Coding - Simons Institute for the Theory of Computing · PDF filePre-coding (Raptor RFC 5053)...
Transcript of Coding - Simons Institute for the Theory of Computing · PDF filePre-coding (Raptor RFC 5053)...
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Coding theory for scalable media delivery Michael Luby
RaptorQ is a product of Qualcomm Technologies, Inc.
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Application layer erasure coding complements traditional error coding
“Erasure Coding”Protects against Data Lost
in Transmission
“Error Coding”Protects against Data Corruption
• Vast majority of current use of FEC
• Probably what you’re familiar with
• Typically applied at layers 1 or 2
• Usually performed in hardware
• PHY-FEC (physical layer FEC)
• Commercial application relatively new
• Applied above layer 2
• Complement to Error Coding
• Typically performed in software
• AL-FEC (application layer FEC)
Forward Error CorrectionTechnology
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Packet transmission
Packet header
Packet payload
Stream of packets
Received corrupted packet
Can identify received packet payloads from packet headers
Received corrupted packet is discarded
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Source data
Source data
Erasure encode
Erasure decode
Transmit
Application Layer erasure codes
Packetize
Depacketize
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AL-FEC and PHY-FEC are complementary
Time
PHY-FECCorrect or discard corrupted packet data over small block
Fixed time diversityFixed amount of protection
AL-FECPacket loss protection over small to large block
Flexible time diversity Flexible amount of protection
Flexible time diversity – from sub-second to hours
Fixed time diversity – e.g., < 1 second
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AL-FEC and PHY-FEC working together
PHY-FEC corrects noise and interference AL-FEC “interleaves” and corrects erasures
− Longer block length (“interleavers”) è better performance
PHY-FEC works
PHY-FEC fails
16QAM CR = 1/3
5.3 Mbit/s p=14%
Source block Repair
AL-FEC Decoding
Source blockAL-FEC CR = 0.8
4.3 Mbit/s p=0%
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Ø Generate as much encoding as desiredØ Recover source from the minimal possible encoding
Ø It doesn’t matter what is received or lost
Ø It only matters that enough is received
What is a fountain code?
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Fountain codes – erasure codes without a rate
Source data
Erasure encode
Encoded data
Ø Fountain codes have no predetermined rate
Ø For fountain codes, for a fixed source data sizeØ Erasure code design is extendable to provide any code rateØ All code rates use the same extendable erasure code designØ Particular encoded symbols are generated independently of one anotherØ Number of encoded symbols that can be generated on the fly is unconstrained
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Source blockB C E D A
LT encoding
Degree Prob
1 0.01
0.502
0.173
0.084
Degree Distribution
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Source block
Insert header, and send
XOR source symbols
Choose degree = 2
Choose 2 random source symbols
B C EDA
B+D
Degree Prob
1 0.01
0.502
0.173
0.084
Degree Distribution
LT encoding
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Source blockB C EDA
Choose degree = 1
Choose 1 random source symbol
Copy sourcesymbol
C
Insert header, and sendDegree Prob
1 0.01
0.502
0.173
0.084
Degree Distribution
LT encoding
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Source block
Insert header, and send
XOR source symbols
Choose 4 random source symbols
B C EDA
B+C+D+E
Degree Prob
1 0.01
0.502
0.173
0.084
Degree Distribution
Choose degree = 4
LT encoding
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Source Block (unknown)
Collect enough encoded symbols and set up graph between encoded symbols and source symbols to be decoded
Belief propagation decoding
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Identify encoded symbol with one unrecovered neighbor STOP if none exists
Source Block
Belief propagation decoding
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Unrecovered source symbol value is the value of all recovered neighbors XORed into the encoded symbol value
B Source Block
Belief propagation decoding
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Identify encoded symbol with one unrecovered neighbor STOP if none exists
