reliable multihop transfer on wireless sensor networks sukun kim, rodrigo fonseca, david culler, ion...
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![Page 1: Reliable Multihop Transfer on Wireless Sensor Networks Sukun Kim, Rodrigo Fonseca, David Culler, Ion Stoica UC Berkeley NEST Retreat – Jun 4, 2004 in Santa](https://reader036.vdocuments.us/reader036/viewer/2022062715/56649d775503460f94a59a3b/html5/thumbnails/1.jpg)
Reliable Multihop Transferon Wireless Sensor Networks
Sukun Kim, Rodrigo Fonseca,David Culler, Ion Stoica
UC Berkeley
NEST Retreat – Jun 4, 2004 in Santa Cruz
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Problem Statement
• Goal– Reliable communication in multihop Wireless
Sensor Networks
• Assumption– Wireless communication– Resource-constrained mote
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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)
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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
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Design Space 3 – Routing Layer
Point-to-point Convergence Divergence
Implementation on Beacon Vector Routing
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Erasure CodeEncoding Channel Decoding
M8 msgs
N
21 code words
N’≥8 code words
M
8 original msgs
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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
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Systematic Code
Encoding one code word takes 1.7msDecoding time varies from 0 to 27msReal time processing is possible
In MICA2
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Alternative Route Discovery
Find Alternative Route
What if
Get 6 best candidates for the next hop from routing table. And try from the best
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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
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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
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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
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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
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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
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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
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Questions
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Encoding Unit
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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
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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
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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
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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
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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
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Encoding Speed
0
2
4
6
8
10
12
14
16
0 2 4 6 8 10
Number of Redundant Codes
Tim
e (
ms)
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Decoding Speed
0
5
10
15
20
25
30
0 2 4 6 8 10
Number of Non-Original Message Code
Tim
e (
ms)
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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)
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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)
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What ifEncoding Channel Decoding
M8 msgs
N
21 code words
N’≥8 code words
M
8 original msgs
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Problem Statement
Application
Network (Routing)
Reliable TransportInterface toarbitrary Routing Layer
Point-to-point, Convergence, Divergence+ Version Upgrade
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Terms
Application
Reliable Transport
Network
Bundle
Bundle Fragmentation
Packet
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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
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Options
1. End-to-end Retransmission (inefficient)
2. Custody Transfer
3. Erasure Code
4. Hybrid of 2 and 3
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Options
1. End-to-end Retransmission (inefficient)
2. Custody Transfer
3. Erasure Code
4. Hybrid of 2 and 3
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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
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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
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Options
1. End-to-end Retransmission (inefficient)
2. Custody Transfer
3. Erasure Code
4. Hybrid of 2 and 3
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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
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Options
1. End-to-end Retransmission (inefficient)
2. Custody Transfer
3. Erasure Code
4. Hybrid of 2 and 3
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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
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Another Option
• Thick path– Traffic multiplied by the width of path– Can be too much overhead
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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
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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
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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?
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Questions
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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)
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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
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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
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Reed-Solomon Code
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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!!!
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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
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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
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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
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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
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Other optimization for erasure code
• Division of message
• Operation table
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• Common requirement regardless of solution
• Different requirements specific for solution
• Erasure code needs separate congestion control
• Is control packet good?