Filip Paluncic

On Helberg's Generalization of the Levenshtein Code for Multiple Deletion/Insertion Error Correction

A proof that the Helberg code is capable of correcting multiple deletion/insertion errors is presented. This code is a generalization of the number-theoretic Levenshtein code which is capable of correcting a single deletion/insertion. However, apart from exhaustive testing of short codes, no proof was hitherto given to verify that the Helberg code is indeed capable of correcting multiple deletions and insertions.

A Multiple Insertion/Deletion Correcting Code for Run-Length Limited Sequences

A code construction is proposed to add a multiple insertion/deletion error correcting capability to a run-length limited sequence. The codewords of this code are themselves run-length limited. The insertion/deletion correcting capability is achieved by requiring several weighted sums of run-lengths in the codewords to satisfy certain congruences modulo primes. The construction is similar to the number-theoretic code proposed by Dolecek and Anantharam, which can correct multiple repetition errors or, equivalently, multiple insertions of zeros. 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. An algorithm is proposed for decoding over a multiple insertion/deletion channel. Following the work of Dolecek and Anantharam, a systematic encoding method is also proposed for the codes. Furthermore, it is shown that the proposed construction has a higher rate asymptotically than the Helberg code, which is unconstrained in terms of run-lengths, even though our construction has the additional run-length constraints. The need for run-length limited codes that can correct insertion/deletion errors is motivated by bit-patterned media for magnetic recording.

Insertion/Deletion Detecting Codes and the Boundary Problem

Insertion/deletion detecting codes were introduced by Konstantinidis In this paper we define insertion/deletion detecting codes in a slightly different manner, and based on this definition, we introduce multiple deletion and multiple insertion detecting codes. It is shown that these codes, which are systematic, are optimal in the sense that there exists no other systematic multiple deletion (insertion) detecting codes with a better rate. One of the limitations of number-theoretic code constructions intended to correct insertion/deletion errors, e.g., the Levenshtein code, is that they require received codeword boundaries to be known in order to successfully decode. In literature, a number of schemes have been proposed to deal with this problem. We show how insertion/deletion detecting codes as presented in this paper can be used to improve and/or extend some of these schemes.

A Variable Length Approach to Moment Balancing

Moment balancing templates have been proposed for channels with a small probability of an insertion/deletion (several orders smaller than additive errors) that add a minimal amount of redundancy. These templates are essentially a systematic way of encoding number-theoretic codes (primarily Levenshteins s = 1 insertion/deletion code). Moment balancing templates proposed up to this point have been of fixed length. In this paper, it is shown that by using variable length templates, it is possible to obtain better performance than the optimal fixed length moment balancing template. Here, performance is defined as the amount of redundancy, which includes the moment balancing bits and the marker, that needs to be added.

Partitioned moment balancing template and the influence of partition distribution thereon

A partitioned moment balancing template (systematic encoding of some number theoretic codes) is presented that can correct a single insertion/deletion. Instead of dispersing the moment balancing bits across the template, they are grouped together. Moment balancing templates are used to add insertion/deletion correcting capability to an additive-error-correcting code. The effect of using a particular additive-error-correcting code on the minimum number of moment balancing bits is investigated.

Modelling distances between genetically related languages using an extended weighted Levenshtein distance

Abstract This article proposes the use of an extended weighted Levenshtein distance to model the time depth between parent and direct descendant languages and also the dialectal separation between sibling languages. The parent language is usually a proto-language, a hypothetical reconstructed language, whose precise date is usually conjectural. Phonology is used as an indicator of language difference, which is modelled by means of an extended weighted Levenshtein distance. This idea is applied specifically to the Iranian language family.

A variable length moment balancing template

Moment balancing templates have been proposed for channels with a small probability of an insertion/deletion (several orders smaller than additive errors) that add a minimal amount of redundancy. These templates are essentially a systematic way of encoding number-theoretic codes (primarily Levenshteinpsilas s = 1 insertion/deletion code). Moment balancing templates proposed up to this point have been fixed length. In this paper, it is shown, that by using variable length templates, it is possible to obtain better performance than the optimal fixed length moment balancing template. Here, performance is defined as the amount of redundancy that needs to be added.