Related papers: Resolvability on Continuous Alphabets
Over any discrete memoryless channel, we build codes such that: for one, their block error probabilities and code rates scale like random codes'; and for two, their encoding and decoding complexities scale like polar codes'. Quantitatively,…
We study the problem of channel resolvability for fixed i.i.d. input distributions and discrete memoryless channels (DMCs), and derive the strong converse theorem for any DMCs that are not necessarily full rank. We also derive the optimal…
We give a short proof of the cross norm characterization of separability due to O. Rudolph and show how its computation, for a fixed chosen error, can be reduced to a linear programming problem whose dimension grows polynomially with the…
The fundamental result of Li, Long, and Srinivasan on approximations of set systems has become a key tool across several communities such as learning theory, algorithms, computational geometry, combinatorics and data analysis. The goal of…
We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and…
Strong typicality and the Markov lemma have been used in the proofs of several multiterminal source coding theorems. Since these two tools can be applied to finite alphabets only, the results proved by them are subject to the same…
We prove several results on linear codes achieving list-recovery capacity. We show that random linear codes achieve list-recovery capacity with constant output list size (independent of the alphabet size and length). That is, over alphabets…
We study the problem of \emph{robust satisfiability} of systems of nonlinear equations, namely, whether for a given continuous function $f:\,K\to\mathbb{R}^n$ on a~finite simplicial complex $K$ and $\alpha>0$, it holds that each function…
The paper derives the optimal second-order coding rate for the continuous-time Poisson channel. We also obtain bounds on the third-order coding rate. This is the first instance of a second-order result for a continuous-time channel. The…
The problem of mismatched decoding for discrete memoryless channels is addressed. A mismatched cognitive multiple-access channel is introduced, and an inner bound on its capacity region is derived using two alternative encoding methods:…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…
We present a proof for the quantum channel coding theorem which relies on the fact that a randomly chosen code space typically is highly suitable for quantum error correction. In this sense, the proof is close to Shannon's original…
Chernoff bound is a fundamental tool in theoretical computer science. It has been extensively used in randomized algorithm design and stochastic type analysis. Discrepancy theory, which deals with finding a bi-coloring of a set system such…
The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Ar{\i}kan proved that…
Linear network coding transmits data through networks by letting the intermediate nodes combine the messages they receive and forward the combinations towards their destinations. The solvability problem asks whether the demands of all the…
In this paper we provide a method to obtain tight lower bounds on the minimum redundancy achievable by a Huffman code when the probability distribution underlying an alphabet is only partially known. In particular, we address the case where…
Let G be a finite group and N be a non-trivial normal subgroup of G, such that the average character degree of irreducible characters in Irr(G|N) is less than or equal to 16=5. Then we prove that N is solvable. Also, we prove the…
In this note, we consider semiclassical scattering on a manifold which is Euclidean near infinity or asymptotically hyperbolic. We show that, if the cut-off resolvent satisfies polynomial estimates in a strip of size $O(h |\log…
Consider a binary word being transmitted through a communication channel that introduces deletable errors where each bit of the word is either retained, flipped, erased or deleted. The simplest code for correcting \emph{all} possible…
We investigate the feasibility of sample average approximation (SAA) for general stochastic optimization problems, including two-stage stochastic programming without the relatively complete recourse assumption. Instead of analyzing problems…