Related papers: On Minimum Distances for Error Correction and Dete…
The process of DNA-based data storage (DNA storage for short) can be mathematically modelled as a communication channel, termed DNA storage channel, whose inputs and outputs are sets of unordered sequences. To design error correcting codes…
For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and little is known about its complexity. Most of the existing solutions rely on very restricted classes of…
Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. Besides a global level, they enable errors to be corrected locally, reducing the need for communication between storage nodes. There is a close…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
We study the hardness of the problem of finding the distance of quantum error-correcting codes. The analogous problem for classical codes is known to be NP-hard, even in approximate form. For quantum codes, various problems related to…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
In order to achieve fault tolerance, highly reliable system often require the ability to detect errors as soon as they occur and prevent the speared of erroneous information throughout the system. Thus, the need for codes capable of…
The optimization foundations of deep linear networks have recently received significant attention. However, due to their inherent non-convexity and hierarchical structure, analyzing the loss functions of deep linear networks remains a…
In this paper, we construct Error-Correcting Graph Codes. An error-correcting graph code of distance $\delta$ is a family $C$ of graphs on a common vertex set of size $n$, such that if we start with any graph in $C$, we would have to modify…
This paper presents an achievability bound that evaluates the exact probability of error of an ensemble of random codes that are decoded by a minimum distance decoder. Compared to the state-of-the-art which demands exponential computation…
Coherent network error correction is the error-control problem in network coding with the knowledge of the network codes at the source and sink nodes. With respect to a given set of local encoding kernels defining a linear network code, we…
We consider linear codes over a field in which the error values are restricted to a subgroup of its unit group. This scenario captures Lee distance codes as well as codes over the Gaussian or Eisenstein integers. Codes correcting restricted…
In contrast to a maximum-likelihood decoder, it is often desirable to use an incomplete decoder that can detect its decoding errors with high probability. One common choice is the bounded distance decoder. Bounds are derived for the total…
We construct error correcting codes for jointly transmitting a finite set of independent messages to an 'informed receiver' which has prior knowledge of the values of some subset of the messages as side information. The transmitter is…
We present a study on connection errors in networks of linear features and methods of error detection. We model networks with special connection specifications as networks with hierarchically connected features and define errors considering…
We present a general theory to obtain linear network codes utilizing forms and obtain explicit families of equidimensional vector spaces, in which any pair of distinct vector spaces intersect in the same small dimension. The theory is…
Traditional error-correcting codes (ECCs) assume a fixed message length, but many scenarios involve ongoing or indefinite transmissions where the message length is not known in advance. For example, when streaming a video, the user should…
Error-correcting pairs were introduced in 1988 by R. Pellikaan, and were found independently by R. K\"otter (1992), as a general algebraic method of decoding linear codes. These pairs exist for several classes of codes. However little or no…
Cyclic codes are an important class of linear codes. Bounding the minimum distance of cyclic codes is a long-standing research topic in coding theory, and several well-known and basic results have been developed on this topic. Recently,…
Bosonic codes with rotational symmetry are currently one of the best performing quantum error correcting codes. Little is known about error propagation and code distance for these rotation codes in contrast with qubit codes and Bosonic…