New time-domain decoder for correcting both errors and erasures of reed-solomon codes

Erl Huei Lu, Tso Cho Chen, Chih Wen Shih*

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

1 Scopus citations


A new time-domain decoder for Reed-Solomon (RS) codes is proposed. Because this decoder can correct both errors and erasures without computing the erasure locator, errata locator, or errata evaluator polynomials, the computational complexity can be substantially reduced. Herein, to demonstrate this benefit, complexity comparisons between the proposed decoder and the Truong-Jeng-Hung and Lin-Costello decoders are presented. These comparisons show that the proposed decoder consistently has lower computational requirements when correcting all combinations of v errors and μ erasures than both of the related decoders under the condition of 2v+μ≤dmin where dmin denotes the minimum distance of the RS code. Finally, the (255, 223) and (63, 39) RS codes are used as examples for complexity comparisons under the upper bounded condition of 2v+μdmin To decode the two RS codes, the new decoder can save about 40% additions and multiplications when μ=dmin 1 as compared with the two related decoders. Furthermore, it can also save 50% of the required inverses for 0≤μ≤dmin-1.

Original languageEnglish
Pages (from-to)612-621
Number of pages10
JournalETRI Journal
Issue number4
StatePublished - 08 2016

Bibliographical note

Publisher Copyright:
© 2016 ETRI.


  • Erasure locator polynomial
  • Errata evaluator polynomial
  • Errata locator polynomial
  • Reed-Solomon codes
  • Time-domain decoding


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