Distributed source coding using syndromes discus design and construction
Download
1 / 26

Distributed Source Coding Using Syndromes (DISCUS): Design and Construction - PowerPoint PPT Presentation


  • 271 Views
  • Uploaded on

Distributed Source Coding Using Syndromes (DISCUS): Design and Construction. S.Sandeep Pradhan, Kannan Ramchandran IEEE Transactions on Information Theory, vol. 49, no.3, pp.626-643, Mar 2003. Outline. Introduction Preliminaries Encoding with a Fidelity Criterion Problem Formulation

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Distributed Source Coding Using Syndromes (DISCUS): Design and Construction' - bela


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Distributed source coding using syndromes discus design and construction l.jpg

Distributed Source Coding Using Syndromes (DISCUS): Design and Construction

S.Sandeep Pradhan, Kannan Ramchandran

IEEE Transactions on Information Theory,

vol. 49, no.3, pp.626-643, Mar 2003


Outline l.jpg
Outline

  • Introduction

  • Preliminaries

  • Encoding with a Fidelity Criterion

    • Problem Formulation

    • Design Algorithm

    • Constructions based on Trellis Codes

  • Simulation Results

  • Conclusion


Introduction l.jpg
Introduction

  • Slepian-Wolf theorem:

    By knowing joint distribution of X and Y, without explicitly knowing Y, encoder of X can perform as well as encoder who knows Y.

  • Both encoder and decoder have access to side information Y

  • Only decoder has access to side information Y


Introduction4 l.jpg
Introduction

  • Wyner-Ziv Problem:

    If decoder knows Y, then the information-theoretic rate-distortion performance for coding X is identical, no matter encoder knows Y or not.(X &Y are Gaussian.)

  • Prior work on source quantizer design.

  • Contributions:

    • Construction of a framework resting on algebraic channel coding principles

    • Performance analysis on Gaussian signals.

Source: discrete-alphabet  continuous-valued

Compression: lossless  lossy


Outline5 l.jpg
Outline

  • Introduction

  • Preliminaries

  • Encoding with a Fidelity Criterion

    • Problem Formulation

    • Design Algorithm

    • Constructions based on Trellis Codes

  • Simulation Results

  • Conclusion


Preliminaries l.jpg
Preliminaries

  • Example:

    X, Y: equiprobable 3-bit binary words

    Hamming distance is no more than 1.

    Y is available to decoder.

    Solution?

    Cosets: {000,111},{100,011},{010,101},{001, 110}

    Only transmit coset index/syndrome.


Preliminaries7 l.jpg

+3

-0.5

1

Preliminaries

  • Quantization:

    Digitizes an analog signal.

    Two parameters: a partition and a codebook.

    Codebook: [-2, 0.4, 2.3, 6]


Preliminaries8 l.jpg

yi-2

ai

yi

ai-1

yi-1

Preliminaries

  • Lloyd Max Quantization:

    partition: ai are midpoints.

    codebook: yiare centroids.

    Optimal scalar quantization.


Preliminaries9 l.jpg
Preliminaries

  • Trellis Coded Quantization (TCQ):[24]

    • Dual of TCM

    • Example:

      • Uniformly distributed source in [-A, A]

    • Implemented by Viterbi algorithm

      [24] M.W. Marcellin and T. R. Fischer, “Trellis coded quantization of memoryless and Gauss-Markov sources,” IEEE Trans. Commun., vol. 38, pp.82–93, Jan. 1990.


Outline10 l.jpg
Outline

  • Introduction

  • Preliminaries

  • Encoding with a Fidelity Criterion

    • Problem Formulation

    • Design Algorithm

    • Constructions based on Trellis Codes

  • Simulation Results

  • Conclusion


Encoding with a fidelity criterion l.jpg
Encoding with a Fidelity Criterion

  • Problem Formulation

    • X, Y: correlated, memoryless, i.i.d distributed sequences

    • Yi = Xi + Ni

    • Xi, Yi, Ni: continuous-valued

    • Ni: i.i.d distributed, independent from X

    • Xi, Ni: zero-mean Gaussian random variables with known variance

    • Decoder alone has access to Y.

    • Goal: Form best approximation to X given R bits per sample

    • Encoding in blocks of length L

    • Distortion measure:

    • Min R, s.t. reconstruction fidelity is less than given value D.


Encoding with a fidelity criterion12 l.jpg
Encoding with a Fidelity Criterion

System Model: encoder and decoder.

