Related papers: Computability of the Channel Reliability Function …
A new approach for upper bounding the channel reliability function using the code spectrum is described. It allows to treat in a unified way both a low and a high rate cases. In particular, the earlier known upper bounds are improved, and a…
The problem of reliable function computation is extended by imposing privacy, secrecy, and storage constraints on a remote source whose noisy measurements are observed by multiple parties. The main additions to the classic function…
We complete the proof of conjecture, which allows to complete the derivation of the random coding bound for the reliability function in quantum channel in the case of arbitrary signal states
The sphere-packing bound $E_{sp}(R)$ bounds the reliability function for fixed-length block-codes. For symmetric channels, it remains a valid bound even when strictly causal noiseless feedback is allowed from the decoder to the encoder. To…
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…
A new approach for upper bounding the channel reliability function using the code spectrum is described. It allows to treat both low and high rate cases in a unified way. In particular, the earlier known upper bounds are improved, and a new…
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…
We introduce the notion of feedback computable functions from $2^\omega$ to $2^\omega$, extending feedback Turing computation in analogy with the standard notion of computability for functions from $2^\omega$ to $2^\omega$. We then show…
We propose a novel approach for bounding the probability of error of discrete memoryless channels with a zero-error capacity based on a combination of Lov\'asz' and Gallager's ideas. The obtained bounds are expressed in terms of a function…
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.…
Information theory tells us that if the rate of sending information across a noisy channel were above the capacity of that channel, then the transmission would necessarily be unreliable. For classical information sent over classical or…
The bandwidth of a signal is an important physical property that is of relevance in many signal- and information-theoretic applications. In this paper we study questions related to the computability of the bandwidth of computable…
An operational approach to the study of computation based on correlations considers black-boxes with one-bit inputs and outputs, controlled by a limited classical computer capable only of performing sums modulo-2. In this setting, it was…
This paper presents some examples of quantum reliability function for the quantum communication system in which classical information is transmitted by quantum states. In addition, the quantum Cut off rate is defined. They will be compared…
We consider a Gelfand-Pinsker discrete memoryless channel (DMC) model and provide a strong converse for its capacity. The strong converse is then used to obtain an upper bound on the reliability function. Instrumental in our proofs is a new…
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…
Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…
We develop a novel framework for proving converse theorems for channel coding, which is based on the analysis technique of multicast transmission with an additional auxiliary receiver, which serves as a genie to the original receiver. The…
The highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1 - exp [-n E(R)+ o(n)] for some function E(R) on noisy quantum channels that are subject to not necessarily independent errors.…
Optimization problems are a staple of today's scientific and technical landscape. However, at present, solvers of such problems are almost exclusively run on digital hardware. Using Turing machines as a mathematical model for any type of…