Network Information Flow

1
Network Information Flow

• Tom Cover

2
Goals

• General goal
• What is the capacity region of communication
  networks with arbitrary interference, noise and
  feedback?
• Subgoal
• Solve special cases.
• Observe general heuristics and principles.

3
Broadcast Channel
Degraded Broadcast Channel
Ideas Superposition Successive
Decoding Applications Lectures Images
4
Multiple Access Channel
Gaussian Channel
Ideas Information flow across cut
sets Applications Music, singing, CDMA,
Cocktail party effect
5
Role of Feedback

• Doesnt help for memoryless channels
• Colored Gaussian noise
• Feedback helps multiple access channel
• Simplifies coding
• Example Erasure channel

Ideas Feedback helps (a little) Feedback
simplifies Applications Dialog
6
Time Synchronization for Multiple Access Channels
Ideas Use joint typicality Applications Time
synchronization is not necessary
7
Joint Data Compression
Slepian-Wolf Theorem
Ideas Hashing works Applications Distributed
source coding
8
Open Problem
Exchanging lists
Find R1 and R2.
How many bits must be exchanged to find the
element common to both lists?
9
Channels with Side Information
Writing on Dirty Paper
Ideas Join the noise dont fight
it Applications Watermarking Terraforming
10
Conclusion

• Superimpose information.
• Use all the band all the time (CDMA).
• Use feedback for simplicity.
• Feedback induces cooperation.
• Use random hashing for descriptions.
• Join noise, dont fight it.