Multiple Criss-Cross Insertion and Deletion Correcting Codes

Welter, Lorenz; Bitar, Rawad; Wachter-Zeh, Antonia; Yaakobi, Eitan

doi:10.1109/tit.2022.3152398

Cited by 6 publications

(8 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3. Crisscross insertions and deletions were studied recently in [1,25], where several code constructions are given.…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

See 1 more Smart Citation

Multilayer crisscross error and erasure correction

Martínez-Peñas¹

2022

Preprint

View full text Add to dashboard Cite

In this work, multilayer crisscross error and erasures are considered, which affect entire rows and columns in the matrices of a list of matrices. To measure such errors and erasures, the multi-cover metric is introduced. Several bounds are derived, including a Singleton bound, and maximum multi-cover distance (MMCD) codes are defined as those attaining it. Duality, puncturing and shortening of linear MMCD codes are studied. It is shown that the dual of a linear MMCD code is not necessarily MMCD, and those satisfying this duality condition are defined as dually MMCD codes. Finally, some constructions of codes in the multi-cover metric are given, including dually MMCD codes, together with efficient decoding algorithms for them.

show abstract

“…3. Crisscross insertions and deletions were studied recently in [1,25], where several code constructions are given.…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

“…Since then, codes in the cover metric with other correcting features (e.g., probabilistic, list-decoding, etc.) were subsequently studied [1,11,13,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

Multilayer crisscross error and erasure correction

Martínez-Peñas¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

“…Codes correcting insertions and deletions in twodimensional arrays have been investigated in [18]- [23]. The model considered in [20]- [23] is that of coding for row/column insertions and deletions in two-dimensional arrays. In [22], Hagiwara constructed codes that can correct up to t c column and t r row deletions where t r and t c are predetermined.…”

Section: Introductionmentioning

confidence: 99%

“…In [22], Hagiwara constructed codes that can correct up to t c column and t r row deletions where t r and t c are predetermined. In [20], [23], the authors constructed codes correcting a variable number of column and row deletions for a predetermined number of total deletions. In addition, they provided a lower bound on the redundancy of codes correcting insertions and deletions in arrays.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Equivalence of Insertion/Deletion Correcting Codes for d-dimensional Arrays

Stylianou

Welter

Bitar

et al. 2022

2022 IEEE International Symposium on Information Theory (ISIT)

Self Cite

View full text Add to dashboard Cite

We consider the problem of correcting insertion and deletion errors in the d-dimensional space. This problem is well understood for vectors (one-dimensional space) and was recently studied for arrays (two-dimensional space). For vectors and arrays, the problem is motivated by several practical applications such as DNA-based storage and racetrack memories. From a theoretical perspective, it is interesting to know whether the same properties of insertion/deletion correcting codes generalize to the d-dimensional space. In this work, we show that the equivalence between insertion and deletion correcting codes generalizes to the d-dimensional space. As a particular result, we show the following missing equivalence for arrays: a code that can correct tr and tc row/column deletions can correct any combination of t ins r + t del r = tr and t ins c + t del c = tc row/column insertions and deletions. The fundamental limit on the redundancy and a construction of insertion/deletion correcting codes in the ddimensional space remain open for future work.

show abstract

Database Matching Under Noisy Synchronization Errors

Bakirtas,

Erkip

2024

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

Multiple Criss-Cross Insertion and Deletion Correcting Codes

Cited by 6 publications

References 28 publications

Multilayer crisscross error and erasure correction

Multilayer crisscross error and erasure correction

Equivalence of Insertion/Deletion Correcting Codes for d-dimensional Arrays

Database Matching Under Noisy Synchronization Errors

Contact Info

Product

Resources

About