Related papers: Computability of the Zero-Error capacity with Kolm…

This paper presents an analysis of the concept of capacity for noisy com- putations, i.e. functions implemented by unreliable or random devices. An information theoretic model of noisy computation of a perfect function f (measurable…

The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…

Transmitting data reliably over noisy communication channels is one of the most important applications of information theory, and well understood when the channel is accurately modelled by classical physics. However, when quantum effects…

This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for…

Memoryless channels with deletion errors as defined by a stochastic channel matrix allowing for bit drop outs are considered in which transmitted bits are either independently deleted with probability $d$ or unchanged with probability…

We begin a systematic study of the problem of the zero--error capacity of noisy binary channels with memory and solve some of the non--trivial cases.

Since the work of Polyanskiy, Poor and Verd\'u on the finite blocklength performance of capacity-achieving codes for discrete memoryless channels, many papers have attempted to find further results for more practically relevant channels.…

We investigate state estimation of linear systems over channels having a finite state not known by the transmitter or receiver. We show that similar to memoryless channels, zero-error capacity is the right figure of merit for achieving…

We show that real-value approximations of Kolmogorov-Chaitin (K_m) using the algorithmic Coding theorem as calculated from the output frequency of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols), is in…

In an effort to develop the foundations for a non-stochastic theory of information, the notion of $\delta$-mutual information between uncertain variables is introduced as a generalization of Nair's non-stochastic information functional.…

The problem of characterising the zero-error capacity region for multiple access channels even in the noiseless case has remained an open problem for over three decades. Motivated by this challenging question, a recently developed theory of…

The concept of ``countable set'' is attributed to Georg Cantor, who set the boundary between countable and uncountable sets in 1874. The concept of ``computable set'' arose in the study of computing models in the 1930s by the founders of…

The capacity of a classical-quantum channel (or in other words the classical capacity of a quantum channel) is considered in the most general setting, where no structural assumptions such as the stationary memoryless property are made on a…

This paper constructively proves the existence of an effective procedure generating a computable (total) function that is not contained in any given effectively enumerable set of such functions. The proof implies the existence of machines…

Bounds on the reliability function for the discrete memoryless relay channel are derived using the method of types. Two achievable error exponents are derived based on partial decode-forward and compress-forward which are well-known…

Emerging applications such as augmented reality and tactile Internet are compute-intensive and latency-sensitive, which hampers their running in constrained end devices alone or in the distant cloud. The stringent requirements of such…

In 1957, Lacombe initiated a systematic study of the different possible notions of "computable topological spaces". However, he interrupted this line of research, settling for the idea that "computably open sets should be computable unions…

Consider a universal Turing machine that produces a partial or total function (or a binary stream), based on the answers to the binary queries that it makes during the computation. We study the probability that the machine will produce a…

In digital systems such as fiber optical communications, the ratio between probability of errors of type $1\to 0$ and $0 \to 1$ can be large. Practically, one can assume that only one type of error can occur. These errors arecalled…

The Church-Turing thesis asserts that if a partial strings-to-strings function is effectively computable then it is computable by a Turing machine. In the 1930s, when Church and Turing worked on their versions of the thesis, there was a…