Self-organized criticality in dynamics without branching

We demonstrate the phenomenon of self-organized criticality (SOC) in a simple random walk model described by a random walk of a myopic ant, i.e., a walker who can see only nearest neighbors. The ant acts on the underlying lattice aiming at uniform digging, i.e., reduction of the height profile of the surface but is unaffected by the underlying lattice. In one, two, and three dimensions we have explored this model and have obtained power laws in the time intervals between consecutive events of "digging." Being a simple random walk, the power laws in space translate to power laws in time. We also study the finite size scaling of asymptotic scale invariant process as well as dynamic scaling in this system. This model differs qualitatively from the cascade models of SOC.

Full-rate full-diversity finite feedback space-time schemes with minimum feedback and transmission duration

A Finite Feedback Scheme (FFS) for a quasi-static MIMO block fading channel with finite N-ary delay-free noise-free feedback consists of N Space-Time Block Codes (STBCs) at the transmitter, one corresponding to each possible value of feedback, and a function at the receiver that generates N-ary feedback. A number of FFSs are available in the literature that provably attain full-diversity. However, there is no known full-diversity criterion that universally applies to all FFSs. In this paper a universal necessary condition for any FFS to achieve full-diversity is given, and based on this criterion the notion of Feedback-Transmission duration optimal (FT-optimal) FFSs is introduced, which are schemes that use minimum amount of feedback N for the given transmission duration T, and minimum T for the given N to achieve full-diversity. When there is no feedback (N = 1) an FT-optimal scheme consists of a single STBC, and the proposed condition reduces to the well known necessary and sufficient condition for an STBC to achieve full-diversity. Also, a sufficient criterion for full-diversity is given for FFSs in which the component STBC yielding the largest minimum Euclidean distance is chosen, using which full-rate (N-t complex symbols per channel use) full-diversity FT-optimal schemes are constructed for all N-t > 1. These are the first full-rate full-diversity FFSs reported in the literature for T < N-t. Simulation results show that the new schemes have the best error performance among all known FFSs.