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

We consider a concatenated code with designed distance d^odⁱ/2, based on an outer code with distance d^o 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 λ-Bounded Distance decoder correcting ε errors and τ erasures if λε + τ ≤ d^o - 1, where a real number 1 < λ ≤ 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 λ. The error-correcting radius of the proposed concatenated decoder is dⁱd^o//λ+1 if the number τ of erasures is fixed, and dⁱd^o/2 (1-(λ-1)/λ)²) for adaptive selection of τ. The error-correcting radius quickly approaches dⁱd^o/2 with decreasing λ. These results can be applied e.g. when punctured Reed-Solomon outer codes are used.