Related papers: Permutation and Multi-permutation Codes Correcting…
This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In…
Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently…
In this paper, we present an optimal metric function on average, which leads to a significantly low decoding computation while maintaining the superiority of the polarization-adjusted convolutional (PAC) codes' error-correction performance.…
In this paper, we construct systematic $q$-ary two-deletion correcting codes and burst-deletion correcting codes, where $q\geq 2$ is an even integer. For two-deletion codes, our construction has redundancy $5\log n+O(\log q\log\log n)$ and…
We investigate lossy compression (source coding) of data in the form of permutations. This problem has direct applications in the storage of ordinal data or rankings, and in the analysis of sorting algorithms. We analyze the rate-distortion…
We propose a method for constructing quantum error-correcting codes based on non-binary low-density parity-check codes with Tanner graph girth 16. While conventional constructions using circulant permutation matrices are limited to girth…
In recent years, the emergence of DNA storage systems has led to a widespread focus on the research of codes correcting insertions, deletions, and classic substitutions. During the initial investigation, Levenshtein discovered the VT codes…
Reconstruction-based anomaly detection models achieve their purpose by suppressing the generalization ability for anomaly. However, diverse normal patterns are consequently not well reconstructed as well. Although some efforts have been…
In this paper we study codes for correcting deletable errors in binary words, where each bit is either retained, substituted, erased or deleted and the total number of errors is much smaller compared to the length of the codeword. We…
In this paper we study array-based codes over graphs for correcting multiple node failures. These codes have applications to neural networks, associative memories, and distributed storage systems. We assume that the information is stored on…
Function-correcting codes are a coding framework designed to minimize redundancy while ensuring that specific functions or computations of encoded data can be reliably recovered, even in the presence of errors. The choice of metric is…
Homomorphic permutation is fundamental to privacy-preserving computations based on batch-encoding homomorphic encryption. It underpins nearly all homomorphic matrix operations and predominantly influences their complexity. Permutation…
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,…
Convolutional codes are a class of error-correcting codes that performs very well over erasure channels with low delay requirements. In particular, Maximum Distance Profile (MDP) convolutional codes, which are defined to have optimal column…
This work proves new results on the ability of binary Reed-Muller codes to decode from random errors and erasures. We obtain these results by proving improved bounds on the weight distribution of Reed-Muller codes of high degrees.…
We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs. It is known that the average minimum…
Guess & Check (GC) codes are systematic binary codes that can correct multiple deletions, with high probability. GC codes have logarithmic redundancy in the length of the message $k$, and the encoding and decoding algorithms of these codes…
Polar codes are a channel coding scheme for the next generation of wireless communications standard (5G). The belief propagation (BP) decoder allows for parallel decoding of polar codes, making it suitable for high throughput applications.…
Finding the largest code with a given minimum distance is one of the most basic problems in coding theory. In this paper, we study the linear programming bound for codes in the Lee metric. We introduce refinements on the linear programming…
This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error…