On multitrial ForneyKovalev decoding of concatenated codes
Anas Chaaban  DCS, RuhrUniversität Bochum, Universitätsstraße 150, 44780 Bochum, Germany (email) Abstract:
A concatenated code $\mathcal{C} $ based on an inner code with Hamming distance $d^i$ and an outer code with Hamming distance $d^o$ is considered. An outer
decoder that corrects $\varepsilon$ errors and $\theta$
erasures with high probability if $\lambda \varepsilon + \theta \le d^o  1,$ where a real number
$1<\lambda\le 2$ is the tradeoff 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 $\mathbb{F}_{q^{l }}$ of length $n^{o} < q$ with locators taken from the subfield $\mathbb{F}_{q}$, where $l\in \{1,2,\ldots\}$ is considered. In this case, the tradeoff is given by $\lambda=1+1/l$. 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.
Keywords: Multitrial decoding, concatenated codes, GMD decoding, error correcting
radius, fixed erasing, adaptive erasing.
Received: January 2011; Revised: June 2013; Available Online: January 2014. 
2016 Impact Factor.8
