Reliable Multihop Transferon Wireless Sensor Networks

Sukun Kim, Rodrigo Fonseca,David Culler, Ion Stoica

UC Berkeley

NEST Retreat – Jun 4, 2004 in Santa Cruz

Problem Statement

• Goal– Reliable communication in multihop Wireless

Sensor Networks

• Assumption– Wireless communication– Resource-constrained mote

Constraints and Options

Sources of Failure• Link Failure• Mote Failure• …

How to obtain reliability? (possible options)1. Add redundancy of information

1. Retransmission – link-level, end-to-end2. Data redundancy – duplication, erasure code3. Path redundancy – Use thick path

2. Increase success rate1. Alternative Route2. Congestion Control

Internet

(# of pkts received) = Psuccess × (# of pkts sent)

Design Space 2 – Unit of Transfer

Fragment

Bundle

N1 N2 N3

Using fragmentation

+ Less buffer space

+ Multiplexing (point-to-point)

- Reordering, Reassembly

- More control traffic overhead

Design Space 3 – Routing Layer

Point-to-point Convergence Divergence

Implementation on Beacon Vector Routing

Erasure CodeEncoding Channel Decoding

M8 msgs

N

21 code words

N’≥8 code words

M

8 original msgs

Systematic Code

Benefit: if receiver has codes containing original messages• Encoding, Decoding are faster• Even if receiver get less than 8 packets, we don’t lose

every message

Systematic Code

Encoding one code word takes 1.7msDecoding time varies from 0 to 27msReal time processing is possible

In MICA2

Alternative Route Discovery

Find Alternative Route

What if

Get 6 best candidates for the next hop from routing table. And try from the best

Systematic Code without Route Fix

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6

Max Number of Retransmission

Su

cce

ss R

ate

012345678

10.37 hops, 17.25% loss rate, 8 original messages

Overhead (10.37 hops, 17.25% loss rate)

0

5

10

15

20

25

30

35

40

45

50

0 1 2 3 4 5 6

Max Number of Retransmission

Nu

mb

er

of

Pa

cke

ts I

nje

cte

d p

er

Da

ta

012345678

10.37 hops, 17.25% loss rate, 8 original messages

Effect of Route Fix

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6

Max Number of Retransmission

Su

cce

ss R

ate

w/o Route Fixw/ Route Fix

Systematic Code with Route Fix

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6

Number of Redundant Packets

Su

cce

ss R

ate

012345678

8 original messages

Conclusion

• Moderate redundancy (2~3) in erasure code and Large maximum number of retransmission is good combination with route fix is good combination

• For ultimate reliability, alternative route approach is very appealing

(# of pkts received) = Psuccess × (# of pkts sent)

• Separate layer like TCP may not work efficiently

Design Spaces and Options

End to endFragment custodyBundle custody

Link-level retransmission

End-to-end retransmission

Erasure codeThick path

Success rate

Overhead

Delay

Routing layer 2

Routing layer 3

Can depend on loss rate, path length

Questions

Encoding Unit

Design Space 1

• How to obtain reliability? (possible options)– Add redundancy of information

• Retransmission – link level, end-to-end

• Data redundancy – duplication, erasure code

• Path redundancy – Use thick path

– Increase success rate• Alternative Route

• Congestion Control

Fragment compared to Bundle

+ Less buffer space

+ Multiplexing (point-to-point)

+ Decouple bundle size from transport

- Reordering, Reassembly

- Different fates to different pages

- More control traffic overhead

- End points must hold buffer longer

Point-to-point

Admission Control

• Node may also refuse to accept custody for a message, in case its local storage, for example, is full

• This mechanism can create a back-pressure signal that may eventually limit the rate at the source– Congestion control

• On-demand vs Credit-based flow control

Effect of Erasure Code

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Raw Loss Rate

Fin

al L

oss

Ra

te

1

2

4

8

16

64

247

Effect of Systematic Code

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Raw Loss Rate

Fin

al L

oss

Ra

te

1

2

4

8

16

64

247

Encoding Speed

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10

Number of Redundant Codes

Tim

e (

ms)

Decoding Speed

0

5

10

15

20

25

30

0 2 4 6 8 10

Number of Non-Original Message Code

Tim

e (

ms)

Decoding Time versus Loss Rate

0

5

10

15

20

25

30

0 0.2 0.4 0.6 0.8 1

Loss Rate

Tim

e (

ms)

Variation in Decoding Time (R = 4)

0

2

4

6

8

10

12

14

16

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Tim

e (

ms)

What ifEncoding Channel Decoding

M8 msgs

N

21 code words

N’≥8 code words

M

8 original msgs

Problem Statement

Application

Network (Routing)

Reliable TransportInterface toarbitrary Routing Layer

Point-to-point, Convergence, Divergence+ Version Upgrade

Terms

Application

Reliable Transport

Network

Bundle

Bundle Fragmentation

Packet

Challenges in Reliable Multihop Transport

• Energy, computational power, and memory space are limited, and call for algorithms that are parsimonious in their use

