1. Digital Fountain Codes V. S
Digital Fountain Codes V.S. Reed-Solomon Code For Streaming Applications
S.K.Chang
2006/11/07

2. 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 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

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

4. 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

5. FEC Code and Erasure Code
Feedback Channel
Real network condition
Disadvantage
Bandwidth
Practice link V.S. Logical Link
Error Concealment
Decoder side technique
No encoder side information
blurring effect

6. 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
Is capable of error correcting from any subset with some amount

7. 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.

8. Reed-Solomon Code 1 bit data 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!
3 bit output
Error Detection

9. Reed-Solomon Code 1 bit data Error Correction 2 bits error
Error corrected fault!
Error Detection
Error corrected capacity
4 bit output
2 bits error can be detected
1 bit error can be corrected
2 bits error can’t be corrected

10. Reed-Solomon Code Base on arithmetic over GF(2n) 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

11. 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

12. Digital 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)

13. Digital Fountain Code Fault!!! d v 2 2 1 2 1 3 (101000) (110000)
(001000) 2
(000101) 1
(000010) 3
(100101)

14. Digital Fountain Code OK!!! d v 2 2 1 1 2 1 3 (101000) (110000)
(001000) 1
(000100) 2
(000101) 1
(000010) 3
(100101)

15. 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

16. RS code and DF Code On Streaming
Packet-Level FEC for Streaming Applications

17. 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

18. 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

19. 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.

20. Some Results

21. Some Results

22. Some Results

23. Some Results

24. Some Results

25. 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.