# Reduced GMD decoding

@article{Weber2003ReducedGD, title={Reduced GMD decoding}, author={Jos H. Weber and Khaled A. S. Abdel-Ghaffar}, journal={IEEE Trans. Inf. Theory}, year={2003}, volume={49}, pages={1013-1027} }

A framework is presented for generalized minimum distance (GMD) decoding with a limited number of decoding trials and a restricted set of reliability values. In GMD decoding, symbols received from the channel may be erased before being fed into an algebraic error-erasure decoder for error correction, in subsequent or simultaneous trials with different erasing patterns. The decision whether or not to erase a symbol in a certain trial is taken by an erasure-choosing algorithm which takes into…

## 17 Citations

Asymptotic single-trial strategies for GMD decoding with arbitrary error-erasure tradeoff

- Computer ScienceProbl. Inf. Transm.
- 2012

This work investigates single-trial strategies for GMD decoding with arbitrary error-erasure tradeoff, based on either erasing a fraction of the received symbols or erasing all symbols whose reliability values are below a certain threshold.

On Asymptotic Strategies for GMD Decoding with Arbitrary Error-Erasure Tradeoff

- Computer Science
- 2015

This work investigates different erasing strategies based on either erasing a fraction of the received symbols or erasing all symbols whose reliability values are below a certain threshold, using multi-trial GMD Forney’s decoder.

Reduced GMD decoding of concatenated codes

- Computer ScienceGLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270)
- 2001

A general version of the generalized minimum distance (GMD) decoding algorithm that accommodates different erasing strategies and can offer a reduction in complexity over Forney's GMD decoding is presented.

Optimal threshold-based multi-trial error/erasure decoding with the Guruswami-Sudan algorithm

- Computer Science2011 IEEE International Symposium on Information Theory Proceedings
- 2011

This work provides formulae which allow to optimally exploit the erasure option of decoders with arbitrary λ, if the decoder can be used z ≥ 1 times, and shows that BMD decoder with zBMD decoding trials can result in lower residual codeword error probability than Guruswami-Sudan (GS) list decodes with zGS trials, if z BMD is only slightly larger than zGS.

On Generalized Minimum Distance Decoding Thresholds for the AWGN Channel

- Computer ScienceArXiv
- 2009

We consider the Additive White Gaussian Noise channel with Binary Phase Shift Keying modulation. Our aim is to enable an algebraic hard decision Bounded Minimum Distance decoder for a binary block…

Optimal erasure selection of M-ary PAM signaling for errors and erasures decoding algorithms

- Computer ScienceIEEE Transactions on Communications
- 2008

An analytical criterion for optimal erasure selection is derived, by which a suboptimal threshold is defined, which can be used for errors and erasures decoding of large code-distance channel codes.

A Unified View on Known Algebraic Decoding Algorithms and New Decoding Concepts

- Computer ScienceIEEE Transactions on Information Theory
- 2013

Known properties of cyclic codes are used to give a unified description of many classical decoding algorithms for Reed-Solomon codes up to half the minimum distance and variants of a new error/erasure decoding algorithm are given.

Generalized minimum distance decoding with arbitrary error, erasure tradeoff

- Computer Science
- 2012

A means of expressing their error-correcting capabilities by a unified function, the Generalized Decoding Radius is introduced, which considers the decoding radius of GMD decoding, i.e., the maximum number of errors that are correctable with guarantee.

On Extended Forney-Kovalev GMD decoding

- Computer Science2009 IEEE International Symposium on Information Theory
- 2009

An m-trial generalized minimum distance (GMD) decoder based on λ is proposed, which extends results of Forney and Kovalev to the whole given range of λ.

Single-trial adaptive decoding of concatenated codes

- Computer Science
- 2008

A Bounded Minimum distance decoder is used for the inner code correcting up to (d − 1)/2 errors and a Bounded Distance 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.

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