Related papers: Duplication-Correcting Codes
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…
Data synchronization is a fundamental problem with applications in diverse fields such as cloud storage, genomics, and distributed systems. This paper addresses the challenge of synchronizing two files, one of which is a subsequence of the…
In this paper, we investigate the problem of designing $(n, N; \mathcal{B})$-reconstruction codes for $N\in \{14,11,9,5\}$, where $\mathcal{B}$ is the single-deletion single-substitution ball function that maps a sequence to the set of all…
This study investigates the capabilities of Cyclic Redundancy Checks(CRCs) to detect burst and random errors. Researchers have favored these error detection codes throughout the evolution of computing and have implemented them in…
In this paper, we consider the mismatched rate-distortion problem, in which the encoding is done using a codebook, and the encoder chooses the minimum-distortion codeword according to a mismatched distortion function that differs from the…
Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual. Numerical…
Matrix multiplication over the real field constitutes a foundational operation in the training of deep learning models, serving as a computational cornerstone for both forward and backward propagation processes. However, the presence of…
By a locally recoverable code (LRC), we will in this paper, mean a linear code in which a given code symbol can be recovered by taking a linear combination of at most $r$ other code symbols with $r << k$. A natural extension is to the local…
Due to their sequential nature, traditional DNA synthesis methods are expensive in terms of time and resources. They also fabricate multiple copies of the same strand, introducing redundancy. This redundancy can be leveraged to enhance the…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
We study two basic problems regarding edit error, i.e. document exchange and error correcting codes for edit errors (insdel codes). For message length $n$ and edit error upper bound $k$, it is known that in both problems the optimal sketch…
Traditional redundancy (lockstep, TMR) executes identical binaries with identical memory layouts. A single correlated fault - for example, an arbitrary program counter value or a perturbation delta-PC in all replicas - redirects all…
One of the main challenges in developing racetrack memory systems is the limited precision in controlling the track shifts, that in turn affects the reliability of reading and writing the data. A current proposal for combating deletions in…
Motivated by applications to DNA storage, we study reconstruction and list-reconstruction schemes for integer vectors that suffer from limited-magnitude errors. We characterize the asymptotic size of the intersection of error balls in…
Motivated by mutation processes occurring in in-vivo DNA-storage applications, a channel that mutates stored strings by duplicating substrings as well as substituting symbols is studied. Two models of such a channel are considered: one in…
Data storage in DNA is developing as a possible solution for archival digital data. Recently, to further increase the potential capacity of DNA-based data storage systems, the combinatorial composite DNA synthesis method was suggested. This…
Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the…
Previous work has shown that the classification of indecomposable off-shell representations of N-supersymmetry, depicted as Adinkras, may be factored into specifying the topologies available to Adinkras, and then the height-assignments for…
Non-overlapping codes have been studied for almost 60 years. In such a code, no proper, non-empty prefix of any codeword is a suffix of any codeword. In this paper, we study codes in which overlaps of certain specified sizes are forbidden.…
This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…