Related papers: An Algebraic Approach for Decoding Spread Codes
Quantum error correcting codes (QECCs) are the means of choice whenever quantum systems suffer errors, e.g., due to imperfect devices, environments, or faulty channels. By now, a plethora of families of codes is known, but there is no…
We introduce a new framework term coding for extremal problems in discrete mathematics and information flow, where one chooses interpretations of function symbols so as to maximise the number of satisfying assignments of a finite system of…
Maximum rank distance codes denoted MRD-codes are the equivalent in rank metric of MDS-codes. Given any integer $q$ power of a prime and any integer $n$ there is a family of MRD-codes of length $n$ over $\FF{q^n}$ having polynomial-time…
Algebraic space-time coding allows for reliable data exchange across fading multiple-input multiple-output channels. A powerful technique for decoding space-time codes in Maximum-Likelihood (ML) decoding, but well-performing and widely-used…
Text compression schemes and compact data structures usually combine sophisticated probability models with basic coding methods whose average codeword length closely match the entropy of known distributions. In the frequent case where basic…
The random matrix uniformly distributed over the set of all m-by-n matrices over a finite field plays an important role in many branches of information theory. In this paper a generalization of this random matrix, called k-good random…
We put forth new models for universal channel coding. Unlike standard codes which are designed for a specific type of channel, our most general universal code makes communication resilient on every channel, provided the noise level is below…
Construction of error-correcting codes achieving a designated minimum distance parameter is a central problem in coding theory. In this work, we study a very simple construction of binary linear codes that correct a given number of errors…
Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the…
We introduce a new family of erasure codes, called group decodable code (GDC), for distributed storage system. Given a set of design parameters {\alpha; \beta; k; t}, where k is the number of information symbols, each codeword of an…
In practice, LDPC codes are decoded using message passing methods. These methods offer good performance but tend to converge slowly and sometimes fail to converge and to decode the desired codewords correctly. Recently, tree-reweighted…
We construct a new family of explicit codes that are list decodable to capacity and achieve an optimal list size of $O(\frac{1}{\epsilon})$. In contrast to existing explicit constructions of codes achieving list decoding capacity, our…
In this paper we look at the problem of adjacency labeling of graphs. Given a family of undirected graphs the problem is to determine an encoding-decoding scheme for each member of the family such that we can decode the adjacency…
Ultra-Reliable Low-Latency Communications have stringent delay constraints, and hence use codes with small block length (short codewords). In these cases, classical models that provide good approximations to systems with infinitely long…
Minimal codes are a class of linear codes which gained interest in the last years, thanks to their connections to secret sharing schemes. In this paper we provide the weight distribution and the parameters of families of minimal codes…
Maximum-likelihood (ML) decoding for arbitrary block codes remains fundamentally hard, with worst-case time complexity-measured by the total number of multiplications-being no better than straightforward exhaustive search, which requires…
Quantum key distribution (QKD) allows two distant parties to share encryption keys with security based on laws of quantum mechanics. In order to share the keys, the quantum bits have to be transmitted from the sender to the receiver over a…
Array codes have been widely used in communication and storage systems. To reduce computational complexity, one important property of the array codes is that only XOR operation is used in the encoding and decoding process. In this work, we…
In this paper, for the purposes of information transmission and network error correction simultaneously, three classes of important linear network codes in network coding, linear multicast/broadcast/dispersion codes are generalized to…
Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…