## Abstract

A concatenated code C based on an inner code with Hamming distance d^{i} 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≤d^{o}-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 F^{l}_{q}, 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 d^{o}. For the adaptive erasing strategy, the error correcting radius quickly approaches d^{i}d^{o}/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 language | English |
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Pages (from-to) | 1-20 |

Number of pages | 20 |

Journal | Advances in Mathematics of Communications |

Volume | 8 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 2014 |

Externally published | Yes |

## Keywords

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