Related papers: Permutation and Multi-permutation Codes Correcting…
We address the problem of multipermutation code design in the Ulam metric for novel storage applications. Multipermutation codes are suitable for flash memory where cell charges may share the same rank. Changes in the charges of cells…
Permutation and multipermutation codes in the Ulam metric have been suggested for use in non-volatile memory storage systems such as flash memory devices. In this paper we introduce a new method to calculate permutation sphere sizes in the…
Permutation codes, in the form of rank modulation, have shown promise for applications such as flash memory. One of the metrics recently suggested as appropriate for rank modulation is the Ulam metric, which measures the minimum…
Permutation codes and multi-permutation codes have been widely considered due to their various applications, especially in flash memory. In this paper, we consider permutation codes and multi-permutation codes against a burst of stable…
Permutation codes are widely studied objects due to their numerous applications in various areas, such as power line communications, block ciphers, and the rank modulation scheme for flash memories. Several kinds of metrics are considered…
New bounds on the cardinality of permutation codes equipped with the Ulam distance are presented. First, an integer-programming upper bound is derived, which improves on the Singleton-type upper bound in the literature for some lengths.…
We study optimal reconstruction codes over the multiple-burst substitution channel. Our main contribution is establishing a trade-off between the error-correction capability of the code, the number of reads used in the reconstruction…
We consider the problem of constructing deletion correcting codes over a binary alphabet and take a graph theoretic view. An $n$-bit $s$-deletion correcting code is an independent set in a particular graph. We propose constructing such a…
This paper presents conditions for constructing permutation-invariant quantum codes for deletion errors and provides a method for constructing them. Our codes give the first example of quantum codes that can correct two or more deletion…
Non-binary codes correcting multiple deletions have recently attracted a lot of attention. In this work, we focus on multiplicity-free codes, a family of non-binary codes where all symbols are distinct. Our main contribution is a new…
A permutation code is a nonlinear code whose codewords are permutation of a set of symbols. We consider the use of permutation code in the deletion channel, and consider the symbol-invariant error model, meaning that the values of the…
Codes in the Damerau--Levenshtein metric have been extensively studied recently owing to their applications in DNA-based data storage. In particular, Gabrys, Yaakobi, and Milenkovic (2017) designed a length-$n$ code correcting a single…
We study error-correcting codes in the space $\mathcal{S}_{n,q}$ of length-$n$ multisets over a $q$-ary alphabet, motivated by permutation channels in which ordering is completely lost and errors act solely by deletions of symbols, i.e., by…
Permutation codes under different metrics have been extensively studied due to their potentials in various applications. Generalized Cayley metric is introduced to correct generalized transposition errors, including previously studied…
This paper studies the cardinality of codes correcting insertions and deletions. We give improved upper and lower bounds on code size. Our upper bound is obtained by utilizing the asymmetric property of list decoding for insertions and…
The rank modulation scheme has been proposed for efficient writing and storing data in non-volatile memory storage. Error-correction in the rank modulation scheme is done by considering permutation codes. In this paper we consider codes in…
Correcting insertions/deletions as well as substitution errors simultaneously plays an important role in DNA-based storage systems as well as in classical communications. This paper deals with the fundamental task of constructing codes that…
One peculiarity with deletion-correcting codes is that perfect $t$-deletion-correcting codes of the same length over the same alphabet can have different numbers of codewords, because the balls of radius $t$ with respect to the…
Explicit non-asymptotic upper bounds on the sizes of multiple-deletion correcting codes are presented. In particular, the largest single-deletion correcting code for $q$-ary alphabet and string length $n$ is shown to be of size at most…
In this paper, we present an efficiently encodable and decodable code construction that is capable of correction a burst of deletions of length at most $k$. The redundancy of this code is $\log n + k(k+1)/2\log \log n+c_k$ for some constant…