Related papers: Neural Lattice Decoders
We characterize the complexity of the lattice decoding problem from a neural network perspective. The notion of Voronoi-reduced basis is introduced to restrict the space of solutions to a binary set. On the one hand, this problem is shown…
We propose two low-complexity lattice code constructions that have competitive coding and shaping gains. The first construction, named systematic Voronoi shaping, maps short blocks of integers to the dithered Voronoi integers, which are…
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…
In this letter, we propose a Voronoi shaping method with reduced encoding complexity. The method works for integer shaping and coding lattices satisfying the chain $\Lambda_s \subseteq \textbf{K}\mathbb{Z}^n \subseteq \Lambda_c$, with…
We propose a recursive lattice reduction framework for finding short non-zero vectors or dense sublattices of a lattice. The framework works by recursively searching for dense sublattices of dense sublattices (or their duals) with…
In this note we give a polynomial time algorithm for solving the closest vector problem in the class of zonotopal lattices. The Voronoi cell of a zonotopal lattice is a zonotope, i.e. a projection of a regular cube. Examples of zonotopal…
Interpolation is a fundamental technique in scientific computing and is at the heart of many scientific visualization techniques. There is usually a trade-off between the approximation capabilities of an interpolation scheme and its…
We introduce VoroFields, a hierarchical neural-field framework for approximating generalized Voronoi diagrams of finite geometric site sets in low-dimensional domains under arbitrary evaluable point-to-site distances. Instead of…
We describe algorithms which address two classical problems in lattice geometry: the lattice covering and the simultaneous lattice packing-covering problem. Theoretically our algorithms solve the two problems in any fixed dimension d in the…
Neural network (NN) denoisers are an essential building block in many common tasks, ranging from image reconstruction to image generation. However, the success of these models is not well understood from a theoretical perspective. In this…
Point lattices and their decoding via neural networks are considered in this paper. Lattice decoding in Rn, known as the closest vector problem (CVP), becomes a classification problem in the fundamental parallelotope with a piecewise linear…
Deep neural networks, in particular convolutional neural networks, have become highly effective tools for compressing images and solving inverse problems including denoising, inpainting, and reconstruction from few and noisy measurements.…
Finding optimal correction of errors in generic stabilizer codes is a computationally hard problem, even for simple noise models. While this task can be simplified for codes with some structure, such as topological stabilizer codes,…
Neural machine translation (NMT) heavily relies on word-level modelling to learn semantic representations of input sentences. However, for languages without natural word delimiters (e.g., Chinese) where input sentences have to be tokenized…
Cellular structures found in nature exhibit remarkable properties such as high strength, high energy absorption, excellent thermal/acoustic insulation, and fluid transfusion. Many of these structures are Voronoi-like; therefore researchers…
For reliable transmission across a noisy communication channel, classical results from information theory show that it is asymptotically optimal to separate out the source and channel coding processes. However, this decomposition can fall…
Voronoi and Delaunay (Delone) cells of the root and weight lattices of the Coxeter-Weyl groups W(an) and W(dn) are constructed. The face centered cubic (fcc) and body centered cubic (bcc)lattices are obtained in this context. Basic…
We present a method for training a neural network to perform image denoising without access to clean training examples or access to paired noisy training examples. Our method requires only a single noisy realization of each training example…
The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder,…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…