Related papers: Encoding and Decoding of Several Optimal Rank Metr…
Recently, codes in the sum-rank metric attracted attention due to several applications in e.g. multishot network coding, distributed storage and quantum-resistant cryptography. The sum-rank analogs of Reed-Solomon and Gabidulin codes are…
We introduce a framework which allows to systematically and arbitrarily scale the code distance of local fermion-to-qubit encodings in one and two dimensions without growing the weights of stabilizers. This is achieved by embedding…
The rapid growth of digital data has heightened the demand for efficient lossless compression methods. However, existing algorithms exhibit trade-offs: some achieve high compression ratios, others excel in encoding or decoding speed, and…
We present a novel iterative decoding algorithm for Reed-Muller (RM) codes, which takes advantage of a graph representation of the code. Vertices of the considered graph correspond to codewords, with two vertices being connected by an edge…
Surface codes exploit topological protection to increase error resilience in quantum computing devices and can in principle be implemented in existing hardware. They are one of the most promising candidates for active error correction, not…
In the search for highly efficient decoders for short LDPC codes approaching maximum likelihood performance, a relayed decoding strategy, specifically activating the ordered statistics decoding process upon failure of a neural min-sum…
Rank-metric codes are subspaces of matrices over finite fields endowed with the rank metric and admit a natural tensorial representation. The tensor rank provides a measure of the minimal size of a decomposition of a code into rank-one…
Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been…
The unit-derived method in coding theory is shown to be a unique optimal scheme for constructing and analysing codes. In many cases efficient and practical decoding methods are produced. Codes with efficient decoding algorithms at maximal…
In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. Using this new concept, we derive properties of maximum rank distance (MRD) codes that parallel…
We present a constraint-coding scheme to correct asymmetric magnitude-$1$ errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared to known…
We show how Gabidulin codes can be list decoded by using a parametrization approach. For this we consider a certain module in the ring of linearized polynomials and find a minimal basis for this module using the Euclidean algorithm with…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical…
The performance of algebraic soft-decision decoding of Reed-Solomon codes using bit-level soft information is investigated. Optimal multiplicity assignment strategies of algebraic soft-decision decoding with infinite cost are first studied…
Index codes reduce the number of bits broadcast by a wireless transmitter to a number of receivers with different demands and with side information. It is known that the problem of finding optimal linear index codes is NP-hard. We…
The most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well-known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on…
The projective space of order $n$ over a finite field $\F_q$ is a set of all subspaces of the vector space $\F_q^{n}$. In this work, we consider error-correcting codes in the projective space, focusing mainly on constant dimension codes. We…
A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…
The multiplicative-additive finite-field matrix channel arises as an adequate model for linear network coding systems when links are subject to errors and erasures, and both the network topology and the network code are unknown. In a…