相关论文: t-Deletion-s-Insertion-Burst Correcting Codes

We study error-correcting codes in the space $\mathcal{S}_{n,q}$ of length-$n$ multisets over a $q$-ary alphabet under the deletion metric, motivated by permutation channels in which ordering is completely lost and errors act only on symbol…

In this paper we describe all pairs of binary vectors $({\bf u}, {\bf v})$ such that the set of vectors obtained by $t$ deletions in ${\bf v}$ is a subset of the set of vectors obtained by $t$ deletions in ${\bf u}$ for $t=1,2$. Such pairs…

Generalized Reed-Solomon (RS) codes are a common choice for efficient, reliable error correction in memory and communications systems. These codes add $2t$ extra parity symbols to a block of memory, and can efficiently and reliably correct…

This paper presents a new construction of error correcting codes which achieves optimal recovery of a streaming source over a packet erasure channel. The channel model considered is the sliding window erasure model, with burst and arbitrary…

Function-correcting codes, introduced by Lenz, Bitar, Wachter-Zeh, and Yaakobi, protect specific function values of a message rather than the entire message. A central challenge is determining the optimal redundancy -- the minimum…

Recent efforts in coding theory have focused on building codes for insertions and deletions, called insdel codes, with optimal trade-offs between their redundancy and their error-correction capabilities, as well as efficient encoding and…

A single deletion error correcting code (SDECC) is a set of fixed-length sequences consisting of two types of symbols, 0 and 1, such that the original sequence can be recovered for at most one deletion error. The upper bound for the size of…

Ongoing research and experiments have enabled quantum memory to realize the storage of qubits. On the other hand, interleaving techniques are used to deal with burst of errors. Effective interleaving techniques for combating burst of errors…

Best and Brouwer [Discrete Math. 17 (1977), 235-245] proved that triply-shortened and doubly-shortened binary Hamming codes (which have length $2^m-4$ and $2^m-3$, respectively) are optimal. Properties of such codes are here studied,…

Private information retrieval (PIR) codes and batch codes are two important types of codes that are designed for coded distributed storage systems and private information retrieval protocols. These codes have been the focus of much…

Levenshtein introduced the problem of constructing $k$-deletion correcting codes in 1966, proved that the optimal redundancy of those codes is $O(k\log N)$, and proposed an optimal redundancy single-deletion correcting code (using the…

The focus of this paper is on linear, binary codes with locality having locality parameter $r$, that are capable of recovering from $t\geq 2$ erasures and that moreover, have short block length. Both sequential and parallel (through…

Despite their significant advantages over competing technologies, nanopore sequencers are plagued by high error rates, due to physical characteristics of the nanopore and inherent noise in the biological processes. It is thus paramount not…

This paper gives a brief survey of binary single-deletion-correcting codes. The Varshamov-Tenengolts codes appear to be optimal, but many interesting unsolved problems remain. The connections with shift-register sequences also remain…

Despite of tremendous research on decoding Reed-Solomon (RS) and algebraic geometry (AG) codes under the random and adversary substitution error models, few studies have explored these codes under the burst substitution error model. Burst…

A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…

Let $n,q,t,s,p$ be non-negative integers where $n\geq s$ and $q\geq 1$. For $\mathbf{x}\in A_{q}^{n}\triangleq\{ 0,1,\ldots,q-1 \}^{n}$, let the $t$-insertion $s$-deletion $p$-substitution ball of $\mathbf{x}$, denoted by…

We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…

Quantum error correction is essential for the development of any scalable quantum computer. In this work we introduce a generalization of a quantum interleaving method for combating clusters of errors in toric quantum error-correcting…

Recent research in ultra-reliable and low latency communications (URLLC) for future wireless systems has spurred interest in short block-length codes. In this context, we analyze arbitrary harmonic bandwidth (BW) expansions for a class of…