Multiaccess Channels with State Known to One Encoder: Another Case of Degraded Message Sets

We consider a two-user state-dependent multiaccess channel in which only one of the encoders is informed, non-causally, of the channel states. Two independent messages are transmitted: a common message transmitted by both the informed and uninformed encoders, and an individual message transmitted by only the uninformed encoder. We derive inner and outer bounds on the capacity region of this model in the discrete memoryless case as well as the Gaussian case. Further, we show that the bounds for the Gaussian case are tight in some special cases.Comment: 5 pages, Proc. of IEEE International Symposium on Information theory, ISIT 2009, Seoul, Kore

Bounds on the Capacity of the Relay Channel with Noncausal State Information at Source

We consider a three-terminal state-dependent relay channel with the channel state available non-causally at only the source. Such a model may be of interest for node cooperation in the framework of cognition, i.e., collaborative signal transmission involving cognitive and non-cognitive radios. We study the capacity of this communication model. One principal problem in this setup is caused by the relay's not knowing the channel state. In the discrete memoryless (DM) case, we establish lower bounds on channel capacity. For the Gaussian case, we derive lower and upper bounds on the channel capacity. The upper bound is strictly better than the cut-set upper bound. We show that one of the developed lower bounds comes close to the upper bound, asymptotically, for certain ranges of rates.Comment: 5 pages, submitted to 2010 IEEE International Symposium on Information Theor

An information theory for preferences

Recent literature in the last Maximum Entropy workshop introduced an analogy between cumulative probability distributions and normalized utility functions. Based on this analogy, a utility density function can de defined as the derivative of a normalized utility function. A utility density function is non-negative and integrates to unity. These two properties form the basis of a correspondence between utility and probability. A natural application of this analogy is a maximum entropy principle to assign maximum entropy utility values. Maximum entropy utility interprets many of the common utility functions based on the preference information needed for their assignment, and helps assign utility values based on partial preference information. This paper reviews maximum entropy utility and introduces further results that stem from the duality between probability and utility

Subfactors and quantum information theory

We consider quantum information tasks in an operator algebraic setting, where we consider normal states on von Neumann algebras. In particular, we consider subfactors $\mathfrak{N} \subset \mathfrak{M}$, that is, unital inclusions of von Neumann algebras with trivial center. One can ask the following question: given a normal state $\omega$ on $\mathfrak{M}$, how much can one learn by only doing measurements from $\mathfrak{N}$? We argue how the Jones index $[\mathfrak{M}:\mathfrak{N}]$ can be used to give a quantitative answer to this, showing how the rich theory of subfactors can be used in a quantum information context. As an example we discuss how the Jones index can be used in the context of wiretap channels. Subfactors also occur naturally in physics. Here we discuss two examples: rational conformal field theories and Kitaev's toric code on the plane, a prototypical example of a topologically ordered model. There we can directly relate aspects of the general setting to physical properties such as the quantum dimension of the excitations. In the example of the toric code we also show how we can calculate the index via an approximation with finite dimensional systems. This explicit construction sheds more light on the connection between topological order and the Jones index.Comment: v2: added more background material, some corrections and clarifications. 23 pages, submitted to QMath 13 (Atlanta, GA) proceeding