1. A Graph-based Framework for Transmission of Correlated Sources over Multiuser Channels Suhan Choi May 2006

2. Multiuser Communication Scenarios

3. Practical Applications Sensor Networks Wireless Cellular Systems, Wireless LAN Broadcasting Systems Many-To-One Communications One-To-Many Communications

4. Contents of Dissertation Many-to-One Communications (Multiple Access Channels) Channel Coding Problem Source Coding Problem Examples and Interpretations One-to-Many Communications (Broadcast Channels) Channel Coding Problem Source Coding Problem Interpretation Conclusion & Future Research Issues

5. Outline of the Presentation Many-to-One Communications Preliminaries Channel Coding Problem Source Coding Problem Motivation & Remarks Example Conclusion & Future Research Issues

6. Outline Many-to-One Communications Preliminaries Channel Coding Problem Source Coding Problem Motivation & Remarks Example Conclusion & Future Research Issues

7. Definition of Bipartite Graphs 1 2 A B C

8. Semi-Regular Bipartite Graphs 1 2 3 4 1 2 3 5 4 6 1 2 3 4 1 2 3 5 4 6

9. Nearly Semi-Regular Bipartite Graphs 1 2 3 4 1 2 3 5 4 6

10. Strongly Typical Sequences  Non-typical set

11. Strongly Jointly Typical Sequences

12. Outline Many-to-One Communications Preliminaries Channel Coding Problem Source Coding Problem Motivation & Remarks Example Conclusion & Future Research Issues

13. Problem Formulation: MAC with Correlated Messages Independent Correlated MAC Channel Encoder 1 Channel Encoder 2 Channel Decoder

14. Problem Formulation: Transmission System MAC Channel Encoder 1 Channel Encoder 2 Channel Decoder

15. Definition of Achievable Rates

16. Remark on Achievable Rates & Capacity Region Find a sequence of nearly semi-regular graphs The number of vertices & the degrees are increasing exponentially with given rates Edges from these graphs are reliably transmitted → Rates are achievable Definition: Capacity region, The set of all achievable tuple of rates Goal: Find the capacity region

17. An Achievable Rate Region for the MAC with Correlated Messages

18. Remark on the Theorem 1

19. Sketch of the Proof of Theorem 1 (1)

20. Sketch of the Proof of Theorem 1 (2)

21. Sketch of the Proof of Theorem 1 (3) Sender 1 Codewords Sender 2 Codewords

22. Sketch of the Proof of Theorem 1 (4)

23. Sketch of the Proof of Theorem 1 (5) Sender 1 Codewords Sender 2 Codewords graph generation

24. Sketch of the Proof of Theorem 1 (6)

25. Converse Theorem for the Sum-Rate of the MAC with Correlated Messages

26. Outline Many-to-One Communications Preliminaries Channel Coding Problem Source Coding Problem Motivation & Remarks Example Conclusion & Future Research Issues

27. Source Coding Problem (Representation of Correlated Sources using nearly semi-regular bipartite graphs) Source Encoder 1 Source Encoder 2 Source Decoder

28. Problem Formulation: Transmission System

29. Definition of Achievable Rates

30. Remark on Achievable Rates & Our Goal Find a sequence of nearly semi-regular graphs The number of vertices & the degrees are increasing exponentially with given rates Given sources are reliably represented by these graphs → Rates are achievable The achievable rate region: The set of all achievable tuple of rates Goal: Find the achievable region

31. The Achievable Rate Region

32. Sketch of the Proof of Theorem 3 (1) (Direct Part)

33. Sketch of the Proof of Theorem 3 (2)

34. Sketch of the Proof of Theorem 3 (3) graph generation

35. Sketch of the Proof of Theorem 3 (4)

36. Sketch of the Proof of Theorem 3 (5)

37. Outline Many-to-One Communications Preliminaries Channel Coding Problem Source Coding Problem Motivation & Remarks Example Conclusion & Future Research Issues

38. Motivation: Why we choose graphs? Jointly Typicality can be captured by the graph Nearly Semi-regular Bipartite Graph Graph Typicality Graph

39. Transmission of Correlated Sources over a Multiple Access Channel (MAC) MAC Encoder 1 Encoder 2 Decoder MAC Channel Encoder 1 Channel Encoder 2 Channel Decoder Source Encoder 1 Source Encoder 2 Source Decoder A Graph-Based Framework Modular approach in multiuser channels Fundamental Concept: Jointly typicality Encoding processes Source coding: map correlated sources into edges of graphs Channel coding: send edges of these graphs reliably

40. Outline Many-to-One Communications Preliminaries Channel Coding Problem Source Coding Problem Motivation & Remarks Example Conclusion & Future Research Issues

41. Gaussian MAC with Jointly Gaussian Channel Input Gaussian MAC

42. A Special Case in the Gaussian MAC

44. Gaussian MAC with Correlated Messages Independent vs. Correlated Codewords

45. Outline Many-to-One Communications Preliminaries Channel Coding Problem Source Coding Problem Motivation & Remarks Example Conclusion & Future Research Issues

46. Conclusion Many-to-One/One-to-Many Communication Problems Channel coding problem → Transmission of correlated messages (edges of graphs) over the channel Source Coding Problem → Representation of Correlated Sources into graphs Graph-based framework for transmission of correlated sources over multiuser channels Modular architecture Interface between source and channel coding → Nearly semi-regular graphs

47. Future Research Issues More detailed characterization of the structure of bipartite graphs Number of different equivalence class with particular parameters Relation between probability distributions and equivalence classes Construction of practical codes for MAC and BC with correlated sources

48. Thank you!

49. Equivalence Classes of the Graphs

50. Limitation Given correlated sources can be reliably transmitted over the multiuser channels only if The graph representing the sources and The graph whose edges can be reliably transmitted Belong to the same equivalence class.