• Wireless communication - Asymmetry of link, correlated loss (obstacles, interference), weak correlation to distance, hidden terminal problems, shared broadcast medium

Options

1. End-to-end Retransmission (inefficient)

2. Custody Transfer

3. Erasure Code

4. Hybrid of 2 and 3

Options

1. End-to-end Retransmission (inefficient)

2. Custody Transfer

3. Erasure Code

4. Hybrid of 2 and 3

Alternative Route Discovery

• Upon a link failure, the node has to try another neighbor (next hop), wait for some time, or return a failure notification– Guarantee that if the message will arrive at the

destination if there is a route

End-to-end argument

• 100% Requires end-to-end feedback– Routing layer has to provide a way for the

routing of ack packets back to the source– Backward Routing

• With Link-level retransmission RTT can vary significantly– Use upper bound for timeout

Options

1. End-to-end Retransmission (inefficient)

2. Custody Transfer

3. Erasure Code

4. Hybrid of 2 and 3

Erasure Code

• Only if M out of N packets arrive, we can construct original M message

• 9X.X% would be enough?– Link failure: correlated consecutive packet loss

until route recovery– Erasure code alone may not be able to

guarantee reliability

• Need separate congestion control

• Implementation finished

Options

1. End-to-end Retransmission (inefficient)

2. Custody Transfer

3. Erasure Code

4. Hybrid of 2 and 3

Hybrid

• Erasure coding can afford missed packets– Even if packet gets stuck due to link failure, we

can forget about it

• Explicit failure notification– Find alternative route when link fails voiding

correlated drops

• “Lemmings” Protocol

Another Option

• Thick path– Traffic multiplied by the width of path– Can be too much overhead

Discussion

• Useful features from routing layer (API)– Find alternative route– Disable link

• For duration of transfer (due to link failure)

• Temporarily (due to contention)

– Or get a list of next hop candidates

• From the application:– No silent drops

Conclusion

• Custody transfer and erasure code have potential of providing high reliability combined with alternative route finding

• End-to-end argument– For eventual reliability, it would be needed– Introduces much overhead

• Preliminary performance evaluation will be available at the end of May

Problem Statement (revisited)

• What mechanisms do we need to achieve reliable multihop transport in sensor networks?

• Is it possible to reason about routing from reliability separately, and provide a proper interface for reliable transport?

• Can we devise a reliable transport layer that can be plugged on top of different kinds of routing layers, such as convergence, divergence, and in-network point-to-point routing?

Questions

Coding

• For encoding process, we would have encoding function C(X) where X is a vector of M message

• Then C(X) is a vector of N code words (N > N)

Linear Code

• If code has a property that C(X) + C(Y) = C(X+Y), then it is called a “linear code”

• Linear can be represented with a matrix A. Code word vector for message vector X is simply AX

• Encoding is matrix-vector multiplication• Decoding is finding X such that AX=W for a

received code word vector W• A should have M linearly independent rows so

that linear equation has unique solution, and in turn unique message vector

Vandermonde Matrices

• Vandermonde is a matrix with element A(i, j) = xij where each xi is nonzero and different from all others

• For N by M Vandermonde matrix (N > M), any M rows are linearly independent forming nonsingular matrix

• In linear equation AX=W where A is Vandermonde matrix, any M rows and corresponding M elements of W forms M by M square matrix and vector of size M, where matrix is nonsingular– Can uniquely determine X

Reed-Solomon Code

Reed-Solomon Code

• Produce N equations with M unknown variables. Then with any M out of N equations, we can find those M unknowns– For a given data, let us break down the data into M

messages w(1), w(2), …, w(n)– Construct P(X) using these messages as coefficients– Evaluate this polynomial P(X) at N different points x1,

x2, …, xn– P(x1), P(x2), …, P(xn) can be represented as

multiplication of matrix and vector

• A is Vandermonde matrix!!!

Field

• For efficient use of bits in packet, we use extension filed with base 2. First of all we need to look at field, and prime filed

• A field is any set of elements which satisfies the field axioms for both addition and multiplication and is commutative division algebra– Field axioms include commutativity,

associativity, ditributivity, identity, and inverse

Prime Field

• A field with a finite number of members is known as a finite field or Galois field

• Prime field is a Galois field, whose elements are integer in [0, p – 1], where p is prime

• Addition and multiplication are normal integer addition and multiplication with modulo operation at the end

Extension Field

• Extension field is a Galois filed whose elements are integer in [0, pr – 1]

• This set still satisfies properties of field. Moreover, by setting p = 2, we can fully utilize bits in message

• Non-singularity of Vandermonde matrix still holds for prime field, and even extension field

Systematic Code

• If some part of erasure code is original message itself so that we can get message without decode when every packets arrive, that code is called systematic code

• For Vandermonde matrix, substitution any part of matrix with identity matrix still keep non-singular, even for prime field and extension field

• When we have all packets encoded identity matrix, decoding is free

Other optimization for erasure code

• Division of message

• Operation table

• Common requirement regardless of solution

• Different requirements specific for solution

• Erasure code needs separate congestion control

• Is control packet good?