Capability of the error-trapping technique in decoding cyclic codes

Benyamin-Seeyar, Anader; Shiva, S.G.S.; Bhargava, V.K.

doi:10.1109/tit.1986.1057170

Cited by 13 publications

(3 citation statements)

References 9 publications

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“…We assume that for any q , the bounded distance decoding problem involves only decoding all error patterns up to half the Gilbert-Varshamov bound, i.e., up to n H i ' ( 1 -R ) / 2 + o ( n ) errors. Theorem 5: Bounded distance decoding using generalized information set decoding has, for virtually all linear codes, a complexity M (8)…”

Section: By the Convexity Of The Entropy Function We Havementioning

confidence: 99%

The complexity of information set decoding

Coffey

Goodman

1990

IEEE Trans. Inform. Theory

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Information set decoding is an algorithm for decoding any linear code. Expressions for the complexity of the procedure that are logarithmically exact for virtually all codes are presented. The expressions cover the cases of complete minimum distance decoding, bounded hard-decision decoding, and the important case of bounded soft-decision decoding. It is demonstrated that these results are vastly better than for the trivial algorithms of searching through all codewords or through all syndromes and are significantly better than those for any other general algorithm currently known. For codes over large symbol fields the procedure tends towards a complexity that is subexponential in the symbol size. n-+ct. n F(q , R) = lim-log, E(q , R) where E (q , R) is the number of computations necessary (i.e., we have E (q , R) = q n F (q * R) + o (n)

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Section: By the Convexity Of The Entropy Function We Havementioning

confidence: 99%

The complexity of information set decoding

Coffey

Goodman

1990

IEEE Trans. Inform. Theory

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“…• First, to study the application domain of this technique and to verify analytically the capability of decoding several codes. Based on the algebraic properties of the code, they investigate (Benyamin-Seeyar et al, 1986;Jia et al, 1992) an exact lower bound on the code length. They show that the size of the permutation group is proportional to the code dimension or to the error correction capability of the code.…”

Section: Fig 1: Simplified Model Of a Digital Communication Systemmentioning

confidence: 99%

Efficient Decoding Algorithm for Binary Quadratic Residue Codes Using Reduced Permutation Sets

Boualame¹,

Belkasmi²,

Chana³

2023

Journal of Computer Science

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The Quadratic Residue (QR) codes have a rich mathematic structure. Unfortunately, their Algebraic Decoding (AD) is not generalizable for all QR codes. In this study, an efficient hard decoding algorithm is proposed to generalize the decoding of the binary systematic Quadratic Residue (QR) codes. The proposed decoder corrects t erroneous bits or less, in the received word, based on a reduced set of permutations derived from the large automorphism group of QR codes. This set of permutations is applied to the received word to move the error positions and trap all of them in redundancy. Then, to evaluate the proposed method, we applied it to many binary QR codes of moderate code length starting with 17 until 113 with reducible and irreducible generator polynomials. The proposed decoder was validated by inserting all possible error patterns, that have t or less erroneous positions, as input of the proposed decoder and the output is always a correct codeword. The complexity study, in terms of the number of operations used, reveals that the light permutation decoding LPD algorithm significantly decreases decoding complexity without performance loss. So, it is qualified to be a good competitor to decode QR codes with lower lengths but is the best for QR codes with higher lengths.

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“…Algorithms capable of determining graph equivalency can be used in optical character recognition [37] and image processing. Further, the automorphism groups and equivalency of cyclic codes can be employed in permutation decoding [8] and determining the weight distribution of a code [29]. While the equivalency of cyclic design find application in optical orthogonal codes [15].…”

Section: Introductionmentioning

confidence: 99%

On the Automorphism Groups and Equivalence of Cyclic Combinatorial Objects

Guenda,

Gulliver

2012

Preprint

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Capability of the error-trapping technique in decoding cyclic codes

Cited by 13 publications

References 9 publications

The complexity of information set decoding

The complexity of information set decoding

Efficient Decoding Algorithm for Binary Quadratic Residue Codes Using Reduced Permutation Sets

On the Automorphism Groups and Equivalence of Cyclic Combinatorial Objects

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