Single-trial decoding of concatenated codes using fixed or adaptive erasing
Single-trial decoding of concatenated codes using fixed or adaptive erasing
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使用固定或自适应擦除对级联码进行单次尝试解码
DOI：
10.3934/amc.2010.4.49
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
V. Zyablov
中科院分区：
文献类型：
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作者：
V. Sidorenko;C. Senger;M. Bossert;V. Zyablov
我们考虑一种级联码，其设计距离为$d_{od_i} / 2$，它基于一个距离为$d_o$的外码和一个距离为$d_i$的内码。为了解码内码，我们使用一个有界最小距离解码器，它最多可纠正$(d_i - 1) / 2$个错误。对于解码外码，我们使用一个$\lambda$-有界距离解码器，如果$\lambda\varepsilon + \tau \leq d_o - 1$，它可纠正$\varepsilon$个错误和$\tau$个删除，其中实数$1 < \lambda \leq 2$是此外解码器在错误和删除之间的权衡率。
考虑一种单次尝试的可纠正错误和删除的外解码器，它将科瓦列夫的方法[4]扩展到给定的整个$\lambda$范围。
如果删除的数量$\tau$是固定的，所提出的级联解码器的纠错半径为$d_id_o / (\lambda + 1)$，对于$\tau$的自适应选择，纠错半径为$(d_id_o / 2) * (1 - (\frac{\lambda - 1}{\lambda})^2)$。随着$\lambda$的减小，纠错半径迅速接近$d_id_o / 2$。这些结果可应用于例如当使用删余的里德 - 所罗门外码时。
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.