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A Graph-based Framework for Transmission of Correlated Sources over Multiuser Channels

This dissertation presents a graph-based framework for efficient transmission of correlated sources over multiuser channels, including practical applications in sensor networks, wireless cellular systems, and broadcasting systems.

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A Graph-based Framework for Transmission of Correlated Sources over Multiuser Channels

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

  2. Multiuser Communication Scenarios

  3. Multiuser Communication Scenarios • 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. A 1 B 2 C Definition of Bipartite Graphs

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

  9. Nearly Semi-Regular Bipartite Graphs 1 1 2 2 3 4 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 Channel Encoder 1 MAC Channel Decoder Channel Encoder 2 Correlated Independent

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

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

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

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

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

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

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

  39. 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 Encoder 1 MAC Decoder Encoder 2 Source Encoder 1 Channel Encoder 1 MAC Channel Decoder Source Decoder Source Encoder 2 Channel Encoder 2 Transmission of Correlated Sources over a Multiple Access Channel (MAC)

  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

  43. 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!

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