Presentation on theme: "Digital Fountain Codes V. S"— Presentation transcript:
1Digital Fountain Codes V. S Digital Fountain Codes V.S. Reed-Solomon Code For Streaming ApplicationsS.K.Chang2006/11/07
2Reference“WHY DIGITAL FOUNTAIN’S RAPTOR CODE IS BETTER THAN REED-SOLOMON ERASURE CODES FOR STREAMING APPLICATIONS”Copyright c 2005 Digital Fountain, Inc. ALL RIGHTS RESERVED.“Raptor versus Reed Solomon Forward Error Correction Codes”Ufuk DEMIR, Ozlem AKTA$Computer Engineering Department Dokuz Eyluil University Izmir, Turkey“Raptor codes”AMIN SHOKROLLAHI DF Digital Fountain Technical Report“ LT Codes ”Michael Luby DigitalFountain,Inc.“CAPACITY APPROACHING CODES DESIGN AND IMPLEMENTATION SPECIAL SECTION --- Fountain codes”D.J.C. MacKay
3Outline FEC Code and Erasure Code Reed-Solomon Code Digital Fountain CodeRS code and DF Code On StreamingSome ResultsConclusion
4FEC Code and Erasure Code Internet traffic problemReliability is very important requirement while over Data transmitting data network.Error TypeBit ErrorsPacket LossSchemeFeedback ChannelError ConcealmentChannel Coding / Error Resilience
5FEC Code and Erasure Code Feedback ChannelReal network conditionDisadvantageBandwidthPractice link V.S. Logical LinkError ConcealmentDecoder side techniqueNo encoder side informationblurring effect
6FEC Code and Erasure Code Channel CodingFEC CodeErasure CodeForward Error Correct CodeNon-feedback channelIs capable of error correcting when error is fewer than correct abilityIs capable of error correcting from any subset with some amount
7Reed-Solomon Code Block-based error correcting codes Takes a block of data and adds extra "redundant" bitsWhen used as error correction codes, are well-known to be capable of correcting any combination of [k-n/2] or fewer errorsBy contrast, when used as erasure codes, are capable of correcting (n-k) erasures from any successfully received set of k symbols.
8Reed-Solomon Code 1 bit data Add redundant on data 1 bit error can be detected2 bit error can’t be detectedBut we don’t know how to correct it!3 bit outputError Detection
9Reed-Solomon Code 1 bit data Error Correction 2 bits error Error corrected fault!Error DetectionError corrected capacity4 bit output2 bits error can be detected1 bit error can be corrected2 bits error can’t be corrected
10Reed-Solomon Code Base on arithmetic over GF(2n) finite field AdvantageSystematic codingLow redundancy (high coding rate)For linear code with the same input and output size, the RS code is the maximum possible coding with minimum distanceIs good at burst-error correctionMemorial channelDisadvantage ：inefficiencies and limitations in packet-level erasure codes.Computing ComplexityMathematicalPrimary elements
11Digital Fountain Code Block/Pixel-based error correcting codes Random selection combination of dataBreak up data into outputBreak up data informationRedundant equationError correction and erasure capacity is depend on selection probability distribution
12Digital Fountain Code d v 2 2 2 1 1 2 1 1 3 1 (101000) (110000) (000011)1(001000)1(000100)2(000101)1(010000)1(000010)3(100101)1(001000)
13Digital Fountain Code Fault!!! d v 2 2 1 2 1 3 (101000) (110000) (001000)2(000101)1(000010)3(100101)
14Digital Fountain Code OK!!! d v 2 2 1 1 2 1 3 (101000) (110000) (001000)1(000100)2(000101)1(000010)3(100101)
15Digital Fountain CodeBase on random distribution and probability decoding processSystematic or Non-systematicAdvantageEfficientNon-block base codingMultiple decoding pathDisadvantageProbability decoding
16RS code and DF Code On Streaming Packet-Level FEC for Streaming Applications
17RS code and DF Code On Streaming RS code block size is limited byComputing complexityMathematicsFor a streaming coded by RS codeData division / Blocks interleaved.Each black is encoded by different RS code
18RS code and DF Code On Streaming When more than one Reed-Solomon code is used and interleaved, the performance can deteriorate because of the randomly distributed nature of packet lossMore data must be transmitted using interleaved short blocks to provide the same level of protectionAdditional data represents interleaving overheadInterleaving overhead is a key reason why RS erasure codes reveal inferior performance in many practical applications
19RS code and DF Code On Streaming By contrast, a digital fountain codes don’t require any such segmentation and thus doesn’t incur any interleaving overhead.Digital fountain code requires almost linear computing complexity on encoding and decoding.
25ConclusionRaptor Codes provide exceptional flexibility, while Reed Solomon codes are subject to constraints that limit their utility and diminish their relative performanceRaptor codes protect against packet loss with greater efficiency than Reed Solomon codes. Raptor codes require less processing power than Reed Solomon erasure codes (increases linearly with the level of provided protection, not quadratic ).Raptor codes allow a given application to be optimally addressed in terms of the degree of packet loss protection, bandwidth expansion, and processing demands.