Network Coding – Algebraic Structure
Transcript of Network Coding – Algebraic Structure
Network Coding – Algebraic Structure
Muriel MédardEECS
Massachusetts Institute of Technology
joint work with Ralf Koetter, Tracey Ho, Desmond Lun
Collaborators
• MIT: Varun Aggarwal, Ebad Ahmed, Wenjun Hu, David Karger, Dina Katabi,Sachin Katti, Minji Kim, Minkyu Kim, Anna Lee, Asuman Ozdaglar, HariharanRahul, Devavrat Shah, Jay-Kumar Sundararajan, Fang Zhao
• MIT Broad Institute: Desmond Lun (previously MIT)• Technical University of Munich: Ralf Koetter (previously UIUC), Danail Traskov
(previously UIUC)• California Institute of Technology: Michelle Effros, Tracey Ho (previously MIT,
UIUC, Lucent)• Ecole Polytechnique Federale Lausanne (Switzerland): Christina Fragouli• Digital Fountain: Payam Pakzad (previously EPFL)• Qualcomm: Niranjan Ratnakar (previously UIUC)• BBN: Karen Haigh, Paul Rubel• Ohio State University: Atilla Eryilmaz (previously UIUC, MIT)• Support from DARPA (ITMANET, CBMANET, seed), NSF (ITR, XOR in the Air),
ARO (DAWN)
Network coding
s
t u
y z
w
b1
b1
b1
b2
b2
b2
x
• Canonical example [Ahslwede et al. 00]
• What choices can we make?
• No longer distinct flows, but information
Network coding
s
t u
y z
w
b1
b1
b1
b1
b2
b2
b2
xb1b1
• Picking a single bit does not work
• Time sharing does not work
• No longer distinct flows, but information
Network coding
s
t u
y z
w
b1
b1
b1
b1 + b2
b2
b2
b2
xb1 + b2b1 + b2
• Need to use algebraic nature of data
• No longer distinct flows, but information
[KM01, 02, 03]
A simple example
A simple example
Transfer matrix
Linear network system
Solutions
Another Example
Multicast
Multicast
Multicast
Multi-source multicasts
Multi-source multicasts
One source, disjoint multicasts
One source, disjoint multicasts plus multicasts
One source, disjoint multicasts plus multicasts
One source, two-level multicast
One source, two-level multicast
Delays
Delays
Delays
Delays
Delays
Delays
Delays and cycles