Related papers: Fountain Codes and Invertible Matrices
Block-encoding operators are one of the essential components in quantum algorithms based on Quantum Signal Processing. Their gate complexity largely determines the overall gate complexity of the full algorithm. Using variational methods, we…
The inverse of the Vandermonde and confluent Vandermonde matrices are presented. In the case of the Vandermonde matrix, we present a decomposition in three factors, one of them a diagonal matrix. The evaluation of such inverse matrices is a…
The rateless and information additive properties of fountain codes make them attractive for use in broadcast/multicast applications, especially in radio environments where channel characteristics vary with time and bandwidth is expensive.…
We consider the problem of succinctly encoding a static map to support approximate queries. We derive upper and lower bounds on the space requirements in terms of the error rate and the entropy of the distribution of values over keys: our…
In this study, a novel feature coding method that exploits invariance for transformations represented by a finite group of orthogonal matrices is proposed. We prove that the group-invariant feature vector contains sufficient discriminative…
In this article, we establish a mathematical framework that utilizes concepts from graph theory to formalize the parity transformation, an encoding strategy for compiling optimization problems on quantum devices. We introduce the…
Machine learning has had a major impact on data compression over the last decade and inspired many new, exciting theoretical and applied questions. This paper describes one such direction -- relative entropy coding -- which focuses on…
Recent video codecs such as VVC and AV1 apply a Non-rectangular (NR) partitioning to combine prediction signals using a smooth blending around the boundary, followed by a rectangular transform on the whole block. The NR signal…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
Generating new molecules is fundamental to advancing critical applications such as drug discovery and material synthesis. Flows can generate molecules effectively by inverting the encoding process, however, existing flow models either…
This note introduces a family of circulant quantum channels -- a subclass of the mixed-permutation channels -- and investigates its key structural and operational properties. We show that the image of the circulant quantum channel is…
Neural methods of molecule property prediction require efficient encoding of structure and property relationship to be accurate. Recent work using graph algorithms shows limited generalization in the latent molecule encoding space. We build…
While 2-level systems, aka qubits, are a natural choice to perform a logical quantum computation, the situation is less clear at the physical level. Encoding information in higher-dimensional physical systems can indeed provide a first…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
Block encoding is a key ingredient in the recently developed quantum singular value transformation (QSVT) framework, which provides a unifying description for many quantum algorithms. Initially introduced to simplify and optimize resource…
We present an algorithm to construct quantum circuits for encoding and inverse encoding of quantum convolutional codes. We show that any quantum convolutional code contains a subcode of finite index which has a non-catastrophic encoding…
Neural machine translation (NMT) models generally adopt an encoder-decoder architecture for modeling the entire translation process. The encoder summarizes the representation of input sentence from scratch, which is potentially a problem if…
We address the problem of improving the performance and in particular the sample complexity of deep neural networks by enforcing and guaranteeing invariances to symmetry transformations rather than learning them from data. Group-equivariant…
Rateless/fountain codes are designed so that all input symbols can be recovered from a slightly larger number of coded symbols, with high probability using an iterative decoder. In this paper we investigate the number of input symbols that…
Transform coding is routinely used for lossy compression of discrete sources with memory. The input signal is divided into N-dimensional vectors, which are transformed by means of a linear mapping. Then, transform coefficients are quantized…