TY - GEN

T1 - Optimal thresholds for GMD decoding with ℓ+1/ℓ-extended Bounded Distance decoders

AU - Senger, Christian

AU - Sidorenko, Vladimir R.

AU - Bossert, Martin

AU - Zyablov, Victor V.

PY - 2010

Y1 - 2010

N2 - We investigate threshold-based multi-trial decoding of concatenated codes with an inner Maximum-Likelihood decoder and an outer error/erasure ℓ+1/ℓ-extended Bounded Distance decoder, i.e. a decoder which corrects ε errors and τ erasures if ℓ+1/ℓ-ε+τ ≤ d° - 1, where d° is the minimum distance of the outer code and ℓ ∈ ℕ\{0}. This is a generalization of Forney's GMD decoding, which was considered only for ℓ =1, i.e. outer Bounded Minimum Distance decoding. One important example for ℓ-1/ℓ-extended Bounded Distance decoders is decoding of ℓ-Interleaved Reed-Solomon codes. Our main contribution is a threshold location formula, which allows to optimally erase unreliable inner decoding results, for a given number of decoding trials and parameter ℓ. Thereby, the term optimal means that the residual codeword error probability of the concatenated code is minimized. We give an estimation of this probability for any number of decoding trials.

AB - We investigate threshold-based multi-trial decoding of concatenated codes with an inner Maximum-Likelihood decoder and an outer error/erasure ℓ+1/ℓ-extended Bounded Distance decoder, i.e. a decoder which corrects ε errors and τ erasures if ℓ+1/ℓ-ε+τ ≤ d° - 1, where d° is the minimum distance of the outer code and ℓ ∈ ℕ\{0}. This is a generalization of Forney's GMD decoding, which was considered only for ℓ =1, i.e. outer Bounded Minimum Distance decoding. One important example for ℓ-1/ℓ-extended Bounded Distance decoders is decoding of ℓ-Interleaved Reed-Solomon codes. Our main contribution is a threshold location formula, which allows to optimally erase unreliable inner decoding results, for a given number of decoding trials and parameter ℓ. Thereby, the term optimal means that the residual codeword error probability of the concatenated code is minimized. We give an estimation of this probability for any number of decoding trials.

UR - http://www.scopus.com/inward/record.url?scp=77955675551&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2010.5513698

DO - 10.1109/ISIT.2010.5513698

M3 - Conference contribution

AN - SCOPUS:77955675551

SN - 9781424469604

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1100

EP - 1104

BT - 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings

T2 - 2010 IEEE International Symposium on Information Theory, ISIT 2010

Y2 - 13 June 2010 through 18 June 2010

ER -