Topology, randomness and noise in process calculus

Formal models of communicating and concurrent systems are one of the most important topics in formal methods, and process calculus is one of the most successful formal models of communicating and concurrent systems. In the previous works, the author systematically studied topology in process calculus, probabilistic process calculus and pi-calculus with noisy channels in order to describe approximate behaviors of communicating and concurrent systems as well as randomness and noise in them. This article is a brief survey of these works. © Higher Education Press 2007

Quantum Stochastic Calculus and Quantum Gaussian Processes

In this lecture we present a brief outline of boson Fock space stochastic calculus based on the creation, conservation and annihilation operators of free field theory, as given in the 1984 paper of Hudson and Parthasarathy. We show how a part of this architecture yields Gaussian fields stationary under a group action. Then we introduce the notion of semigroups of quasifree completely positive maps on the algebra of all bounded operators in the boson Fock space $\Gamma (\mathbb{C}^n)$ over $\mathbb{C}^n.$ These semigroups are not strongly continuous but their preduals map Gaussian states to Gaussian states. They were first introduced and their generators were shown to be of the Lindblad type by Vanheuverzwijn. They were recently investigated in the context of quantum information theory by Heinosaari, Holevo and Wolf. Here we present the exact noisy Schr\"odinger equation which dilates such a semigroup to a quantum Gaussian Markov process

Backlog and Delay Reasoning in HARQ Systems

Recently, hybrid-automatic-repeat-request (HARQ) systems have been favored in particular state-of-the-art communications systems since they provide the practicality of error detections and corrections aligned with repeat-requests when needed at receivers. The queueing characteristics of these systems have taken considerable focus since the current technology demands data transmissions with a minimum delay provisioning. In this paper, we investigate the effects of physical layer characteristics on data link layer performance in a general class of HARQ systems. Constructing a state transition model that combines queue activity at a transmitter and decoding efficiency at a receiver, we identify the probability of clearing the queue at the transmitter and the packet-loss probability at the receiver. We determine the effective capacity that yields the maximum feasible data arrival rate at the queue under quality-of-service constraints. In addition, we put forward non-asymptotic backlog and delay bounds. Finally, regarding three different HARQ protocols, namely Type-I HARQ, HARQ-chase combining (HARQ-CC) and HARQ-incremental redundancy (HARQ-IR), we show the superiority of HARQ-IR in delay robustness over the others. However, we further observe that the performance gap between HARQ-CC and HARQ-IR is quite negligible in certain cases. The novelty of our paper is a general cross-layer analysis of these systems, considering encoding/decoding in the physical layer and delay aspects in the data-link layer