University of Alberta Department of Electrical and Computer Engineering Rateless Reed-Solomon Codes Masoud Ardakani Reza Rafie Borujeny
Overview • We propose a new class of erasure codes based on Reed-Solomon codes that are truly rateless. • These rateless Reed-Solomon (RLRS) codes offer zero reception overhead regardless of the block length. • The coding complexity of RLRS codes is lower than competitive solutions. Slide 2 of 8
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. Slide 3 of 8
Benefits • In comparison with Random Linear Fountain codes, RLRS have a lower coding complexity, 𝑃(𝑙 3 ) vs. 𝑃(𝑙 2 ) . • 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. Slide 4 of 8
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. Slide 5 of 8
Appendix 1: Preservative Field Extension × 0 1 0 0 0 1 0 1 Multiplication Table for 𝔾 2 × 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 an Isomorphism of 𝔾 4 That is a Preservative Extension of 𝔾 2 Slide 6 of 8
Appendix 2: Cauchy Based RS Codes Slide 7 of 8
University of Alberta Department of Electrical and Computer Engineering Rateless Reed-Solomon Codes Masoud Ardakani Reza Rafie Borujeny reza.rafie@ualberta.ca ardakani@ualberta.ca
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