Presentation is loading. Please wait.

Presentation is loading. Please wait.

Digital Fountain Codes V. S

Similar presentations

Presentation on theme: "Digital Fountain Codes V. S"— Presentation transcript:

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.

Download ppt "Digital Fountain Codes V. S"

Similar presentations

Ads by Google