A regularizing commutant duality for a kinematically covariant partial ordered net of observables

We consider a net of *-algebras, locally around any point of observation, equipped with a natural partial order related to the isotony property. Assuming the underlying manifold of the net to be a differentiable, this net shall be kinematically covariant under general diffeomorphisms. However, the dynamical relations, induced by the physical state defining the related net of (von Neumann) observables, are in general not covariant under all diffeomorphisms, but only under the subgroup of dynamical symmetries. We introduce algebraically both, IR and UV cutoffs, and assume that these are related by a commutant duality. The latter, having strong implications on the net, allows us to identify a 1-parameter group of the dynamical symmetries with the group of outer modular automorphisms. For thermal equilibrium states, the modular dilation parameter may be used locally to define the notions of both, time and a causal structure.Comment: LaTeX, to appear in: Proc. XXI. Int. Sem. on Group Theor. Methods, Goslar (1996), eds. Doebner et a

Composite CDMA - A statistical mechanics analysis

Code Division Multiple Access (CDMA) in which the spreading code assignment to users contains a random element has recently become a cornerstone of CDMA research. The random element in the construction is particular attractive as it provides robustness and flexibility in utilising multi-access channels, whilst not making significant sacrifices in terms of transmission power. Random codes are generated from some ensemble, here we consider the possibility of combining two standard paradigms, sparsely and densely spread codes, in a single composite code ensemble. The composite code analysis includes a replica symmetric calculation of performance in the large system limit, and investigation of finite systems through a composite belief propagation algorithm. A variety of codes are examined with a focus on the high multi-access interference regime. In both the large size limit and finite systems we demonstrate scenarios in which the composite code has typical performance exceeding sparse and dense codes at equivalent signal to noise ratio.Comment: 23 pages, 11 figures, Sigma Phi 2008 conference submission - submitted to J.Stat.Mec