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Shannon-Kotel’nikov Mappings for Joint Source-Channel Coding

Shannon-Kotel’nikov Mappings for Joint Source-Channel Coding. Thesis Defence Lecture Fredrik Hekland 1. June 2007. Outline. Some fundamentals on communications Shannon-Kotel’nikov mappings Key results. RAW: 8MB. JPEG: 1MB. 87 photos. 700 photos. 64kbit/s. 13kbit/s. Source Coding.

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Shannon-Kotel’nikov Mappings for Joint Source-Channel Coding

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  1. Shannon-Kotel’nikov Mappings for Joint Source-Channel Coding Thesis Defence Lecture Fredrik Hekland 1. June 2007

  2. Outline • Some fundamentals on communications • Shannon-Kotel’nikov mappings • Key results

  3. RAW: 8MB JPEG: 1MB 87 photos 700 photos 64kbit/s 13kbit/s Source Coding • Analog sources • Infinite information • To meet a rate constraint SC can • Remove redundancy • Remove irrelevancy • Reduce perceptual quality • Processing power OBJECTIVES Minimize rate given a distortionconstraint Minimize distortion given a rate constraint

  4. Information Channel Information Channel Coding Noise No channel coding/ error protection: Minimize impact of channel noise, while still trying to maximize channel utilization Channel space Code word

  5. Joint or Separate Coding JOINT SOURCE-CHANNEL CODING - Same performance as separated system, while requiring lower delay/complexity. - Good performance for a larger range of source-channel pairs.

  6. Heterogeneous Networks ADSL & WLAN Base station PDA with Skype Mobile phone Old school telephone Telephone central • Incompatible communication systems demand transcoding where they interface

  7. S2 Y2 ●   Uncertainty due to noise S1 Y1 Shannon-Kotel’nikov Mappings • Non-linear mappings • Discrete time, continuous amplitude • Robust • Low delay • Bandwidth expansion • Noise reduction • Bandwidth reduction • Compression

  8. The Guys Claude E. Shannon Vladimir A. Kotel'nikov

  9. Research Objectives • Bandwidth-efficient and robust (lossy) source-channel coding systems • Transcoding schemes for Shannon-Kotel’nikov mappings • How to interface with digital transport networks • Determine whether or not joint optimization of transcoding/mapping is necessary • Propose simple and effective schemes

  10. Assumptions • Point-to-point channels • Source, S, is independent and identically distributed • Channel noise, Z, is Additive White Gaussian Noise (AWGN)

  11. Key Results • Description of performance losses in source-channel coding • Bandwidth reducing mappings • Transcoding of mappings for heterogeneous networks • Mappings in multi-hop scenarios

  12. Quantifying Performance Losses in Source-Channel Coding • Mismatched channel symbol distribution • Mismatched error-sequence distribution • Incorrect assumption of source distributions • Rate lower than channel capacity • Correlation • Receiver structures • Decoding errors

  13. Bandwidth-Reducing Mappings • 2:1 - Gaussian source and AWGN channel • 2:1 - Laplacian source and AWGN channel • Warping LG is a viable alternative. • 4:1 through cascading two 2:1 mappings.

  14. Bandwidth-Reducing Mappings

  15. Transcoding for Heterogeneous Networks • Simple scalar quantizer performs well • Joint optimization of mapping and quantizer • Quantize either at transmitter or receiver side

  16. Transcoding for Heterogeneous Networks

  17. Multi-hop Communication • Pre-quantized mapping necessary • Worst link determines performance

  18. Errata • P.112, last bullet belongs to Section 5.2.

  19. Now, unleash the opponents ...

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