On multi-trial forney-Kovalev decoding of concatenated codes

Anas Chaaban, Vladimir R. Sidorenko, Christian Senger

Research output: Contribution to journalArticlepeer-review

Abstract

A concatenated code C based on an inner code with Hamming distance di and an outer code with Hamming distance do is considered. An outer decoder that corrects ε errors and θ erasures with high probability if λε+θ≤do-1, where a real number 1<λ≤2 is the trade-off rate between errors and erasures for this decoder is used. In particular, an outer l-punctured RS code, i.e., a code over the field F of length with locators taken from the sub-field Flq, where l ∈ {1,2,} is considered. In this case, the trade-off is given by λ=1+1/l. An m-trial decoder, where after inner decoding, in each trial we erase an incremental number of symbols and decode using the outer decoder is proposed. The optimal erasing strategy and the error correcting radii of both fixed and adaptive erasing decoders are given. Our approach extends results of Forney and Kovalev (obtained for λ=2) to the whole given range of. For the fixed erasing strategy the error correcting radius approaches for large do. For the adaptive erasing strategy, the error correcting radius quickly approaches dido/2 if l or m grows. The minimum number of trials required to reach an error correcting radius is. This means that 2 or 3 trials are sufficient in many practical cases if l >1.

Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalAdvances in Mathematics of Communications
Volume8
Issue number1
DOIs
Publication statusPublished - Feb 2014
Externally publishedYes

Keywords

  • Adaptive erasing
  • Concatenated codes
  • Error correcting radius
  • Fixed erasing
  • GMD decoding
  • Multi-trial decoding

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