Interplay of source coding, channel coding and estimation


Encoding with a fidelity criterion13 l.jpg
Encoding with a Fidelity Criterion

  • Design Algorithm

    • Source Coding (M1, M2):

      • Partition source space:

      • Defining source codebook (S)

      • Characterizing active codeword by W (r.v.)

    • Estimation (M3):

      Get best estimate of X (minimizing distortion) conditioned on outcome of Y and the element in .

    • Channel Coding (M4, M5):

      • Transmit over an error-free channel with rate R (less than Rs)

      • Doable: I(W;Y) > 0, so H(W|Y) = H(W) – I(W;Y)

      • Build channel code with rate Rc on channel P(Y|W)

      • R = Rs – Rc.


Encoding with a fidelity criterion14 l.jpg
Encoding with a Fidelity Criterion

  • Summary of Design Algorithm:

    • M1 and M3:

      • minimize Rs, s.t. reconstruction distortion within given criterion.

    • M2: maximize I(W;Y).

    • M4:

      • maximize Rc, s.t. error probability meets a desired tolerance level.

    • M5: minimize decoding computational complexity.


Encoding with a fidelity criterion15 l.jpg
Encoding with a Fidelity Criterion

  • Scalar Quantization and Memoryless Coset Construction (C1):

    • Lloyd-Max (memoryless) quantizer

    • Memoryless coset partition (M4)

    • Example:

      L=1, (sample by sample)

      Quantization codebook: {r0, r1, …, r7}, (Rs = 3)

      Channel coding codebook: {r0, r2, r4, r6}, {r1, r3, r5, r7}. (Rc = 2)

      R = Rs – Rc = 1 bit/sample.


Encoding with a fidelity criterion16 l.jpg
Encoding with a Fidelity Criterion

  • Scalar Quantization and Trellis-Based Coset Construction (C2):

    • Scalar quantizer for {Xi}i=1L

    • Coset partition (M4) by trellis code.

Codebook (size of 8L), Rs = 3 bits/sample, two cosets


Encoding with a fidelity criterion17 l.jpg
Encoding with a Fidelity Criterion

  • Example:

    Computing syndrome (Rs = 3, Rc = 2)

    outcome of quantization be 7, 3, 2, 1, 4.

    L = 5,

    Syndrome is given by 10110 for 5 samples.


Encoding with a fidelity criterion18 l.jpg
Encoding with a Fidelity Criterion

  • Trellis-Based Quantization and Memoryless Coset Construction (C3):

    • Trellis coded quantizer

    • Memoryless coset partition

    • Example:

      Quantization codebook: Rs = 2

      D0={r0, r4}, D1={r1, r5}, D2={r2, r6}, D3={r3, r7}.

      Memoryless channel code: Rc = 1

      1 coded bit with another 1 uncoded bit (from Y) to recover Di.


Encoding with a fidelity criterion19 l.jpg
Encoding with a Fidelity Criterion

  • Trellis-Based Quantization and Trellis-Based Coset Coset Construction (C4):

    • Trellis coded quantizer

    • Trellis coded coset partition

Comparison between C3 and C4.


Encoding with a fidelity criterion20 l.jpg
Encoding with a Fidelity Criterion

  • Distance Property

    • Given a uniform partition, four cases of coset constructions have same distance property.

    • Non-uniform quantizer, analyze performance by simulations.


Outline21 l.jpg
Outline

  • Introduction

  • Preliminaries

  • Encoding with a Fidelity Criterion

    • Problem Formulation

    • Design Algorithm

    • Four Constructions

  • Simulation Results

  • Conclusion


Simulation results l.jpg
Simulation Results

Quantization levels decrease distortion. (C1)

Correlation

-SNR:

ratio of X’s

variance and

N’s variance.


Simulation results23 l.jpg
Simulation Results

Correlation

-SNR:

ratio of X’s

variance and

N’s variance.

Quantization levels increase prob. Of error. (C1)


Simulation results24 l.jpg
Simulation Results

Correlation

-SNR:

ratio of X’s

variance and

N’s variance.

Error probability comparison of C1 and C2

(3-4dB gain)


Simulation results25 l.jpg
Simulation Results

Correlation

-SNR:

ratio of X’s

variance and

N’s variance.

Error probability of C4 codes.


Conclusions l.jpg
Conclusions

  • Constructive practical framework based on algebraic trellis codes.

  • Promising performance.


ad