Digital Fountain Codes V.S. Reed-Solomon Code For Streaming Applications

S.K.Chang

2006/11/07

Reference

     “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 DF2003-06-001 Digital Fountain Technical Report “ LT Codes ” – Michael Luby DigitalFountain,Inc. [email protected]

“CAPACITY APPROACHING CODES DESIGN AND IMPLEMENTATION SPECIAL SECTION --- Fountain codes” – D.J.C. MacKay

Outline

 FEC Code and Erasure Code  Reed-Solomon Code  Digital Fountain Code  RS code and DF Code On Streaming  Some Results  Conclusion

FEC Code and Erasure Code

 Internet traffic problem – Reliability is very important requirement while over Data transmitting data network.

– – Error Type  Bit Errors  Packet Loss Scheme  Feedback Channel  Error Concealment  Channel Coding / Error Resilience

FEC Code and Erasure Code

  Feedback Channel – Real network condition – Disadvantage  Bandwidth  Practice link V.S. Logical Link Error Concealment – Decoder side technique – Disadvantage  No encoder side information  blurring effect

FEC Code and Erasure Code

   Channel Coding – – FEC Code Erasure Code Forward Error Correct Code – – Non-feedback channel Is capable of error correcting when error is fewer than correct ability Erasure Code – – Non-feedback channel Is capable of error correcting from any subset with some amount

Reed-Solomon Code

  Block-based error correcting codes Takes a block of data and adds extra "redundant" bits   When used as error correction codes, are well-known to be capable of correcting any combination of [k-n/2] or fewer errors By contrast, when used as erasure codes, are capable of correcting (n-k) erasures from any successfully received set of k symbols.

Reed-Solomon Code

1 bit data 3 bit output Error Detection Add redundant on data 1 bit error can be detected 2 bit error can’t be detected But we don’t know how to correct it!

Reed-Solomon Code

1 bit data Error Correction Error Detection 4 bit output 2 bits error Error corrected fault!

Error corrected capacity 2 bits error can be detected 1 bit error can be corrected 2 bits error can’t be corrected

Reed-Solomon Code

   Base on arithmetic over GF(2 n ) finite field Advantage – – Systematic coding Low redundancy (high coding rate)  For linear code with the same input and output size, the RS code is the maximum possible coding with minimum distance – Is good at burst-error correction  Memorial channel Disadvantage ： – inefficiencies and limitations in packet-level erasure codes.

  Computing Complexity Mathematical – Primary elements

Digital Fountain Code

 Block/Pixel-based error correcting codes  Random selection combination of data – Break up data into output  Break up data information  Redundant equation  Error correction and erasure capacity is depend on selection probability distribution

Digital Fountain Code

d 2 2 2 1 1 2 1 1 3 1 v (101000) (110000) (000011) (001000) (000100) (000101) (010000) (000010) (100101) (001000)

Digital Fountain Code

d 2 2 1 2 1 3 v (101000) (110000) (001000) (000101) (000010) (100101)

Fault!!!

Digital Fountain Code

d 2 2 1 1 2 1 3 v (101000) (110000) (001000) (000100) (000101) (000010) (100101)

OK!!!

Digital Fountain Code

 Base on random distribution and probability decoding process  Systematic or Non-systematic   Advantage – – Efficient Non-block base coding – Multiple decoding path Disadvantage – Probability decoding

RS code and DF Code On Streaming

 Packet-Level FEC for Streaming Applications

RS code and DF Code On Streaming

 RS code block size is limited by – Computing complexity – Mathematics  For a streaming coded by RS code – Data division / Blocks interleaved. – Each black is encoded by different RS code

RS 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 loss  More data must be transmitted using interleaved short blocks to provide the same level of protection  Additional data represents interleaving overhead – Interleaving overhead is a key reason why RS erasure codes reveal inferior performance in many practical applications

RS 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.

Some Results

Some Results

Some Results

Some Results

Some Results

Conclusion

   Raptor Codes provide exceptional flexibility, while Reed Solomon codes are subject to constraints that limit their utility and diminish their relative performance Raptor 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.