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

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

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

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

5. 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. 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. 6 Heterogeneous Networks ●Incompatible communication systems demand transcoding where they interface Mobile phone Base station ADSL & WLAN Telephone central Old school telephone PDA with Skype

7. 7 Shannon-Kotel’nikov Mappings ●Non-linear mappings  Discrete time, continuous amplitude  Robust  Low delay ●Bandwidth expansion  Noise reduction ●Bandwidth reduction  Compression S1S1 S2S2   ● Uncertainty due to noise Y1Y1 Y2Y2

8. 8 The Guys Claude E. ShannonVladimir A. Kotel'nikov

9. 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. 10 Assumptions ●Point-to-point channels ●Source, S, is independent and identically distributed ●Channel noise, Z, is Additive White Gaussian Noise (AWGN)

11. 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. 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. 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. 14 Bandwidth-Reducing Mappings

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

16. 16 Transcoding for Heterogeneous Networks

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

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

19. 19 Now, unleash the opponents...

20. 20 Publication List [1] – Hekland, Øien, Ramstad. ”Using 2:1 Shannon mapping for joint source-channel coding”, DCC’05, Utah, USA. [2] – Hekland, Ramstad. ”Digitising Shannon mappings for heterogeneous networks and storage”, NORSIG’05, Stavanger, Norway. [3] – Hekland, Ramstad. ”Digitising Shannon mappings for heterogeneous networks”, DCC’06, Utah, USA. [4] – Hekland, Ramstad. ”Optimal rate-constrained transcoding for a 2:1 bandwidth reducing Shannon Mapping”, SPAWC’06, Cannes, France. [5] – Hekland, Øien, Ramstad. ”Quantifying performance losses in source-channel coding”, EW’07, Paris, France. [6] – Hekland, Floor, Ramstad. ”Shannon-Kotel’nikov mappings in joint source-channel coding”, accepted for publication in IEEE Trans. Commun.