B Source Block
Belief propagation decoding
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Unrecovered source symbol value is the value of all recovered neighbors XORed into the encoded symbol value
B H Source Block
Belief propagation decoding
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Identify encoded symbol with one unrecovered neighbor STOP if none exists
B H Source Block
Belief propagation decoding
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Unrecovered source symbol value is the value of all recovered neighbors XORed into the encoded symbol value
B H D Source Block
Belief propagation decoding
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B H D E A G F C Source Block (recovered)
Belief propagation decoding
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Intuition for Soliton degree distribution
Consider a symbol of degree d − Releases when exactly 1 of its d neighbors remains unrecovered− Degree d releases when 1/d fraction of the symbols remain to be decoded
A probability distribution on degrees so release distribution is uniform− p(d) “covers” the interval 1/(d-1) to 1/d of the uniform distribution
− Length of interval 1/(d-1) to 1/d is− For d = 2, 3, …
p(2)
1 1/2 1/3 1/4
p(3)
1/6 1/5
p(5) p(4) p(6)
p(d) = 1d ⋅ (d −1)
1d ⋅ (d −1)
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y ∈R [0,1]
d =
1y"
##$
%% if y ≥ 1
k
1 if y < 1k
'
(
))
*
))
Choosing from Soliton distribution
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Raptor codes in standards
Ø Raptor codes (IETF RFC 5053, 3GPP, DVB, ITU, ATIS)Ø Systematic fountain codesØ Linear time encoding and decodingØ Standardized – 3GPP MBMS, DVB-H IPDCØ Good recovery properties – like a random code over GF(2) Ø Good flexibility
Ø Up to 8,192 source symbolsØ Up to 65,384 source + repair symbols
Ø RaptorQ codes (IETF RFC 6330)Ø Systematic fountain codesØ Linear time encoding and decodingØ Great recovery properties – like a random code over GF(256)Ø Great flexibility
Ø Up to 56,403 source symbolsØ Up to 16,777,216 source + repair symbols (essentially unlimited)
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Major technical features (first appearance)
LT code (Raptor RFC 5053)− fountain property
Pre-coding (Raptor RFC 5053)− linear time
Inactivation decoding (Raptor RFC 5053)− linear time
Systematic construction (Raptor RFC 5053)− encoding includes original source
Larger finite fields (RaptorQ RFC 6330)− reduced reception overhead
Permanent inactivations (RaptorQ RFC 6330)− reduced reception overhead
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In comparison to other typical alternative FEC technologies, Raptor codes are an order of magnitude or more less complex
1
10
100
1000
0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0%
maximum packet loss
Sym
bol o
pera
tions
per
out
put s
ymbo
l
RS encoding (n=255) RS decoding (n=255) Raptor encoding Raptor decoding
Reed-Solomon encoding/decoding
Raptor encoding/decoding
Raptor codes computational complexity
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Raptor code (IETF RFC 5053) RaptorQ code (IETF RFC 6330)
10-0
10-1
10-2
10-3
10-4
10-5
10-6
0 2 4 6 8 10 12 14 16 18 20 22 24Number of encoded symbols received beyond k
Probability decoding fails
• k = number of source symbols in source block • Valid for all supported values of k • Valid for all loss probabilities: 1% to 99%
Raptor codes overhead
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IETF RMT Broadcast/Multicast Object Delivery Suite
LCT BB RFC 5651
FEC BB RFC 5052
WEBRC BB RFC 3738
ALC PI RFC 5775
Reliable object delivery protocol instantiation
Reliability using FEC codes Framework and packet format Congestion control
FLUTE RFC 3926
Unidirectional broadcast/multicast reliable file delivery
FEC INFO RFC 3453
BB FRAME RFC 3048
BULK DATA RFC 2887
RaptorQ RFC 6330
Raptor RFC 5053
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3GPP LTE Broadcast (eMBMS) Service Layer
Broadcast file delivery services
IETF RMT Suite FLUTE, ALC PI, LCT BB, FEC BB,
Raptor
Reliable object delivery using FEC codes
Broadcast streaming services
Video streaming delivery
MPEG-DASH Suite
LTE Broadcast HTTP Adaptive
Streaming
MPEG-DASH Suite
HTTP 1.1
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Why Fountain codes? Some applications that you may (not)
have thought about
RaptorQ is a product of Qualcomm Technologies, Inc.
