SINGLE-TRIAL DECODING OF CONCATENATED CODES USING FIXED OR ADAPTIVE ERASING
We consider a concatenated code with designed distance d(o)d(i)/2, based on an outer code with distance do and an inner code with distance d(i). To decode the inner code, we use a Bounded Minimum Distance decoder correcting up to (d(i) - 1)/2 errors. For decoding the outer code, we use a lambda-Bounded Distance decoder correcting epsilon errors and tau erasures if lambda epsilon + tau <= d(o) - 1, where a real number 1 < lambda <= 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 d(i)d(o)/lambda+1 if the number tau of erasures is fixed, and d(i)d(o)/2 (1 - (lambda-1/lambda)(2)) for adaptive selection of tau. The error-correcting radius quickly approaches d(i)d(o)/2 with decreasing lambda. These results can be applied e. g. when punctured Reed-Solomon outer codes are used.
decoding concatenated codes gmd decoding