Efficient Error Estimating Coding:Efficient Error Estimating Coding:Feasibility and ApplicationsFeasibility and Applications
Binbin Chen Ziling Zhou Yuda Zhao Haifeng Yu
School of Computing
National University of Singapore
Background: Error Correcting CodesBackground: Error Correcting Codes Error correcting codes play fundamental roles in
communication systems:
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1 0
decode
1 1 1 0 0 0 1 0 1 0 0 0
encode
Philosophy behind over 50 years of research on error correcting codes:
Only want to deal with entirely correct data
1 0
sender receiver
network
Our Key ContributionOur Key Contribution
Many state-of-art designs in wireless networking leverage partially correct packets More on these designs later…
Look beyond error correcting codes?
Our main contribution:
Novel concept of Error Estimating Coding (EEC) Enable the receiver to estimate the number of errors
(i.e., flipped bits) in a partially correct packet
But cannot tell the positions of the errors
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EEC: New TradeoffsEEC: New Tradeoffs
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Weaker functionality
Smaller overhead
Stronger functionality
Larger overhead
error correcting codes
error estimating codes
EEC – Why is it interesting?EEC – Why is it interesting?
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small redundancy overhead large redundancy overhead
error correcting codes
error estimating codes
(n) 2% can only correct rather small # errors (e.g., 24 errors out of 12000 bits)
O(log n) E.g., 2% overhead on 1500-byte packet If only want to know whether # errors exceeds some threshold -- just 4 bytes Can be viewed as generalized CRC
EEC – Why is it interesting?EEC – Why is it interesting?
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small computational overhead large computational overhead
error correcting codes
error estimating codes
Often need hardware support to be fast enough Some codes (e.g., Reed-Solomon codes) have highly optimized software implementation 10 to 100 times slower than EEC Hard to support 802.11a/g data rates
Pure software implementation can support all 802.11a/g data rates on typical hardware platform today
EEC – Why is it interesting?EEC – Why is it interesting?
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weaker functionality stronger functionality
error correcting codes
error estimating codes
Estimate the number of errors Provable estimation quality No assumption needed on error correlation or independence
RoadmapRoadmap
Applications of EEC What designs deal with partial packets?
How can EEC help them?
Feasibility of Efficient EEC
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Example Scenario: Streaming VideoExample Scenario: Streaming Video
Source adds forward error correction Can recover a packet if BER below some threshold
Router forwards all packets (even if partially correct)
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source
destination
1 0 1 1 0 1
1 0 1 1
decode
1 0 1 0 0 11 0 1 0 0 1
1 0 1 1 0 1
router
Streaming Video: How can EEC help?Streaming Video: How can EEC help?
Packets with many errors cannot be recovered – router should have asked for retransmission
BER-aware retransmission: Routers use EEC to determine whether to request retransmission Bit Error Rate: Fraction of corrupted bits
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source
destination
1 0 1 1 0 1
1 0 0 0 0 11 0 0 0 0 1
1 0 1 1 0 1 decode
decoding failure
router
Summary of Experimental ResultsSummary of Experimental Results
Implementation on Soekris Net5501-70 routers
BER-aware retransmission consistently outperforms other schemes that do not have access to BER info In all experimental settings (e.g., with/without
interference, different link quality)
Up to 5dB gain on PSNR of the streamed video
0.5dB gain is usually considered visually noticeable
Details in paper…
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Generalization: Generalization: Treat different partial packets differentlyTreat different partial packets differently
BER-aware packet forwarding Context: Cooperative relay
Use analog-amplify for packets with large BER
Use digital-amplify for packets with small BER
BER-aware packet scheduling Context: Image sensor network for emergency
response (e.g., [Kamra et al., SIGCOMM’06])
Let packets with small BER (and thus more valuable) go through first
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Example Scenario: Bulk data transfer Example Scenario: Bulk data transfer
Leverage partial packets and correct errors end-to-end Combining multiple partial packets[Dubois-Ferriere et
al., Sensys’05]
Use network coding as in MIXIT[Katti et al., SIGCOMM’08]
Destination requests extra error correcting redundancy if needed (i.e., similar to ZipTX [Lin et al.,
MobiCom’08])
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Bulk data transfer: How can EEC help?Bulk data transfer: How can EEC help?
