Related papers: Network-Error Correcting Codes using Small Fields
We consider a network coding setting where some of the messages and edges have fixed alphabet sizes, that do not change when we increase the common alphabet size of the rest of the messages and edges. We prove that the problem of deciding…
Erasure codes are an efficient means of storing data across a network in comparison to data replication, as they tend to reduce the amount of data stored in the network and offer increased resilience in the presence of node failures. The…
The rate of a network code is the ratio of the block size of the network's messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general…
This paper proposes Fulcrum network codes, a network coding framework that achieves three seemingly conflicting objectives: (i) to reduce the coding coefficient overhead to almost n bits per packet in a generation of n packets; (ii) to…
We describe a new class of list decodable codes based on Galois extensions of function fields and present a list decoding algorithm. These codes are obtained as a result of folding the set of rational places of a function field using…
We consider the problem of adding a fixed number of new edges to an undirected graph in order to minimize the diameter of the augmented graph, and under the constraint that the number of edges added for each vertex is bounded by an integer.…
In distributed storage systems built using commodity hardware, it is necessary to have data redundancy in order to ensure system reliability. In such systems, it is also often desirable to be able to quickly repair storage nodes that fail.…
Communication in poor network environment is always a difficult problem, since troubles such as bit errors and packet loss may often occur. It is generally believed that it is impossible to transmit data both accurately and efficiently in…
In this work, we study linear error-correcting codes against adversarial insertion-deletion (indel) errors. While most constructions for the indel model are nonlinear, linear codes offer compact representations, efficient encoding, and…
We design a heuristic method, a genetic algorithm, for the computation of an upper bound of the minimum distance of a linear code over a finite field. By the use of the row reduced echelon form, we obtain a permutation encoding of the…
Network coding is studied when an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than when the adversary controls a given number of edges in the…
In this paper, the class of random irregular block-hierarchical networks is defined and algorithms for generation and calculation of network properties are described. The algorithms presented for this class of networks are more efficient…
We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC) algorithm to address the issue of field size in random network coding. ARCNC operates as a convolutional code, with the coefficients of local encoding kernels…
We show that errors in data transmitted through linear codes can be thought of as codewords of minimum weight of new linear codes. To determine errors we can then use methods specific to finding such special codewords. One of these methods…
Folded Reed-Solomon codes are an explicit family of codes that achieve the optimal trade-off between rate and error-correction capability: specifically, for any $\eps > 0$, the author and Rudra (2006,08) presented an $n^{O(1/\eps)}$ time…
Many quantum technologies are now reaching a high level of maturity and control, and it is likely that the first demonstrations of suppression of naturally occurring quantum noise using small topological error correcting codes will soon be…
The theory of quantum error correction was established more than a decade ago as the primary tool for fighting decoherence in quantum information processing. Although great progress has already been made in this field, limited methods are…
Regenerating codes and codes with locality are two schemes that have recently been proposed to ensure data collection and reliability in a distributed storage network. In a situation where one is attempting to repair a failed node,…
Analyzing network topologies and communication graphs plays a crucial role in contemporary network management. However, the absence of a cohesive approach leads to a challenging learning curve, heightened errors, and inefficiencies. In this…
Constructing Reed--Solomon (RS) codes that can correct insertions and deletions (insdel errors) has been considered in numerous recent works. For the special case of two-dimensional RS-codes, it is known [CST23] that an $[n,2]_q$ RS-code…