Single-Trial Adaptive Decoding of Concatenated Codes

In this paper decoding of a concatenated code is considered. We use a Bounded Minimum Distance (BMD) decoder for the inner code correcting up to (d − 1)/2 errors and a Bounded Distance (BD) decoder for the outer code, which corrects ε errors and τ erasures if λε + τ ≤ d − 1, where a real number 1 < λ ≤ 2 is the tradeoff rate between errors and erasures for this outer decoder. Here d and d are the minimum distances of the outer and the inner code, respectively. We consider a single-trial outer decoder, which extends Kovalev’s approach [1] for the whole given range of λ. The error correcting radius of the suggested concatenated decoder is d ido 2 ( 1− (λ−1 λ )2) . When using an outer Reed–Solomon code over Fq`m of length n ≤ q with the BD decoder suggested in [2], λ = `+1 ` , and the error correcting radius d ido 2 ( 1− 1 (1−`)2 ) of the concatenated decoder quickly approaches dd/2 with increasing `.