In these systems, EEC can help to do better WiFi rate adaptation Select the data rate with the best goodput Based on current tradeoff between data rates and
packet BER
The mapping between data rates and BER is the key info needed by rate adaptation EEC exactly provides the BER info at current rate
Comparison: Previous Rate Adaptation SchemesComparison: Previous Rate Adaptation Schemes
Based on packet loss ratio Coarse grained info
Need multiple packets to observe properly
Based on signal-to-noise ratio Indirect measure and needs training
SoftRate [Vutukuru et al., SIGCOMM’09]: Modify physical layer to obtain BER info Not supported by today’s commercial hardware
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Summary of Experimental ResultsSummary of Experimental Results EEC-Rate implemented in MadWifi 0.9.4.
Use per-packet BER to guide rate adaptation
EEC-Rate consistently outperforms state-of-art schemes based on packet loss ratio or SNR In all experimental settings (e.g., indoor/walking/
outdoor, with/without interference)
Up to 50% higher goodput in walking scenario
Up to 130% higher goodput in outdoor scenario
Details in paper…16
Generalization: Wireless carrier selectionGeneralization: Wireless carrier selection
General problem of wireless carrier selection Multiple wireless carriers (e.g., sending rates)
Dynamically select the carrier with the best goodput
More examples:1.Wireless channel selection
2.Transmission power selection
3.Directional antenna orientation selection
4.Routing in multi-hop wireless networks
…
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RoadmapRoadmap
Applications of EEC More application scenarios in paper…
Feasibility of Efficient EEC
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ModelModel A packet holds n data bits and k EEC bits, in
n+k slots
p fraction of the slots are erroneous p is not a probability
Positions of erroneous slots can be arbitrary (e.g., fully clustered or fully spread)
Goal: Generate an estimation for p (with certain target estimation quality)
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Naïve Sampling Using Pilot BitsNaïve Sampling Using Pilot Bits
Problem: Ineffective for small p p = 0.01: needs roughly 100 pilot bits to see one error
BER is usually a small value…
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X X XXX X XX data bit
pilot bit
4 slots erroneous out of 12 slots X erroneous slot
p estimated to be 1/3
need enough errors on the pilot bits to estimate properly
Use a Parity Bit to Sample a Group of BitsUse a Parity Bit to Sample a Group of Bits Hope to sample a group of 100 slots together
Use a parity bit to sample a group of data bits
Larger group size More likely to see errors
Helps to deal with small p – Just use larger groups
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Parity bit for a group of 4 data bits
data bit
parity bit
(EEC bit)
ChallengesChallenges
1. Parity information is limited -- Cannot even distinguish 1 error from 3 errors in the group
2. Parity bits themselves may be erroneous
3. Error prob of an parity bit and error prob of data bits in the group are correlated
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X X XX
X X XX
Data bits error prob higher
Data bits error prob lower
Will leave details on these challenges to paper…
permuteEEC Encoding on Sender
Single-level EECSingle-level EEC
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data bits EEC bits
packet
On receiver, let q be the fraction of parity check failures:
If q [0.25, 0.4], BER can be estimated as f(q)
(see paper for the closed-form of f())
Each EEC bit is the parity bit of a group of randomly selected data bits (all groups have the same size).
Multi-level EECMulti-level EEC
Single-level EEC succeeds only for q [0.25, 0.4]
Multi-level EEC: log(n) levels with geometrically distributed group sizes 2, 4, 8, 16, …, n Claim: There almost always exists some level such
that q [0.25, 0.4] on that level
Complication: With multiple levels, undesirable rare events will be more common…see paper
Various extensions…see paper
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Formal GuaranteesFormal Guarantees
(Rough) Theorem: For any given 0<<1 and 0<<1, using log(n) levels with O(1) EEC bits per level will ensure:
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1])1(ˆ)1Pr[( ppp
EEC and SoftPHYEEC and SoftPHY SoftPHY [Jamieson et al., SIGCOMM’07]
Physical layer exposing confidence level for each bit received
Can estimate BER – in fact, offer additional info beyond BER
Today’s commercial WiFi hardware does not provide such functionality
EEC is a pure software solution Flexibility, easier to adopt or upgrade
Will be attractive for lower-end wireless devices even if SoftPHY becomes available on future WiFi devices
But if need per-bit confidence info, EEC cannot substitute SoftPHY
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ConclusionsConclusions
Key contribution: Error estimating coding Estimate the # of errors (with provable estimation
quality), without correcting them
New tradeoff between functionality and overhead
Why is EEC interesting? EEC functionality significantly benefits modern
designs in wireless networks
EEC overhead orders of magnitude smaller than error correcting codes (e.g., allows highly efficient software implementation)