Related papers: Computability of the Zero-Error capacity with Kolm…
The deterministic notions of capacity and entropy are studied in the context of communication and storage of information using square-integrable, bandlimited signals subject to perturbation. The $(\epsilon,\delta)$-capacity, that extends…
The purpose of this paper is to answer two questions left open in [B. Durand, A. Shen, and N. Vereshchagin, Descriptive Complexity of Computable Sequences, Theoretical Computer Science 171 (2001), pp. 47--58]. Namely, we consider the…
In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data $\omega$-words). The notion of computability is defined through Turing machines with infinite inputs which can…
We consider compound as well as arbitrarily varying classical-quantum channel models. For classical-quantum compound channels, we give an elementary proof of the direct part of the coding theorem. A weak converse under average error…
We show that unbounded number of channel uses may be necessary for perfect transmission of quantum information. For any n we explicitly construct low-dimensional quantum channels ($d_A$=4, $d_E$=2 or 4) whose quantum zero-error capacity is…
This paper studies the zero error capacity of the Nearest Neighbor Error (NNE) channels with a multilevel alphabet. In the NNE channels, a transmitted symbol is a $d$-tuple of elements in $\{0,1,2,\dots, n-1 \}$. It is assumed that only one…
Shannon defined channel capacity as the highest rate at which there exists a sequence of codes of block length $n$ such that the error probability goes to zero as $n$ goes to infinity. In this definition, it is implicit that the block…
Ahlswede, Cai, and Zhang proved that, in the noise-free limit, the zero-undetected-error capacity is lower bounded by the Sperner capacity of the channel graph, and they conjectured equality. Here we derive an upper bound that proves the…
Tradeoffs between the information rate and fidelity of quantum error-correcting codes are discussed. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely…
Kawamura and Cook have developed a framework for studying the computability and complexity theoretic problems over "large" topological spaces. This framework has been applied to study the complexity of the differential operator and the…
In this thesis we present several results in coding theory, concerning error-correcting codes and the Shannon capacity. 1. We give a general symmetry reduction of matrices occuring in semidefinite programs in coding theory. 2. We apply the…
Computability on uncountable sets has no standard formalization, unlike that on countable sets, which is given by Turing machines. Some of the approaches to define computability in these sets rely on order-theoretic structures to translate…
Channel capacity describes the size of the nearly ideal channels, which can be obtained from many uses of a given channel, using an optimal error correcting code. In this paper we collect and compare minor and major variations in the…
The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…
We investigate the connection between measure, capacity and algorithmic randomness for the space of closed sets. For any computable measure m, a computable capacity T may be defined by letting T(Q) be the measure of the family of closed…
We study the problem of computing the capacity of a discrete memoryless channel under uncertainty affecting the channel law matrix, and possibly with a constraint on the average cost of the input distribution. The problem has been…
A ternary ring of operators (TRO) in finite dimensions is a diagonal sum of spaces of rectangular matrices. TRO as operator space corresponds to quantum channels that are diagonal sums of partial traces, which we call TRO channels. TRO…
Synchronization channels, such as the well-known deletion channel, are surprisingly harder to analyze than memoryless channels, and they are a source of many fundamental problems in information theory and theoretical computer science. One…
The Shannon capacity of a graph is a fundamental quantity in zero-error information theory measuring the rate of growth of independent sets in graph powers. Despite being well-studied, this quantity continues to hold several mysteries.…
Memoryless channels with synchronization errors as defined by a stochastic channel matrix allowing for symbol insertions and deletions in addition to random errors are considered. Such channels are information stable, hence their Shannon…