Title | Lecture 1 - EE 290S |
---|---|
Author | StuDocu Stud |
Course | Advanced Topics in Electrical Engineering: Advanced Topics in Communications and Information Theory |
Institution | University of California, Berkeley |
Pages | 18 |
File Size | 473.1 KB |
File Type | |
Total Downloads | 72 |
Total Views | 154 |
EE 290S...
EECS 290S: Network Information Flow Anant Sahai David Tse
Logistics • Anant Sahai: 267 Cory (office hours in 258 Cory), sahai@eecs. Office hours: Mon 4-5pm and Tue 2:30-3:30pm. • David Tse, 257 Cory (enter through 253 Cory), dtse@eecs. Office hours: Tue 10-11am, and Wed 9:30-10:30am. • Prerequisite: some background in information theory, particularly for the second half of the course. • Evaluations: – – – –
Two problem sets (10%) Take-home midterm (15%) In-class participation and a lecture (25%) Term paper/project (50%)
Logistics • Text: – Raymond Yeung, Information Theory and Network Coding, preprint available at http://iest2.ie.cuhk.edu.hk/~whyeung/post/main2.pdf. – Papers
• References – T. Cover and J. Thomas, Elements of Information Theory, 2nd edition.
Classical Information Theory
• • • • •
A Mathematical Theory of Communication 1948
Source has entropy rate H bits/sample. Channel has capacity C bits/sample. Reliable communication is possible iff H < C. Information is like fluid passing through a pipe. How about for networks?
General Problem
• Each source is observed by some nodes and needs to be sent to other nodes • Question: Under what conditions can the sources be reliably sent to their intended nodes?
Simplest Case
S
D
• Single-source-single-destination (single unicast flow) • All links are orthogonal and non-interfering (wireline)
C = m incut ( S; D ) (Ford-Fulkerson 1956)
• Applies to commodities or information. • Applies even if each link is noisy. • Fluid through pipes analogy still holds.
Extensions • More complex traffic patterns • More complex signal interactions.
Multicast • Single source needs to send the same information to multiple destinations.
s b1
• What choices can we make at node w?
t
• Or can it?
b1
b2 w
b1 • One slave cannot serve two masters.
b2 u b2
x y
z
Multicast • Picking a single bit does not achieve the min-cut of both destinations
s b1 t
b2 b1
b2 w
b1
b1
u b2
x y b 1
b1
z
Network coding • Needs to combine the bits and forward equations. s b1
• Each destination collects all the equations and solves for the unknown bits. • Can achieve the min-cut bound simultaneously for both destinations.
t
b2 b1
b2 w
b1
b1 + b 2
u b2
x y b +b 1 2
b1 + b 2 z
Other traffic patterns • Multiple sources send independent information to the same destination. • Single source sending independent information to several destinations. • Multiple sources each sending information to their respective destinations. • The last two problems are not easy due to interference
Complex Signal Interactions: Wireless Networks
S
D
relays
• Key properties of wireless medium: broadcast and superposition. • Signals interact in a complex way. • Standard physical-layer model: linear model with additive Gaussian noise.
Gaussian Network Capacity: Known Results
Rx
Tx point-to-point (Shannon 48)
C = log2 (1 + SNR)
Tx 1
Rx1 Rx
Tx 2 multiple-access (Alshwede, Liao 70’s)
Tx Rx 2 broadcast (Cover, Bergmans 70’s) (Weintgarten et al 05)
What We Don’t Know Unfortunately we don’t know the capacity of most other Gaussian networks. Tx 1
Rx 1
Tx 2
Rx 2
Interference (Best known achievable region: Han & Kobayashi 81) Relay
S
relay
D
(Best known achievable region: El Gamal & Cover 79)
Bridging between Wireline and Wireless Models • There is a huge gap between wireline and Gaussian channel models: – signal interactions – Noise
• Approach: deterministic channel models that bridge the gap by focusing on signal interactions and forgoing the noise.
Two-way relay example R 1)
A
b1
B
R 2)
3)
4)
A
A
A
R b1
R b2
b2
B
RAB =RBA=1/4 B
B
Network coding exploits broadcast medium
R 1)
A
b1
B
R 2)
A
b2
B
b1⊕b2 3)
A
B RAB=RBA=1/3
Nature does the coding via superposition
1)
A
b1
b1⊕b2
b2
B
b1⊕b2 2)
A
B
RAB=RBA=1/2
But what happens when the signal strengths of the two links are different?...