相关论文: On the Symmetries of the Deletion Channel

We study the asymptotic behavior of the output states of sequences of quantum channels. Under a natural assumption, we show that the output set converges to a compact convex set, clarifying and substantially generalizing results in [BCN13].…

We consider classical hard-core particles moving on two parallel chains in the same direction. An interaction between the channels is included via the hopping rates. For a ring, the stationary state has a product form. For the case of…

The problem of channel coding with the erasure option is revisited for discrete memoryless channels. The interplay between the code rate, the undetected and total error probabilities is characterized. Using the information spectrum method,…

Symmetry transformations induce invariances which are frequently described with deep latent variable models. In many complex domains, such as the chemical space, invariances can be observed, yet the corresponding symmetry transformation…

Symmetry -- invariance to certain operators -- is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent…

Diffusive transport of particles or, more generally, small objects is a ubiquitous feature of physical and chemical reaction systems. In configurations containing confining walls or constrictions transport is controlled both by the…

This paper is a tutorial in a general and explicit procedure to simplify semidefinite programs which are invariant under the action of a symmetry group. The procedure is based on basic notions of representation theory of finite groups. As…

We consider the source-channel separation architecture for lossy source coding in communication networks. It is shown that the separation approach is optimal in two general scenarios, and is approximately optimal in a third scenario. The…

In this paper, fading Gaussian multiuser channels are considered. If the channel is perfectly known to the transmitter, capacity has been established for many cases in which the channels may satisfy certain information theoretic orders such…

In this paper, we consider a broadcasting process in which information is propagated from a given root node on a noisy tree network, and answer the question that whether the symbols at the nth level of the tree contain non-vanishing…

For most discrete memoryless channels, there does not exist a linear code for the channel which uses all of the channel's input symbols. Therefore, linearity of the code for such channels is a very restrictive condition and there should be…

This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…

Two channels are equivalent if their maximum likelihood (ML) decoders coincide for every code. We show that this equivalence relation partitions the space of channels into a generalized hyperplane arrangement. With this, we define a coding…

We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding…

In this paper we discuss the implication of the existence of a sliding symmetry, equivalent to the absence of a shear modulus, on the low-energy theory of the quantum hall smectic (QHS) state. We show, through renormalization group…

The quantum capacity captures the value of a quantum channel for transmitting quantum information, establishing the fundamental limits on quantum communication. In spite of its central role in quantum information theory, the quantum…

We prove that families of polar codes with multiple kernels over certain symmetric channels can be viewed as polar decreasing monomial-Cartesian codes, offering a unified treatment for such codes, over any finite field. We define decreasing…

In this paper, we study normalization methods for neural networks from the perspective of elimination singularity. Elimination singularities correspond to the points on the training trajectory where neurons become consistently deactivated.…

Symmetrized Kullback-Leibler (KL) information (\(I_{\mathrm{SKL}}\)), which symmetrizes the traditional mutual information by integrating Lautum information, has been shown as a critical quantity in communication~\cite{aminian2015capacity}…

Symmetry principles play an important role in geometry, and physics, allowing for the reduction of complicated systems to simpler, more comprehensible models that preserve the system's features of interest. Biological systems are often…