A False Acceptance Error Controlling Method for Hyperspherical Classifiers

Controlling false acceptance errors is of critical importance in many pattern recognition applications, including signature and speaker verification problems. Toward this goal, this paper presents two post-processing methods to improve the performance of hyperspherical classifiers in rejecting patterns from unknown classes. The first method uses a self-organizational approach to design minimum radius hyperspheres, reducing the redundancy of the class region defined by the hyperspherical classifiers. The second method removes additional redundant class regions from the hyperspheres by using a clustering technique to generate a number of smaller hyperspheres. Simulation and experimental results demonstrate that by removing redundant regions these two post-processing methods can reduce the false acceptance error without significantly increasing the false rejection error

Rateless Coding for Gaussian Channels

A rateless code-i.e., a rate-compatible family of codes-has the property that codewords of the higher rate codes are prefixes of those of the lower rate ones. A perfect family of such codes is one in which each of the codes in the family is capacity-achieving. We show by construction that perfect rateless codes with low-complexity decoding algorithms exist for additive white Gaussian noise channels. Our construction involves the use of layered encoding and successive decoding, together with repetition using time-varying layer weights. As an illustration of our framework, we design a practical three-rate code family. We further construct rich sets of near-perfect rateless codes within our architecture that require either significantly fewer layers or lower complexity than their perfect counterparts. Variations of the basic construction are also developed, including one for time-varying channels in which there is no a priori stochastic model.Comment: 18 page

Unidirectional Quorum-based Cycle Planning for Efficient Resource Utilization and Fault-Tolerance

In this paper, we propose a greedy cycle direction heuristic to improve the generalized $\mathbf{R}$ redundancy quorum cycle technique. When applied using only single cycles rather than the standard paired cycles, the generalized $\mathbf{R}$ redundancy technique has been shown to almost halve the necessary light-trail resources in the network. Our greedy heuristic improves this cycle-based routing technique's fault-tolerance and dependability. For efficiency and distributed control, it is common in distributed systems and algorithms to group nodes into intersecting sets referred to as quorum sets. Optimal communication quorum sets forming optical cycles based on light-trails have been shown to flexibly and efficiently route both point-to-point and multipoint-to-multipoint traffic requests. Commonly cycle routing techniques will use pairs of cycles to achieve both routing and fault-tolerance, which uses substantial resources and creates the potential for underutilization. Instead, we use a single cycle and intentionally utilize $\mathbf{R}$ redundancy within the quorum cycles such that every point-to-point communication pairs occur in at least $\mathbf{R}$ cycles. Without the paired cycles the direction of the quorum cycles becomes critical to the fault tolerance performance. For this we developed a greedy cycle direction heuristic and our single fault network simulations show a reduction of missing pairs by greater than 30%, which translates to significant improvements in fault coverage.Comment: Computer Communication and Networks (ICCCN), 2016 25th International Conference on. arXiv admin note: substantial text overlap with arXiv:1608.05172, arXiv:1608.05168, arXiv:1608.0517

Succinct Representations of Permutations and Functions

We investigate the problem of succinctly representing an arbitrary permutation, \pi, on {0,...,n-1} so that \pi^k(i) can be computed quickly for any i and any (positive or negative) integer power k. A representation taking (1+\epsilon) n lg n + O(1) bits suffices to compute arbitrary powers in constant time, for any positive constant \epsilon <= 1. A representation taking the optimal \ceil{\lg n!} + o(n) bits can be used to compute arbitrary powers in O(lg n / lg lg n) time. We then consider the more general problem of succinctly representing an arbitrary function, f: [n] \rightarrow [n] so that f^k(i) can be computed quickly for any i and any integer power k. We give a representation that takes (1+\epsilon) n lg n + O(1) bits, for any positive constant \epsilon <= 1, and computes arbitrary positive powers in constant time. It can also be used to compute f^k(i), for any negative integer k, in optimal O(1+|f^k(i)|) time. We place emphasis on the redundancy, or the space beyond the information-theoretic lower bound that the data structure uses in order to support operations efficiently. A number of lower bounds have recently been shown on the redundancy of data structures. These lower bounds confirm the space-time optimality of some of our solutions. Furthermore, the redundancy of one of our structures "surpasses" a recent lower bound by Golynski [Golynski, SODA 2009], thus demonstrating the limitations of this lower bound.Comment: Preliminary versions of these results have appeared in the Proceedings of ICALP 2003 and 2004. However, all results in this version are improved over the earlier conference versio