Related papers: Channel Metrization
Latent Euclidean embedding models a given network by representing each node in a Euclidean space, where the probability of two nodes sharing an edge is a function of the distances between the nodes. This implies that for two nodes to share…
So far, there have been plenty of literatures on the metric in the space of probability distributions and quantum states. As for channels, however, only a little had been known. In this paper, we impose monotonicity by concatenation of…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
We consider the problem of embedding a subset of $\mathbb{R}^n$ into a low-dimensional Hamming cube in an almost isometric way. We construct a simple, data-oblivious, and computationally efficient map that achieves this task with high…
The fundamental limits of channels with mismatched decoding are addressed. A general formula is established for the mismatch capacity of a general channel, defined as a sequence of conditional distributions with a general decoding metrics…
In this paper, we study the hardness of decoding a random code endowed with the cover metric. As the cover metric lies in between the Hamming and rank metric, it presents itself as a promising candidate for code-based cryptography. We give…
We determine the optimal achievable rate at which entanglement can be reliably transmitted when the memoryless channel used during transmission is unknown both to sender and receiver. To be more precise, we assume that both of them only…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
We introduce harmonization, an ensembling method that combines several "noisy" decoders to generate highly accurate decoding predictions. Harmonized ensembles of MWPM-based decoders achieve lower logical error rates than their individual…
The speed at which millimeter-Wave (mmWave) channel estimation can be carried out is critical for the adoption of mmWave technologies. This is particularly crucial because mmWave transceivers are equipped with large antenna arrays to combat…
This article investigates the probabilistic relationship between quantum classification of Boolean functions and their Hamming distance. By integrating concepts from quantum computing, information theory, and combinatorics, we explore how…
Quantum channels describe the most general dynamics of open quantum systems. A quantum channel, as a linear map on vectorized quantum states, can be represented by a single matrix, whose spectrum is called the channel spectrum. Here we…
We study the Closest Pair Problem in Hamming metric, which asks to find the pair with the smallest Hamming distance in a collection of binary vectors. We give a new randomized algorithm for the problem on uniformly random input…
The distance metric plays an important role in nearest neighbor (NN) classification. Usually the Euclidean distance metric is assumed or a Mahalanobis distance metric is optimized to improve the NN performance. In this paper, we study the…
Millimeter-wave (mmWave) channels, which occupy frequency ranges much higher than those being used in previous wireless communications systems, are utilized to meet the increased throughput requirements that come with 5G communications. The…
We consider the topic of universal decoding with a decoder that does not have direct access to the codebook, but only to noisy versions of the various randomly generated codewords, a problem motivated by biometrical identification systems.…
We present an efficient tensor-network based algorithm for finding the optimal adaptive quantum channel discrimination strategies inspired by recently developed numerical methods in quantum metrology to find the optimal adaptive channel…
This paper investigates the channel estimation for holographic MIMO systems by unmasking their distinctions from the conventional one. Specifically, we elucidate that the channel estimation, subject to holographic MIMO's electromagnetically…
Embedding-based similarity metrics between text sequences can be influenced not just by the content dimensions we most care about, but can also be biased by spurious attributes like the text's source or language. These document confounders…
We study the power of measurements implementable with local quantum operations and classical communication (or LOCC measurements for short) in the setting of quantum channel discrimination. More precisely, we consider discrimination…