Related papers: Algorithmic Computability and Approximability of C…
Inspired by the ideas from the field of stochastic approximation, we propose a randomized algorithm to compute the capacity of a finite-state channel with a Markovian input. When the mutual information rate of the channel is concave with…
This article presents a theoretical investigation of computation beyond the Turing barrier from emergent behavior in distributed systems. In particular, we present an algorithmic network that is a mathematical model of a networked…
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…
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…
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 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…
We study the classical problem of characterizing the channel capacity and its achieving distribution in a generic fashion. We derive a simple relation between three parameters: the input-output function, the input cost function and the…
While there are various approaches to benchmark physical processors, recent findings have focused on computational phase transitions. This is due to several factors. Importantly, the hardest instances appear to be well-concentrated in a…
The quantization of the output of a binary-input discrete memoryless channel to a smaller number of levels is considered. An algorithm which finds an optimal quantizer, in the sense of maximizing mutual information between the channel input…
This paper studies several properties of channel codes that approach the fundamental limits of a given (discrete or Gaussian) memoryless channel with a non-vanishing probability of error. The output distribution induced by an…
This work considers a binomial noise channel. The paper can be roughly divided into two parts. The first part is concerned with the properties of the capacity-achieving distribution. In particular, for the binomial channel, it is not known…
This paper deals with the multiplicative finite-field matrix channel, a discrete memoryless channel whose input and output are matrices (over a finite field) related by a multiplicative transfer matrix. The model considered here assumes…
We consider a generalization of the discrete memoryless channel, in which the channel probability distribution is replaced by a uniform distribution over clouds of channel output sequences. For a random ensemble of such channels, we derive…
We address the problems of estimating the computer efficiency and the computer capacity. We define the computer efficiency and capacity and suggest a method for their estimation, based on the analysis of processor instructions and kinds of…
The quantum capacity of a memoryless channel is often used as a single figure of merit to characterize its ability to transmit quantum information coherently. The capacity determines the maximal rate at which we can code reliably over…
Recently the theory of communication developed by Shannon has been extended to the quantum realm by exploiting the rules of quantum theory. This latter stems on complex vector spaces. However complex (as well as real) numbers are just…
This paper provides new insight into the classical problem of determining both the capacity of the discrete-time channel with uniform output quantization and the capacity achieving input distribution. It builds on earlier work by Gallager…
Motivated by communication systems with constrained complexity, we consider the problem of input symbol selection for discrete memoryless channels (DMCs). Given a DMC, the goal is to find a subset of its input alphabet, so that the optimal…
Zero-error capacity plays an important role in a whole range of operational tasks, in addition to the fact that it is necessary for practical applications. Due to the importance of zero-error capacity, it is necessary to investigate its…
In this paper, we investigate the quantization of the output of a binary input discrete memoryless channel that maximizing the mutual information between the input and the quantized output under an entropy-constrained of the quantized…