# American Institute of Mathematical Sciences

February  2010, 4(1): 49-60. doi: 10.3934/amc.2010.4.49

## Single-trial decoding of concatenated codes using fixed or adaptive erasing

 1 TAIT, Ulm University, Albert-Einstein-Allee 43, 89081, Ulm, Germany, Germany, Germany 2 IITP, Russian Academy of Sciences, B. Karetnyi per. 19, Moscow GSP-4, Russian Federation

Received  May 2009 Revised  November 2009 Published  February 2010

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.
Citation: Vladimir Sidorenko, Christian Senger, Martin Bossert, Victor Zyablov. Single-trial decoding of concatenated codes using fixed or adaptive erasing. Advances in Mathematics of Communications, 2010, 4 (1) : 49-60. doi: 10.3934/amc.2010.4.49
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