Related papers: Enhanced Algebraic Error Control for Random Linear…
In the practical network communications, many internal nodes in the network are required to not only transmit messages but decode source messages. For different applications, four important classes of linear network codes in network coding…
Hinging on ideas from physical-layer network coding, some promising proposals of coded random access systems seek to improve system performance (while preserving low complexity) by means of packet repetitions and decoding of linear…
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…
The distance profiles of linear block codes can be employed to design variational coding scheme for encoding message with variational length and getting lower decoding error probability by large minimum Hamming distance. %, e.g. the design…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…
This paper investigates the decoding of certain Gabidulin codes that were transmitted over a channel with space-symmetric errors. Space-symmetric errors are additive error matrices that have the property that their column and row spaces are…
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 this article we present a construction of error correcting codes, that have representation as very sparse matrices and belong to the class of Low Density Parity Check Codes. LDPC codes are in the classical Hamming metric. They are very…
We study the problem of reducing the communication overhead from a noisy wire-tap channel or storage system where data is encoded as a matrix, when more columns (or their linear combinations) are available. We present its applications to…
High-rate concatenated quantum codes offer a promising pathway toward fault-tolerant quantum computation, yet designing efficient decoders that fully exploit their error-correction capability remains a significant challenge. In this work,…
This paper studies the parameters for which Reed-Muller (RM) codes over $GF(2)$ can correct random erasures and random errors with high probability, and in particular when can they achieve capacity for these two classical channels.…
In this paper we introduce and investigate rank-metric intersecting codes, a new class of linear codes in the rank-metric context, inspired by the well-studied notion of intersecting codes in the Hamming metric. A rank-metric code is said…
Random linear network coding (RLNC) provides a powerful framework for non-coherent communication, where reliable transmission requires correcting errors and erasures induced by network mixing and motivates the use of subspace codes. In this…
In this paper an interpolation-based decoding algorithm to decode Gabidulin codes, transmitted through a finely restricted channel, is proposed. The algorithm is able to decode rank errors beyond half the minimum distance by one unit. Also…
Random linear network coding (RLNC) in theory achieves the max-flow capacity of multicast networks, at the cost of high decoding complexity. To improve the performance-complexity tradeoff, we consider the design of sparse network codes. A…
Random jammers that overpower transmitted signals are a practical concern for many wireless communication protocols. As such, wireless receivers must be able to cope with standard channel noise and jamming (intentional or unintentional). To…
Neural network decoding algorithms are recently introduced by Nachmani et al. to decode high-density parity-check (HDPC) codes. In contrast with iterative decoding algorithms such as sum-product or min-sum algorithms in which the weight of…
This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
This paper presents a novel coding scheme for distributed storage systems containing nodes with adversarial errors. The key challenge in such systems is the propagation of erroneous data from a single corrupted node to the rest of the…