相关论文: On the Symmetries of the Deletion Channel

We analyze a slow-fading interference network with MN non-cooperating single-antenna sources and M non-cooperating single-antenna destinations. In particular, we assume that the sources are divided into M mutually exclusive groups of N…

In deep learning, neural networks serve as noisy channels between input data and its representation. This perspective naturally relates deep learning with the pursuit of constructing channels with optimal performance in information…

In this paper, we present a novel communication channel, called the absorption channel, inspired by information transmission in neurons. Our motivation comes from in-vivo nano-machines, emerging medical applications, and brain-machine…

We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…

In a physical neural system, learning rules must be local both in space and time. In order for learning to occur, non-local information must be communicated to the deep synapses through a communication channel, the deep learning channel. We…

We consider the discrete memoryless symmetric primitive relay channel, where, a source $X$ wants to send information to a destination $Y$ with the help of a relay $Z$ and the relay can communicate to the destination via an error-free…

In projected descriptions of quantum dynamics, the importance of an eliminated degree of freedom is routinely assessed by deleting it and measuring the system's response. This conflates two effects: the channel's intrinsic contribution and…

Quantum transport through left-right symmetric chaotic cavities in the presence of the symplectic symmetry, is studied through the statistical distribution of the dimensionless conductance. With this particular point symmetry, their…

Most communication channels are subjected to noise. One of the goals of Information Theory is to add redundancy in the transmission of information so that the information is transmitted reliably and the amount of information transmitted…

Starting from the classical results of Shubnikov and Zamorzayev, computer models of shapes are implemented, which allow to visualize the action of discrete subgroups of continuous topological groups. The action is visualize by performing…

In this paper, we study the asymptotic performance of Abelian group codes for the lossy source coding problem for arbitrary discrete (finite alphabet) memoryless sources as well as the channel coding problem for arbitrary discrete (finite…

Scattering matrices with block symmetry, which corresponds to scattering process on cavities with geometrical symmetry, are analyzed. The distribution of transmission coefficient is computed for different number of channels in the case of a…

This paper presents the first proof of polarization for the deletion channel with a constant deletion rate and a regular hidden-Markov input distribution. A key part of this work involves representing the deletion channel using a trellis…

The recently developed information-theoretic approach to crystallographic symmetry classifications and quantifications in two dimensions (2D) from digital transmission electron and scanning probe microscope images is adapted for the…

We investigate the renormalization group flows and fixed point structure of many coupled minimal models. The models are coupled two by two by energy-energy couplings. We take the general approach where the bare couplings are all taken to be…

Given the possibility of communication systems failing catastrophically, we investigate limits to communicating over channels that fail at random times. These channels are finite-state semi-Markov channels. We show that communication with…

The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…

We develop a new unsupervised symmetry learning method that starts with raw data and provides the minimal generator of an underlying Lie group of symmetries, together with a symmetry-equivariant representation of the data, which turns the…

Given a finite group with a generating subset there is a well-established notion of length for a group element given in terms of its minimal length expression as a product of elements from the generating set. Recently, certain quantities…

We consider the classic joint source-channel coding problem of transmitting a memoryless source over a memoryless channel. The focus of this work is on the long-standing open problem of finding the rate of convergence of the smallest…