Rateless Reed-Solomon Codes Masoud Ardakani Reza Rafie Borujeny - - PowerPoint PPT Presentation

Rateless Reed-Solomon Codes

Reza Rafie Borujeny Masoud Ardakani

University of Alberta Department of Electrical and Computer Engineering

Overview

• We propose a new class of erasure codes

based on Reed-Solomon codes that are truly rateless.

• These rateless Reed-Solomon (RLRS) codes
• ffer zero reception overhead regardless of

the block length.

• The coding complexity of RLRS codes is

lower than competitive solutions.

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Procedure

• RLRS codes start with a high rate (low

complexity) Cauchy-based* RS code.

• When needed, using Preservative Field

Extension*, RLRS codes reduce their rate, while staying MDS.

• Because of their MDS property, their

reception overhead is always zero.

• They are rateless since further field

extensions can be performed as needed.

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Benefits

• In comparison with Random Linear Fountain

codes, RLRS have a lower coding complexity, 𝑃(𝑙3) vs. 𝑃(𝑙2).

• RLRS codes have zero overhead while short

block length Raptor codes suffer from a relatively large overhead.

• The main advantage of our RLRS codes over

a very low rate MDS code is that our code has a lower coding complexity.

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Conclusion

• RLRS codes seem to be a good choice for

applications with small block length, where Raptor codes are too costly in terms of overhead and Random Fountain Codes are too costly in terms of decoding complexity.

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Appendix 1: Preservative Field Extension

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× 1 1 1 × 00 01 10 11 00 00 00 00 00 01 00 01 10 11 10 00 10 11 01 11 00 11 01 10 Multiplication Table for 𝔾2 Multiplication Table for an Isomorphism of 𝔾4 That is a Preservative Extension of 𝔾2

Appendix 2: Cauchy Based RS Codes

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Rateless Reed-Solomon Codes

Reza Rafie Borujeny reza.rafie@ualberta.ca Masoud Ardakani ardakani@ualberta.ca

University of Alberta Department of Electrical and Computer Engineering