Related papers: Universal Polarization for Processes with Memory
Consider communication over a channel whose probabilistic model is completely unknown vector-wise and is not assumed to be stationary. Communication over such channels is challenging because knowing the past does not indicate anything about…
We consider the problem of universally communicating over an unknown and arbitrarily varying channel, using feedback. The focus of this paper is on determining the input behavior, and specifically, a prior distribution which is used to…
We put forth new models for universal channel coding. Unlike standard codes which are designed for a specific type of channel, our most general universal code makes communication resilient on every channel, provided the noise level is below…
We study a hidden Markov process which is the result of a transmission of the binary symmetric Markov source over the memoryless binary symmetric channel. This process has been studied extensively in Information Theory and is often used as…
This paper investigates universal polar coding schemes. In particular, a notion of ordering (called convolutional path) is introduced between probability distributions to determine when a polar compression (or communication) scheme designed…
We investigate quantum channels, which after a finite number $k$ of repeated applications erase all input information, i.e., channels whose $k$-th power (but no smaller power) is a completely depolarizing channel. We show that on a system…
In this work, a novel data-driven methodology for designing polar codes for channels with and without memory is proposed. The methodology is suitable for the case where the channel is given as a "black-box" and the designer has access to…
Using a mild variant of polar codes we design linear compression schemes compressing Hidden Markov sources (where the source is a Markov chain, but whose state is not necessarily observable from its output), and to decode from Hidden Markov…
The quantum capacity of a memoryless channel is often used as a single figure of merit to characterize its ability to transmit quantum information coherently. The capacity determines the maximal rate at which we can code reliably over…
The notion of forgetfulness, used in discrete quantum memory channels, is slightly weakened in order to be applied to the case of continuous channels. This is done in the context of quantum memory channels with Markovian noise. As a case…
Optical memory effects are well-known types of amplitude-domain wave correlation enabling control over light scattered through diffusive materials or multimode fibers. In this letter, we report the phenomenon of random polarization memory…
We discuss algorithms for combining sequential prediction strategies, a task which can be viewed as a natural generalisation of the concept of universal coding. We describe a graphical language based on Hidden Markov Models for defining…
Completely depolarising channels are often regarded as the prototype of physical processes that are useless for communication: any message that passes through them along a well-defined trajectory is completely erased. When two such channels…
Polar codes provably achieve the symmetric capacity of a memoryless channel while having an explicit construction. This work aims to increase the throughput of polar decoder hardware by an order of magnitude relative to the state of the art…
Polar codes are an exciting new class of error correcting codes that achieve the symmetric capacity of memoryless channels. Many decoding algorithms were developed and implemented, addressing various application requirements: from…
Opacity is a generic security property, that has been defined on (non probabilistic) transition systems and later on Markov chains with labels. For a secret predicate, given as a subset of runs, and a function describing the view of an…
The classical product state capacity of a noisy quantum channel with memory is investigated. A forgetful noise-memory channel is constructed by Markov switching between two depolarizing channels which introduces non-Markovian noise…
We consider classical-quantum (cq-)channels with memory, and establish that Ar{\i}kan-constructed polar codes achieve the classical capacity for two key noise models, namely for (i) qubit erasures and (ii) unital qubit noise with channel…
The problem of polar coding for an arbitrary sequence of independent binary-input memoryless symmetric (BMS) channels $\left\{W_i\right\}_{i=1}^{N}$ is considered. The sequence of channels is assumed to be completely known to both the…
We consider a model of bosonic memory channel, which induces correlations among the transmitted signals. The application of suitable unitary transformations at encoding and decoding stages allows the complete removal of correlations,…