View
227
Download
2
Tags:
Embed Size (px)
Citation preview
A Graph-based Framework for A Graph-based Framework for Transmission of Correlated SourcesTransmission of Correlated Sources
over Multiuser Channelsover Multiuser Channels
Suhan ChoiMay 2006
Multiuser Communication ScenariosMultiuser Communication Scenarios
Multiuser Communication ScenariosMultiuser Communication Scenarios
Practical Applications Sensor Networks Wireless Cellular Systems, Wireless LAN Broadcasting Systems
Many-To-OneCommunications
One-To-ManyCommunications
Contents of DissertationContents 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
Outline of the PresentationOutline of the Presentation
Many-to-One Communications Preliminaries
Channel Coding Problem
Source Coding Problem
Motivation & Remarks
Example
Conclusion & Future Research Issues
OutlineOutline
Many-to-One Communications Preliminaries
Channel Coding Problem
Source Coding Problem
Motivation & Remarks
Example
Conclusion & Future Research Issues
Definition of Bipartite GraphsDefinition of Bipartite Graphs
1
2
A
B
C
Semi-Regular Bipartite GraphsSemi-Regular Bipartite Graphs
1
2
3
4
1
2
3
5
4
6
1
2
3
4
1
2
3
5
4
6
Nearly Semi-Regular Bipartite GraphsNearly Semi-Regular Bipartite Graphs
1
2
3
4
1
2
3
5
4
6
Strongly Typical Sequences Strongly Typical Sequences
Non-typical set
Strongly Jointly Typical Sequences Strongly Jointly Typical Sequences
OutlineOutline
Many-to-One Communications Preliminaries
Channel Coding Problem
Source Coding Problem
Motivation & Remarks
Example
Conclusion & Future Research Issues
Problem Formulation:Problem Formulation:MAC with Correlated MessagesMAC with Correlated Messages
1
2
3
1
2
3
1
2
3
1
2
3
Independent
Correlated
MACChannel
Encoder 1
ChannelEncoder 2
ChannelDecoder
Problem Formulation: Problem Formulation: Transmission SystemTransmission System
MACChannel
Encoder 1
ChannelEncoder 2
ChannelDecoder
Definition of Achievable RatesDefinition of Achievable Rates
Remark on Achievable Rates Remark on Achievable Rates & Capacity Region& 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
An Achievable Rate Region for the An Achievable Rate Region for the MAC with Correlated MessagesMAC with Correlated Messages
Remark on the Theorem 1Remark on the Theorem 1
Sketch of the Proof of Theorem 1 (1)Sketch of the Proof of Theorem 1 (1)
Sketch of the Proof of Theorem 1 (2)Sketch of the Proof of Theorem 1 (2)
Sketch of the Proof of Theorem 1 (3)Sketch of the Proof of Theorem 1 (3)
Sender 1Codewords
n n
Sender 2Codewords
Sketch of the Proof of Theorem 1 (4)Sketch of the Proof of Theorem 1 (4)
Sketch of the Proof of Theorem 1 (5)Sketch of the Proof of Theorem 1 (5)
n
Sender 1Codewords
n
Sender 2Codewords
graphgeneration
1
2
3
4
1
2
3
4
Sketch of the Proof of Theorem 1 (6)Sketch of the Proof of Theorem 1 (6)
Converse Theorem for the Sum-Rate Converse Theorem for the Sum-Rate of the MAC with Correlated Messagesof the MAC with Correlated Messages
OutlineOutline
Many-to-One Communications Preliminaries
Channel Coding Problem
Source Coding Problem
Motivation & Remarks
Example
Conclusion & Future Research Issues
Source Coding ProblemSource Coding Problem(Representation of Correlated Sources using (Representation of Correlated Sources using nearly semi-regular bipartite graphs)nearly semi-regular bipartite graphs)
SourceEncoder 1
SourceEncoder 2
SourceDecoder
Problem Formulation: Problem Formulation: Transmission SystemTransmission System
Definition of Achievable RatesDefinition of Achievable Rates
Remark on Achievable Rates Remark on Achievable Rates & Our Goal& 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
The Achievable Rate RegionThe Achievable Rate Region
Sketch of the Proof of Theorem 3 (1) Sketch of the Proof of Theorem 3 (1) (Direct Part)(Direct Part)
Sketch of the Proof of Theorem 3 (2)Sketch of the Proof of Theorem 3 (2)
Sketch of the Proof of Theorem 3 (3)Sketch of the Proof of Theorem 3 (3)
graphgeneration
1
2
3
4
1
2
3
4
Sketch of the Proof of Theorem 3 (4)Sketch of the Proof of Theorem 3 (4)
Sketch of the Proof of Theorem 3 (5)Sketch of the Proof of Theorem 3 (5)
OutlineOutline
Many-to-One Communications Preliminaries
Channel Coding Problem
Source Coding Problem
Motivation & Remarks
Example
Conclusion & Future Research Issues
Motivation: Why we choose graphs?Motivation: Why we choose graphs?
Jointly Typicality can be captured by the graph
n
2
1
1
2
n
1
22
1
Nearly Semi-regularBipartite Graph
GraphTypicality Graph
Transmission of Correlated Sources over a Transmission of Correlated Sources over a Multiple Access Channel (MAC)Multiple Access Channel (MAC)
MACEncoder 1
Encoder 2
Decoder
MACChannel
Encoder 1
ChannelEncoder 2
ChannelDecoder
SourceEncoder 1
SourceEncoder 2
SourceDecoder
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
OutlineOutline
Many-to-One Communications Preliminaries
Channel Coding Problem
Source Coding Problem
Motivation & Remarks
Example
Conclusion & Future Research Issues
Gaussian MAC with Jointly Gaussian Gaussian MAC with Jointly Gaussian Channel InputChannel Input
Gaussian MAC
Z
1X
2XY
A Special Case in the Gaussian MACA Special Case in the Gaussian MAC
A Special Case in the Gaussian MACA Special Case in the Gaussian MAC
Gaussian MAC with Correlated Gaussian MAC with Correlated MessagesMessages
Independent vs. Correlated Codewords
OutlineOutline
Many-to-One Communications Preliminaries
Channel Coding Problem
Source Coding Problem
Motivation & Remarks
Example
Conclusion & Future Research Issues
ConclusionConclusion
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
Future Research IssuesFuture 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
Thank you!Thank you!