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When studying a general system of delay differential equation with a single constant delay, we encounter a certain lack of uniqueness in determining the coefficient of one of the third order terms of the series defining the center manifold.…
The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian Discrepancy Measure for testing precise statistical hypotheses. In particular, we derive results on third-order…
A pure-loss bosonic channel is a simple model for communication over free-space or fiber-optic links. More generally, phase-insensitive bosonic channels model other kinds of noise, such as thermalizing or amplifying processes. Recent work…
Quantum Fisher information is the principal tool used to give the ultimate precision bound on the estimation of parameters for quantum channels. In this work, we present analytical expressions for the quantum Fisher information with three…
A new achievability scheme for the compound channel with discrete memoryless (DM) state noncausally available at the encoder is established. Achievability is proved using superposition coding, Marton coding, joint typicality encoding, and…
Finite blocklength and second-order (dispersion) results are presented for the arbitrarily-varying channel (AVC), a classical model wherein an adversary can transmit arbitrary signals into the channel. A novel finite blocklength…
A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output $p$-norm can be…
This paper presents a new derivation method of converse bounds on the non-asymptotic achievable rate of discrete weakly symmetric memoryless channels. It is based on the finite blocklength statistics of the channel, where with the use of an…
We derive the optimum second-order coding rates, known as second-order capacities, for erasure and list decoding. For erasure decoding for discrete memoryless channels, we show that second-order capacity is $\sqrt{V}\Phi^{-1}(\epsilon_t)$…
We recently showed in [1] the superiority of certain structured coding matrices ensembles (such as partial row-orthogonal) for sparse superposition codes when compared with purely random matrices with i.i.d. entries, both…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
We study the fundamental limits of covert communications over general memoryless additive-noise channels. We assume that the legitimate receiver and the eavesdropper share the same channel and therefore see the same outputs. Under mild…
This paper determines the range of feasible values of standard error exponents for binary-input memoryless symmetric channels of fixed capacity $C$ and shows that extremes are attained by the binary symmetric and the binary erasure channel.…
We survey coding techniques that enable reliable transmission at rates that approach the capacity of an arbitrary discrete memoryless channel. In particular, we take the point of view of modern coding theory and discuss how recent advances…
Worst-case models of erasure and symmetric channels are investigated, in which the number of channel errors occurring in each sliding window of a given length is bounded. Upper and lower bounds on their zero-error capacities are derived,…
This study investigates the fundamental limits of variable-length compression in which prefix-free constraints are not imposed (i.e., one-to-one codes are studied) and non-vanishing error probabilities are permitted. Due in part to a…
We consider energy-constrained infinite-dimensional quantum channels from a given system (satisfying a certain condition) to any other systems. We show that dealing with basic capacities of these channels we may assume (accepting…
Evaluating the channel capacity is one of many key problems in information theory. In this work we derive rather-mild sufficient conditions under which the capacity is finite and achievable. These conditions are derived for generic,…
We give a unified treatment of some inequalities that are used in the proofs of channel polarization theorems involving a binary-input discrete memoryless channel.
A switched quantum channel with indefinite causal order is studied for the fundamental metrological task of phase estimation on a qubit unitary operator affected by quantum thermal noise. Specific capabilities are reported in the switched…