Two-dimensional interleaving with burst error-correcting codes

Rocha, Valdemar C. da; Guimarães, Walter P. S.; Farrell, P.G.

doi:10.1049/el:20020676

Cited by 9 publications

(4 citation statements)

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“…Most 2-D burst error correcting codes that have been studied in the literature correct only error bursts of given rectangular [1,5,6,10,12,15,16,21] or other prescribed shapes [2,7,11,20]. See also [17,18] for related interleaving schemes on tori, paths, and cycles, and [4,9,19] for 2-D interleaving schemes for multiple random error correction codes. In [3], the authors have considered arbitrarily shaped error bursts and studied the problem of interleaving a minimum number of codewords in a 2-D (or 3-D) array such that any error burst of given size t can be corrected.…”

Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

Optimal interleaving schemes for correcting two-dimensional cluster errors

Golomb

2007

Discrete Applied Mathematics

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We present an elementary theory of optimal interleaving schemes for correcting cluster errors in two-dimensional digital data. It is assumed that each data page contains a fixed number of, say n, codewords with each codeword consisting of m code symbols and capable of correcting a single random error (or erasure). The goal is to interleave the codewords in the m × n array such that different symbols from each codeword are separated as much as possible, and consequently, an arbitrary error burst with size up to t can be corrected for the largest possible value of t. We show that, for any given m, n, the maximum possible interleaving distance, or equivalently, the largest size of correctable error bursts in an m × n array, is given by t = √ 2n if n m 2 /2 , and t = m + (n − m 2 /2 )/m if n m 2 /2 . Furthermore, we develop a simple cyclic shifting algorithm that can provide a systematic construction of an m × n optimal interleaving array for arbitrary m and n. This extends important earlier work on the complementary problem of constructing interleaving arrays that, given the burst size t, minimize the interleaving degree, that is, the number of different codewords in a 2-D (or 3-D) array such that any error burst with given size t can be corrected. Our interleaving scheme thus provides the maximum burst error correcting power without requiring prior knowledge of the size or shape of an error burst.

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Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

Optimal interleaving schemes for correcting two-dimensional cluster errors

Golomb

2007

Discrete Applied Mathematics

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“…resultando na troca da posição dos elementos indexados por (i ′ , j ′ ) para (i, j) [11]. O entrelaçador bloco a blocoé definido conforme ilustrado na Figura 2, a partir do vetor y na entrada do entrelaçador, seguindo os seguintes passos:…”

Section: Entrelaç Ador Bloco a Blocounclassified

“…A correção de manchas de erros binários tem sido objeto de estudo de muitos pesquisadores [2]- [11], podendo tais manchas aparecerem em diferentes formatos geométricos como por exemplo quadrado, retangular ou em cruz [11]. As manchas também podem ser definidas através de um determinado caminho de comprimento específico ao longo do arranjo [2], [3].…”

Section: Introductionunclassified