On multiple insertion/deletion correcting codes

@article{Helberg2000OnMI,
  title={On multiple insertion/deletion correcting codes},
  author={Albert Helberg and Hendrik C. Ferreira},
  journal={2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060)},
  year={2000},
  pages={6-}
}
  • A. Helberg, H. C. Ferreira
  • Published 27 June 1994
  • Computer Science
  • 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060)
New results on insertion and/or deletion correcting codes are presented. Firstly, new properties relating codewords to subwords are investigated. Secondly, a new error correcting scheme based on convolutional coding, is proposed. 
A new linear, quasicyclic multiple insertion/deletion correcting code
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  • Computer Science
    2003 IEEE Pacific Rim Conference on Communications Computers and Signal Processing (PACRIM 2003) (Cat. No.03CH37490)
  • 2003
TLDR
A new binary, block-coding scheme for the correction of multiple insertion/deletion errors is presented, based on similar theory to cyclic codes.
New Multiple Insertion/Deletion Correcting Codes for Non-Binary Alphabets
TLDR
Helberg's number-theoretic construction of binary multiple insertion/deletion correcting codes to non-binary alphabets is generalized and a linear decoding algorithm for correcting multiple deletions is described.
On ordered syndromes for multi insertion/deletion error-correcting codes
  • M. Hagiwara
  • Computer Science
    2016 IEEE International Symposium on Information Theory (ISIT)
  • 2016
Classes of multi insertion/deletion error-correcting codes based on order theory and axiomatic algebra are proposed by an abstraction of Helberg's construction.
A note on double insertion/deletion correcting codes
By using a run-length representation of sequences, ways to determine suband supersequences are discussed. This is then used in determining the number of sub- and supersequences of a sequence after
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TLDR
The results show the effectiveness of this scheme to re-establish bit-synchronisation after the deletion of bits and investigate the correction of multiple deletions or insertions using standard concatenated coding schemes employing convolutional inner codes, and Reed-Solomon outer codes.
A note on non-binary multiple insertion/deletion correcting codes
TLDR
The cardinality of the proposed construction is evaluated based on the asymptotic upper bound on the Cardinality of a maximal binary multiple insertion/deletion correcting code derived by Levenshtein.
An Improvement of Non-binary Code Correcting Single b-Burst of Insertions or Deletions
TLDR
A decoding algorithm is proposed for this code and an asymptotic upper bound on the cardinality of codes which correct a single burst of insertions or deletions is evaluated.
An algorithmic approach for finding deletion correcting codes
TLDR
The experimental results show that cardinalities of the codebooks exceed sizes of all previously known constructions, and are comparable to Levenshteins lower bound.
Moment Balancing Templates: Universal Constructions to Add Insertion/Deletion Correction Capability to Arbitrary Error Correcting or Constrained Codes
We investigate extending a chosen block or convolutional code which has additive error correction capability, as predetermined by the usual communication systems or coding considerations. Our
A Multiple Insertion/Deletion Correcting Code for Run-Length Limited Sequences
TLDR
It is shown that if the codewords in this code are run-length limited, then the code is capable of correcting both insertions and deletions of zeros and ones, and the proposed construction has a higher rate asymptotically than the Helberg code, which is unconstrained in terms of run- lengths, even though the construction has the additional run- length constraints.
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References

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A new class of nonbinary codes is proposed that correct a single deletion or insertion in digital communications systems and the cardinality of these codes is close to optimal.
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A relation is established between the insertion-and-deletion correcting capability of a code and its minimum distance for suitable Levenshtein-type distance measures.
Insertion/deletion correction with spectral nulls
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Some coding schemes and spectral shaping markers are presented which alleviate the fundamental restriction on Levenshtein's codes that the boundaries of each codeword should be known before insertion/deletion correction can be effected.
Synchronization and substitution error-correcting codes for the Levenshtein metric
Block codes are constructed that are capable of simultaneously correcting e or fewer synchronization errors in t consecutive words, for any t \geq 2e + 1 , and s or fewer substitution errors in
On perfect codes in deletion and insertion metric
The packing and covering problem for the metric space J3J consisting of g-ary words of length n and provided with the deletion and insertion metric is considered. For any n = 1,2,... partitions of Β
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TLDR
A new family of codes is described for representing serial binary data, subject to constraints on the maximum separation between successive changes in value, or between successive like digits, that have application to the recording or transmission of digital data without an accompanying clock.
Binary codes capable of correcting deletions, insertions, and reversals
Helberg & H
  • C. Ferreira, "Multiple insertion/deletion correcting codes," submitted to IEEE Transactions on Information Theory,
  • 1998