Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Symposium on Information Theory (ISIT)

Optimal decoding strategy for a simple concatenated coding scheme

Jos H. Weber, Khaled Abdel-Ghaffar

Published Nov 22, 2002• 5 citations
Publisher

Abstract

For a simple concatenated coding scheme, the decoding strategy for the inner code is optimized such that the number of correctable errors in a concatenated codeword is maximum.
DOI
10.1109/isit.1997.613366

Related papers

Achieving the optimal guaranteed error correction rate in a simple concatenated coding scheme with single-trial decoding

Jos H. Weber, Khaled Abdel-Ghaffar

For a concatenated coding scheme using a single inner code, a single outer code, and an optimal single-trial decoding strategy, we study the guaranteed error correction rate, i.e., the number of correctable errors per transmitted symbol. In particular, it is investigated whether the optimal guaranteed error correction rate can be achieved by finite length codes or only be approached by an infinite sequence of codes of increasing lengths. It is shown that optimizing the guaranteed error correction rate for a given inner or outer code does not necessarily mean pushing the code rate to zero. Furthermore, to optimize the guaranteed error correction rate over all inner and outer codes of fixed dimensions and alphabets, the code rate of one (but not both) of these two codes should be pushed to zero.

IEEE International Symposium on Information Theory (ISIT)•Nov 27, 2002•0 citations

Qubit-Oscillator Concatenated Codes: Decoding Formalism and Code Comparison

Yijia Xu, Yixu Wang, En-Jui Kuo +1 more

The strategy of concatenating Gottesman-Kitaev-Preskill with qubit error-correcting codes is investigated, providing insights on the advantages over established schemes and on how to build efficient decoders.

PRX Quantum•Jun 14, 2023•15 citations

Improved Analysis of List Decoding and Its Application to Convolutional Codes and Turbo Codes

Chunlong Bai, Bartosz Mielczarek, Witold A. Krzymień +1 more

A list decoder generates a list of more than one codeword candidates, and decoding is erroneous if the transmitted codeword is not included in the list. This decoding strategy can be implemented in a system that employs an inner error correcting code and an outer error detecting code that is used to choose the correct codeword from the list. Probability of codeword error analysis for a linear block code with list decoding is typically based on the “worst case” lower bound on the effective weights of codewords for list decoding evaluated from the weight enumerating function of the code.

IEEE Transactions on Information Theory•Jan 23, 2007•10 citations

Reduced GMD decoding of concatenated codes

Jos H. Weber, Khaled Abdel-Ghaffar

We present a general version of the generalized minimum distance (GMD) decoding algorithm (see Forney, G.D., Jr, 1966) that accommodates different erasing strategies. This version is called reduced GMD decoding since, depending on the erasing strategy used, it can offer a reduction in complexity over Forney's GMD decoding. We apply reduced GMD decoding to concatenated codes. In particular, we study the error correction capability and the unsuccessful decoding probability of concatenated codes with reduced GMD decoding.

Globecom•Nov 13, 2002•0 citations

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

Vladimir R. Sidorenko, Christian Senger, Martin Bossert +1 more

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 $1dido$/(\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.

Advances in Mathematics of Communications•Jan 1, 2010•5 citations

On the minimum distance of concatenated codes and decoding based on the true minimum distance

Toshiyuki Kohnosu, T. Nishijima, Shigeichi Hirasawa

We show some conditions that the minimum distance of concatenated codes is beyond the lower bound. Furthermore a new decoding method is proposed up to the true minimum distance.

IEEE International Symposium on Information Theory (ISIT)•Nov 22, 2002•0 citations
For a concatenated coding scheme using a single inner code, a single outer code, and an optimal single-trial decoding strategy, we study the guaranteed error correction rate, i.e., the number of correctable errors per transmitted symbol. In particular, it is investigated whether the optimal guaranteed error correction rate can be achieved by finite length codes or only be approached by an infinite sequence of codes of increasing lengths. It is shown that optimizing the guaranteed error correction rate for a given inner or outer code does not necessarily mean pushing the code rate to zero. Furthermore, to optimize the guaranteed error correction rate over all inner and outer codes of fixed dimensions and alphabets, the code rate of one (but not both) of these two codes should be pushed to zero.
A list decoder generates a list of more than one codeword candidates, and decoding is erroneous if the transmitted codeword is not included in the list. This decoding strategy can be implemented in a system that employs an inner error correcting code and an outer error detecting code that is used to choose the correct codeword from the list. Probability of codeword error analysis for a linear block code with list decoding is typically based on the “worst case” lower bound on the effective weights of codewords for list decoding evaluated from the weight enumerating function of the code.
We present a general version of the generalized minimum distance (GMD) decoding algorithm (see Forney, G.D., Jr, 1966) that accommodates different erasing strategies. This version is called reduced GMD decoding since, depending on the erasing strategy used, it can offer a reduction in complexity over Forney's GMD decoding. We apply reduced GMD decoding to concatenated codes. In particular, we study the error correction capability and the unsuccessful decoding probability of concatenated codes with reduced GMD decoding.
We consider a concatenated code with designed distance dodi/2/2/2, 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−1-1−1)/2/2/2 errors. For decoding the outer code, we use a λ\lambdaλ-Bounded Distance decoder correcting ε\varepsilonε errors and τ\tauτ erasures if λε+τ≤\lambda\varepsilon+\tau \leqλε+τ≤do−1-1−1, where a real number 1dido1dido1dido/(\lambda +1)$ if the number τ\tauτ of erasures is fixed, and (dido/2/2/2)∗(1−(λ−1λ)2)(1-(\frac{\lambda-1}{\lambda})^2)(1−(λλ−1​)2) for adaptive selection of τ\tauτ. The error-correcting radius quickly approaches dido/2/2/2 with decreasing λ\lambdaλ. These results can be applied e.g. when punctured Reed-Solomon outer codes are used.