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