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We design a quasi-interpolation operator from the Sobolev space $H^1_0(\Omega)$ to its finite-dimensional finite element subspace formed by piecewise polynomials on a simplicial mesh with a computable approximation constant. The operator 1)…
We study the use of quantum entanglement in the zero-error source-channel coding problem. Here, Alice and Bob are connected by a noisy classical one-way channel, and are given correlated inputs from a random source. Their goal is for Bob to…
The deletion channel is the simplest point-to-point communication channel that models lack of synchronization. Despite significant effort, little is known about its capacity, and even less about optimal coding schemes. In this paper we…
In communication networks, cooperative strategies are coding schemes where network nodes work together to improve network performance metrics such as sum-rate. This work studies encoder cooperation in the setting of a discrete multiple…
Given any quantum error correcting code permitting universal fault-tolerant quantum computation and transversal measurement of logical X and Z, we describe how to perform time-optimal quantum computation, meaning the execution of an…
Let $f$ denote length preserving function on words. A classical algorithm can be considered as $T$ iterated applications of black box representing $f$, beginning with input word $x$ of length $n$. It is proved that if $T=O(2^{n/(7+e)}), e…
We derive an analytical calculation formula for the channel capacity of a classical channel without any iteration while its existing algorithms require iterations and the number of iteration depends on the required precision level. Hence,…
We study the limits of communication efficiency for function computation in collocated networks within the framework of multi-terminal block source coding theory. With the goal of computing a desired function of sources at a sink, nodes…
The topological properties of a set have a strong impact on its computability properties. A striking illustration of this idea is given by spheres and closed manifolds: if a set $X$ is homeomorphic to a sphere or a closed manifold, then any…
In this paper, we put forward secure network function computation over a directed acyclic network. In such a network, a sink node is required to compute with zero error a target function of which the inputs are generated as source messages…
We propose an iterative method for approximately computing the capacity of discrete memoryless channels, possibly under additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and…
The listsize capacity of a discrete memoryless channel is the largest transmission rate for which the expectation---or, more generally, the $\rho$-th moment---of the number of messages that could have produced the output of the channel…
This paper shows that the logarithm of the epsilon-error capacity (average error probability) for n uses of a discrete memoryless channel is upper bounded by the normal approximation plus a third-order term that does not exceed 1/2 log n +…
Quantum Lov\'asz number is a quantum generalization of the Lov\'asz number in graph theory. It is the best known efficiently computable upper bound of the entanglement-assisted zero-error classical capacity of a quantum channel. However, it…
This paper concerns the capacity of the discrete noiseless channel introduced by Shannon. A sufficient condition is given for the capacity to be well-defined. For a general discrete noiseless channel allowing non-integer valued symbol…
Recently the power of positive partial transpose preserving (PPTp) and no-signalling (NS) codes in quantum communication has been studied. We continue with this line of research and show that the NS/PPTp/NS$\cap$PPTp codes assisted…
One of the main theoretical motivations for the emerging area of network coding is the achievability of the max-flow/min-cut rate for single source multicast. This can exceed the rate achievable with routing alone, and is achievable with…
We investigate the computational power of particle methods, a well-established class of algorit hms with applications in scientific computing and computer simulation. The computational power of a compute model determines the class of…
We study relative precompleteness in the context of the theory of numberings, and relate this to a notion of lowness. We introduce a notion of divisibility for numberings, and use it to show that for the class of divisible numberings,…
Motivated by results on generic-case complexity in group theory, we apply the ideas of effective Baire category and effective measure theory to study complexity classes of functions which are "fractionally computable" by a partial…