Optimization in IntraIntersession Network Coding

1
Optimization in Intra/Inter-session Network
Coding
Dongsuk Shin and Junseop Ahn shinds and junsuby
_at_kaist.ac.kr

• Department of Electrical Engineering
• Korea Advanced Institute of Science and
  Technology (KAIST)

2
Outline
1. Introduction 2. Motivation 3. System
model 4. Problem formulation 5. Proposed
Algorithm 6. Big Picture 7. Criticism and
conclusion
3
Introduction

• Network coding is a particular in-network data
  processing technique that exploits the
  characteristics of the wireless medium (in
  particular, the broadcast communication channel)
  in order to increase the capacity or the
  throughput of the network

• TERMINOLOGY
• Communication network finite directed graph
• Acyclic communication network network without
  any direct cyclic
• Source node node without any incoming edges
  (square)
• Channel noiseless communication link for the
  transmission of a data unit per unit time (edge)

4
Introduction

• Without network coding
• Simple store and forward
• Multicast rate of 1.5 bits per time unit

5
Introduction

• With network coding
• X-OR ? is one of the simplest form of data coding
• Multicast rate of 2 bits per time unit
• Disadvantages
• Coding/decoding scheme has to be agreed upon
  beforehand

6
NC and wireless communications
(a)

• Problem send b1 from A to B and b2 from B to A
  using node C as a relay
• A and B are not in communication range (r)
• Without network coding, 4 transmissions are
  required.
• With network coding, only 3 transmissions are
  needed

(b)
(c)
b2
b2
b1
C
C
B
A
B
A
7
Linear network coding

• When we refer to linear network coding, we intend
  that
• The output flow at a given node is obtained as a
  linear combination of its input flows. The
  coefficients of the combination are, by
  definition, selected from a finite field
• Coding can be implemented at low computational
  cost
• Moreover, the information traversing a non source
  node has the following property
• The content of any information flowing out of a
  set of non source nodes can be derived from the
  accumulated information that has flown into the
  set of nodes

8
Theoretical model for linear NC

• Graph (V,E) having unit capacity edges
• Sender s in V, set of receivers Tt, in V

Source node of h symbols
Intermediate node
Destination node
9
Linear coding phase
Local encoding vector
Transmitted symbol
Global encoding vector
10
Decoding phase
Node t can recover the source symbols x1, . . . ,
xh as long as the matrix Gt, formed by the global
encoding vectors, has (full) rank h.
11
Inverting Gt

• Gt will be invertible with high probability if
  local encoding vectors are random and the field
  size is sufficiently large
• P 1 - F (where F is the cardinality of the
  finite field of coefficients)
• Example
• If field size 216 and E 28 then Gt will be
  invertible with probability 1-2-8 0.996

12
Motivation
13
System model
14
Problem formulation
15
Proposed Algorithm
16
Big Picture
17
Criticism and conclusion