 3, 2002
6
Our Approach Turbo Codes
  • Turbo Codes
  • Developed for channel coding
  • Perform close to Shannon channel capacity limit
    (Berrou, et al., 1993)
  • Similar work
  • Garcia-Frias and Zhao, 2001 (Univ. of Delaware)
  • Bajcsy and Mitran, 2001 (McGill Univ.)

Compression with Side Information Using Turbo
Codes
April 3, 2002
7
System Set-up
  • X and Y are i.i.d binary sequences X1X2XL and
    Y1Y2YL with equally probable ones and zeros.
    Let Xi be independent of Yj for i?j, but
    dependent on Yi. X and Y dependency described by
    pmf P(xy).
  • Y is sent at rate RY?H(Y) and is available as
    side information at the decoder

Compression with Side Information Using Turbo
Codes
April 3, 2002
8
Turbo Coder
Compression with Side Information Using Turbo
Codes
April 3, 2002
9
Turbo Decoder
Pchannel
SISO Decoder
Pa posteriori
Pextrinsic
Pa priori
L bits out
Pextrinsic
Pa priori
SISO Decoder
Pchannel
Pa posteriori
Compression with Side Information Using Turbo
Codes
April 3, 2002
10
Simulation Binary Sequences
  • X-Y relationship
  • P(XiYi)1-p and P(Xi?Yi)p
  • System
  • 16-state, Rate 4/5 constituent convolutional
    codes
  • RX0.5 bit per input bit with no puncturing
  • Theoretically, must be able to send X without
    error when H(XY)?0.5

Compression with Side Information Using Turbo
Codes
April 3, 2002
11
Results Compression of Binary Sequences
RX0.5
0.15 bit
Compression with Side Information Using Turbo
Codes
April 3, 2002
12
Results for different rates
  • Punctured the parity bits to achieve lower rates

Compression with Side Information Using Turbo
Codes
April 3, 2002
13
Extension to Continuous-Valued Sequences
  • X and Y are sequences of i.i.d continuous-valued
    random variables X1X2XL and Y1Y2YL. Let Xi be
    independent of Yj for i?j, but dependent on Yi. X
    and Y dependency described by pdf f(xy).
  • Y is known as side information at the decoder

To decoder
Compression with Side Information Using Turbo
Codes
April 3, 2002
14
Simulation Gaussian Sequences
  • X-Y relationship
  • X is a sequence of i.i.d Gaussian random
    variables
  • YiXiZi, where Z is also a sequence of i.i.d
    Gaussian random variables, independent of X.
    f(xy) is a Gaussian probability density function
  • System
  • 4-level Lloyd-Max scalar quantizer
  • 16-state, rate 4/5 constituent convolutional
    codes
  • No puncturing so rate is 1 bit/source sample

Compression with Side Information Using Turbo
Codes
April 3, 2002
15
Results Compression of Gaussian Sequences
RX1 bit/sample
2.8 dB
CSNR ratio of the variance of X and Z
Compression with Side Information Using Turbo
Codes
April 3, 2002
16
Joint Source-Channel Coding
  • Assume that the parity bits pass through a
    memoryless channel with capacity C
  • We can include the channel statistics in the
    decoder calculations for Pchannel.
  • From Slepian-Wolf theorem and definition of
    Channel capacity

Compression with Side Information Using Turbo
Codes
April 3, 2002
17
Results Joint Source-Channel Coding
RX0.5 BSC with q0.03
0.15 bit
0.12 bit
Compression with Side Information Using Turbo
Codes
April 3, 2002
18
Conclusion
  • We can use turbo codes for compression of binary
    sequences. Can perform close to the Slepian-Wolf
    bound for lossless distributed source coding.
  • We can apply the system for compression of
    distributed continuous-valued sequences.
    Performs better than previous techniques.
  • Easy extension to joint source-channel coding

Compression with Side Information Using Turbo
Codes
April 3, 2002
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