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Abstract
We consider a concatenated code with designed distance dodi$/2$, based on an outer code with distance do and an inner code with distance di. To decode the inner code, we use a Bounded Minimum Distance decoder correcting up to (di$-1$)$/2$ errors. For decoding the outer code, we use a $\lambda$-Bounded Distance decoder correcting $\varepsilon$ errors and $\tau$ erasures if $\lambda\varepsilon+\tau \leq$do$-1$,
where a real number $1<\lambda\leq 2$ is the tradeoff rate between errors and erasures for this outer decoder.
A single-trial erasures-and-errors-correcting outer decoder is considered, that extends Kovalev's approach [4] for the whole given range of $\lambda$.
The error-correcting radius of the proposed concatenated decoder is dido$/(\lambda +1)$ if the number $\tau$ of erasures is fixed, and (dido$/2$)∗$(1-(\frac{\lambda-1}{\lambda})^2)$ for adaptive selection of
$\tau$. The error-correcting radius quickly approaches dido$/2$ with decreasing
$\lambda$. These results can be applied e.g. when punctured
Reed-Solomon outer codes are used.
Mathematics Subject Classification: 94B35.
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