Algebraic information theory for binary channels

AbstractWe study the algebraic structure of the monoid of binary channels and show that it is dually isomorphic to the interval domain over the unit interval with the operation from Martin (2006) [4]. We show that the capacity of a binary channel is Scott continuous as a map on the interval domain and that its restriction to any maximally commutative submonoid of binary channels is an order isomorphism onto the unit interval. These results allows us to solve an important open problem in the analysis of covert channels: a provably correct method for injecting noise into a covert channel which will reduce its capacity to any level desired in such a way that the practitioner is free to insert the noise at any point in the system

Probabilistic Monads, Domains and Classical Information

Shannon's classical information theory uses probability theory to analyze channels as mechanisms for information flow. In this paper, we generalize results of Martin, Allwein and Moskowitz for binary channels to show how some more modern tools - probabilistic monads and domain theory in particular - can be used to model classical channels. As initiated Martin, et al., the point of departure is to consider the family of channels with fixed inputs and outputs, rather than trying to analyze channels one at a time. The results show that domain theory has a role to play in the capacity of channels; in particular, the (n x n)-stochastic matrices, which are the classical channels having the same sized input as output, admit a quotient compact ordered space which is a domain, and the capacity map factors through this quotient via a Scott-continuous map that measures the quotient domain. We also comment on how some of our results relate to recent discoveries about quantum channels and free affine monoids.Comment: In Proceedings DCM 2011, arXiv:1207.682

A Formulation of the Potential for Communication Condition using C2KA

An integral part of safeguarding systems of communicating agents from covert channel communication is having the ability to identify when a covert channel may exist in a given system and which agents are more prone to covert channels than others. In this paper, we propose a formulation of one of the necessary conditions for the existence of covert channels: the potential for communication condition. Then, we discuss when the potential for communication is preserved after the modification of system agents in a potential communication path. Our approach is based on the mathematical framework of Communicating Concurrent Kleene Algebra (C2KA). While existing approaches only consider the potential for communication via shared environments, the approach proposed in this paper also considers the potential for communication via external stimuli.Comment: In Proceedings GandALF 2014, arXiv:1408.556