Related papers: Asymmetric numeral systems
It is well known that n bits of entropy are necessary and sufficient to perfectly encrypt n bits (one-time pad). Even if we allow the encryption to be approximate, the amount of entropy needed doesn't asymptotically change. However, this is…
Anomalies are strange data points; they usually represent an unusual occurrence. Anomaly detection is presented from the perspective of Wireless sensor networks. Different approaches have been taken in the past, as we will see, not only to…
We consider the problem of universal decoding for arbitrary unknown channels in the random coding regime. For a given random coding distribution and a given class of metric decoders, we propose a generic universal decoder whose average…
Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…
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…
Quantum computers create new security risks for today's encryption systems. This paper presents an improved version of the Advanced Encryption Standard (AES) that uses quantum technology to strengthen protection. Our approach offers two…
An additive noise channel is considered, in which the distribution of the noise is nonparametric and unknown. The problem of learning encoders and decoders based on noise samples is considered. For uncoded communication systems, the problem…
We give new combinatorial constructions for codes providing authentication and secrecy for equiprobable source probability distributions. In particular, we construct an infinite class of optimal authentication codes which are multiple-fold…
Exponential error bounds achievable by universal coding and decoding are derived for frame-asynchronous discrete memoryless %asynchronous multiple access channels with two senders, via the method of subtypes, a refinement of the method of…
Equivariant neural networks (ENNs) have been shown to be extremely effective in applications involving underlying symmetries. By construction ENNs cannot produce lower symmetry outputs given a higher symmetry input. However, symmetry…
Sorted data is usually easier to compress than unsorted permutations of the same data. This motivates a simple compression scheme: specify the sorted permutation of the data along with a representation of the sorted data compressed…
The analysis of random coding error exponents pertaining to erasure/list decoding, due to Forney, is revisited. Instead of using Jensen's inequality as well as some other inequalities in the derivation, we demonstrate that an exponentially…
We study the problem of extracting a prescribed number of random bits by reading the smallest possible number of symbols from non-ideal stochastic processes. The related interval algorithm proposed by Han and Hoshi has asymptotically…
It is recently conjectured in quantum information processing that phase-shift errors occur with high probability than qubit-flip errors, hence the former is more disturbing to quantum information than the later one. This leads us to…
Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a…
Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher…
In this work, we present a novel inner product design for stochastic computing. Stochastic computing is an emerging computing technique, that encodes a number in the probability of observing a one in a random bit stream. This leads to…
In network communications, information transmission often encounters wiretapping attacks. Secure network coding is introduced to prevent information from being leaked to adversaries. The investigation of performance bounds on the numbers of…
The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…
In quantum Shannon theory, various kinds of quantum entropies are used to characterize the capacities of noisy physical systems. Among them, min-entropy and its smooth version attract wide interest especially in the field of quantum…