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Servers
LTE broadcast (eMBMS)
Applications:• Streaming• Delivery of popular content• Media• Games
Challenge: reliable file delivery to mobile devices
Receivers
• Millions of mobile devices
Mobile File Delivery Services Over Cellular Network
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Receive less than 10 symbols
LTE broadcast offload service for HTTP
ONLY broadcast repair symbols
Content (10 source symbols)
Device
Receive 10 symbols Decode
Decoding not possible
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File download completion using HTTP 1.1 byte range requests Origin Server
HTTP edge cache server
Device 1 Device 2 Device 3
Received 5 repair symbols
Need 5 additional symbols to decode
Received 9 repair symbols
Need 1 additional symbol to decode
Received 7 repair symbols
Need 3 additional symbols to decode
Request 5 symbol prefix of content Request 1 symbol prefix of content Request 3 symbol prefix of content
Decode Decode Decode
On Demand Caching
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LTE broadcast offload service for HTTP
Content package Media
content AMedia
content BMedia
content C
Decode Decode Decode
Device 1
Media content A
Media content B
Device 2
Media content B
Media content C
Device 3
Media content A
Media content C
30 symbols total
ONLY broadcast repair symbols 10 symbols
Media content C
Media content A
Media content B
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Just-in-Time recovery
LTE broadcast data stored directly on the SD card − Original multimedia data is never stored on the SD card − SD card stores one copy of file – not two!
Multimedia content available immediately after reception − Avoids FEC decode post-processing of file after reception
Just-in-Time recovery − Based on user actions – player requests data to playback multimedia content − Relevant data read from SD card, FEC decoded, provided directly to player − Trick play response time − Playback starts after one sub-block of data read from SD card and FEC decoded − Size of sub-block and decode speed determines the response time
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Just-in-Time recovery avoids costly post-processing Portions of multimedia never played back are never processed
Storage usage is minimized – avoids double the writes to SD card
Receiver
LTE broadcast Write encoded interleaved
data as received
Read sub-block encoded data to RaptorQ decode and playback requested media in real-time
SD card
RAM
Just-in-Time recovery
Player
Playback of requested media Request playback of media
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Just-in-Time recovery advantages
Good user experience – media available immediately after reception Minimizes UE CPU, I/O, and storage resources
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Just-in-Time recovery demo Demonstrates − Just-in-Time recovery (importance of sub-blocking to support this) − Only repair symbols sent in the original broadcast session − Provides ability to efficient combine with HTTP-based repair service − Provides ability to provide broadcast/HTTP hybrid services
Demo parameters − Elephant’s Dream – 91.3 MB file − Partitioned into 10 source blocks (each of size 9.13 MB) − Provides reasonable network efficiency
− Each source block is partitioned into 41 sub-blocks (each of size 223 KB, Symsize = 36 bytes, K ~ 6300) − Read encoded data from SD card and decode sub-block when requested by app
− Original broadcast session − Transmit repair symbols only − 20% packet loss according to Markov model applied before reception
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References in this presentation to “Qualcomm” may mean Qualcomm Incorporated, Qualcomm Technologies, Inc., and/or other subsidiaries or business units within the Qualcomm corporate structure, as applicable.
Qualcomm Incorporated includes Qualcomm’s licensing business, QTL, and the vast majority of its patent portfolio. Qualcomm Technologies, Inc., a wholly-owned subsidiary of Qualcomm Incorporated, operates, along with its subsidiaries, substantially all of Qualcomm’s engineering, research and development functions, and substantially all of its product and services businesses, including its semiconductor business.
For more information on Raptor products or to request your free RaptorQ™ Evaluation Kit
please go to www.qualcomm.com/raptor
For questions please email <[email protected]>