Related papers: Majority Logic Decoding of Affine Grassmann Codes …
The Grassmannian space $\Gr$ is the set of all $k-$dimensional subspaces of the vector space~\smash{$\F_q^n$}. Recently, codes in the Grassmannian have found an application in network coding. The main goal of this paper is to present…
Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…
The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of…
We present several results on quantum codes over general alphabets (that is, in which the fundamental units may have more than 2 states). In particular, we consider codes derived from finite symplectic geometry assumed to have additional…
Recently a framework for assisted quantum error correction was proposed in which a specific type of error is allowed to occur on auxiliary qubits, which is in contrast to standard entanglement assistance that requires noiseless auxiliary…
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…
We propose an efficient encoding algorithm for the binary and non-binary low-density parity-check codes. This algorithm transforms the parity part of the parity-check matrix into a block triangular matrix with low weight diagonal…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
Binary matrix codes with restricted row and column weights are a desirable method of coded modulation for power line communication. In this work, we construct such matrix codes that are obtained as products of affine codes - cosets of…
Different choices of quantum error-correcting codes can reduce the demands on the physical hardware needed to build a quantum computer. To achieve the full potential of a code, we must develop practical decoding algorithms that can correct…
Quantum low-density parity-check codes are promising candidates for low-overhead fault-tolerant quantum computing, but degeneracy is known to impair the convergence of belief-propagation (BP) decoding of these codes. In this work, we show…
The performance of iterative decoding techniques for linear block codes correcting erasures depends very much on the sizes of the stopping sets associated with the underlying Tanner graph, or, equivalently, the parity-check matrix…
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…
A systematic way of constructing Grassmannian codes endowed with the subspace distance as lifts of matrix codes over the prime field $GF(p)$ is introduced. The matrix codes are $GF(p)$-subspaces of the ring $M_2(GF(p))$ of $2 \times 2$…
Linear codes have attracted considerable attention in coding theory and cryptography due to their significant applications in secret sharing schemes, secure two-party computation, Galois geometries, among others. As two special subclasses…
In this paper, we propose to study and optimize a very general class of LDPC codes whose variable nodes belong to finite sets with different orders. We named this class of codes Hybrid LDPC codes. Although efficient optimization techniques…
This paper consists of three parts. The first part presents a large class of new binary quasi-cyclic (QC)-LDPC codes with girth of at least 6 whose parity-check matrices are constructed based on cyclic subgroups of finite fields.…
Recently, we introduced a new class of finite alphabet iterative decoders (FAIDs) for low-density parity-check (LDPC) codes. These decoders are capable of surpassing belief propagation in the error floor region on the Binary Symmetric…
The problem of error correction for Gallager's low-density parity-check codes is famously equivalent to that of computing marginal Boltzmann probabilities for an Ising-like model with multispin interactions in a non-uniform magnetic field.…
We generalize Helberg's number-theoretic construction of multiple insertion-deletion correcting binary codes to non-binary alphabets and describe a linear decoding algorithm for correcting multiple deletions.