Network
This presentation is the property of its rightful owner.
Sponsored Links
1 / 19

Network Coding Tomography for Network Failures PowerPoint PPT Presentation


  • 80 Views
  • Uploaded on
  • Presentation posted in: General

Network Coding Tomography for Network Failures. Hongyi Yao. Sidharth Jaggi Minghua Chen. Tomography (CAT Scan). Computerized Axial. 1. Tomography. Heart. Y=TX T?. 2. Network Tomography. [V96]…. Objectives : Topology estimation Failure localization. @#$%&*. 001001.

Download Presentation

Network Coding Tomography for Network Failures

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Network coding tomography for network failures

Network Coding Tomography forNetwork Failures

Hongyi Yao

Sidharth Jaggi

Minghua Chen


Tomography cat scan

Tomography (CAT Scan)

Computerized Axial

1


Tomography

Tomography

Heart

Y=TX

T?

2


Network tomography

Network Tomography

[V96]…

  • Objectives:

    • Topology estimation

    • Failure localization

@#$%&*

001001

  • Failure type:

    • Adversarial error: The corrupted packets are carefully chosen by the enemies for specific reasons.

    • Random error: The network packets are randomly polluted.

3


Tomography type

Tomography type

  • Active tomography[RMGR04,CAS06]:

    • All network nodes work cooperativelyfor tomography.

    • Probe packets from the sources are required.

    • Heavy overhead on computation & throughput.

  • Passive tomography [RMGR04, CA05, Ho05, This work]:

    • Tomography is done during normal communications.

    • Zero overhead on computation & throughput.

4


Network coding

Network coding

S

  • Network coding suffices to achieve to the optimal throughput for multicast[RNSY00].

  • Random linear network coding suffices, in addition to its distributed feature and low design complexity[TMJMD03].

m1

m2

m1

m2

am1+bm2

m1+m2

m1

m2

r1

r2

5


Random linear network coding

Random Linear Network Coding

  • Source: Sends packets. Organized as:

  • Internal Nodes: Random linear coding

  • Sink gets Y:

X

I

v1

v2

v1

a1v1+a2v2

a1v1+a2v2

v2

Information T: Recover Topology [Sharma08]

TX

X

I

T

Y=T

=

6


Network coding aids tomography

back

e1

x

x

x

x

x=2

.

3+2 2

e1

e3

Network Coding Aids Tomography

  • Network coding scheme is used by u:x(e3)=x(e1)+2x(e2), x(e4)=x(e1)+x(e2).

  • Routing scheme is used by u:x(e3)=x(e1), x(e4)=x(e2).

Probe messages:

M=[1, 2]

e1

e3

3

1

3

2x

7

3

x

YE=[3, 2]

YM=[1,2]

E=YE-YM=[2,0]

YE=[7, 5]

YM=[5,3]

E=YE-YM=[2,2]

s

r

2

2

u

2

2

x

5

0

x[1,1]

x[2,1]

x[0,1]

x[1,0]

3+2

e2

e4

  • Network coding scheme is enough for r to locate error edge e1.

  • Routing scheme is not enough for r to locate error edge e1.

7


Summary of contribution

Summary of Contribution

  • It turns out that the idea underlying the exampleholds even the coding is done in a random fashion.

  • Random linear network coding has great advantages.

  • Passive = low overhead.

Passive tomography for random linear network coding

WHY?

Failure type

Topology estimation

Failure localization

Exponential

No result

[HLCWK05]

Adversary

error

Exponential

Hardness proof

[This work]

[This work]

Exponential

No result

[FM05,HLCWK05]

Random

error

Polynomial

Polynomial

[This work]

[This work]

8


Network coding tomography for network failures

Core Concept: IRV

0

0

Edge Impulse Response Vector (IRV):

The linear transform from the edge to the receiver.

UsingIRVswe can estimate topology and locate failures.

1

[2 9 6]

e1

[0 3 2]

3

1

2

e3

3

1

3

1

1. Relation between IRVs and network structure:

2

3

4

2

1

3

9

IRV(e1) is in the linear space spanned by IRV(e2) and IRV(e3).

[1 0 0]

6

2

e2

2

1

0

9

6

0

2. Unique mapping from edge to IRV:

For random linear network coding, two independent edges has independentIRVs with high probability.

9


Network tomography by irvs

Network tomography by IRVs

  • The concept of IRV significantly aids network tomography:

    • The relations between IRVs and network structure is used to estimate network topology.

    • The unique mapping between network edge and its IRV is used to locate network failures.


Topology estimation for random errors

Topology Estimation for Random Errors

  • Why study random failures:

    • For network without errors, the only information about the network is the transform matrix T. Thus recovering network topology is hard [SS08].

    • Surprisingly, for network with random failures (errors, or packet loss), the IRV of the failure edge will be exposed, letting us recovering network topology efficiently.


Topology estimation for random errors1

Topology Estimation for Random Errors

  • Stage 1: Collect IRVs

[2,1]

4 , 2

0 , 0

[1,3]

E1=

E2=

27 , 15

3 , 3

[0 3 2]

18 , 10

6 , 14

[1,1]

[3,2]

[0 3 2]

<E1> <E2>= < >

10


Topology estimation for random errors2

Topology Estimation for Random Errors

  • Stage 2: Recover topology

[2 9 6]

[0 0 4]

[0 3 2]

[2 9 6]

[0 0 4]

IRVs from Stage 1:

[0 3 2]

[0 0 2]

According to: IRV(e1) is in the linear space

spanned by IRV(e2) and IRV(e3).

[1 0 0]

[0 1 0]

[0 0 1]

e1

e2

e3

11


Network coding tomography for network failures

[2 9 6]

[0 3 2]

Random Failure Localization

Exp

Preliminaries: The Impulse Response Vector (IRV) of each edge.

As long as the topology is given, we can do error localization.

[4 27 18]

[2 15 10]

[1 0 0]

[2 9 6]

[0 3 2]

[0 0 2]

[0 0 4]

[0 1 0]

[0 0 1]

[2 9 6]

in < >?

[2,1]

IRVs:

[0 3 2]

[3,2]

Locating random failures:

[2 9 6]

[0 3 2]

4 , 2

E= [2,1] + [3,2] =

27 , 15

18 , 10

12


Summary of our contribution

Summary of our contribution

Failure type

Topology estimation

Failure localization

Exponential

No result

[HLCWK05]

Adversary

error

Exponential

Hardness proof

[This work]

[This work]

Exponential

No result

[FM05,HLCWK05]

Random

error

Polynomial

Polynomial

[This work]

[This work]


Future direction

Future direction

  • Current work: From existing good network codes to tomography algorithms.

  • Another direction: From some criteria to new network codes.

  • For instance, network Reed-Solomon code[HS10], satisfies:

    • Optimal multicast throughput

    • Low complexity and distributed designing.

    • Significantly aids tomography:

      • Failure localization without centralized topology information.

      • Adversary localization can be done in polynomial time.


Related works

Related works


Network coding tomography for network failures

Network Coding Tomography forNetwork Failures

  • Thanks!

  • Questions?

Details in: Hongyi Yao and Sidharth Jaggi and Minghua Chen, Network Tomography for Network Failures, under submission to IEEE Trans. on Information Theory, and arxiv: 0908-0711

14


  • Login