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Том 54, № 2 (2018)
- Год: 2018
- Статей: 7
- URL: https://journal-vniispk.ru/0032-9460/issue/view/10147
Coding Theory
On the Smallest Size of an Almost Complete Subset of a Conic in PG(2, q) and Extendability of Reed–Solomon Codes
Аннотация
Abstract—In the projective plane PG(2, q), a subset S of a conic C is said to be almost complete if it can be extended to a larger arc in PG(2, q) only by the points of C \ S and by the nucleus of C when q is even. We obtain new upper bounds on the smallest size t(q) of an almost complete subset of a conic, in particular,
101-115
Compositional Restricted Multiple Access Channel
Аннотация
We introduce the notion of a q-ary s-compositional code and prove that the rate, R, of the best such code satisfies for large s the asymptotic inequalities
116-123
Methods of Signal Processing
On Discrimination between Classes of Distribution Tails
Аннотация
We propose a test to distinguish between two classes of distribution tails using only higher order statistics of a sample and prove its consistency. We do not assume the corresponding distribution functions to belong to any maximum domain of attraction.
124-138
Large Systems
Improved Frankl–Rödl Theorem and Some of Its Geometric Consequences
Аннотация
We substantially improve a presently known explicit exponentially growing lower bound on the chromatic number of a Euclidean space with forbidden equilateral triangle. Furthermore, we improve an exponentially growing lower bound on the chromatic number of distance graphs with large girth. These refinements are obtained by improving known upper bounds on the product of cardinalities of two families of homogeneous subsets with one forbidden cross-intersection.
139-164
Clique Numbers of Random Subgraphs of Some Distance Graphs
Аннотация
We consider a class of graphs G(n, r, s) = (V (n, r),E(n, r, s)) defined as follows:
165-175
Communication Network Theory
Maximum Remaining Service Time in Infinite-Server Queues
Аннотация
We study the maximum remaining service time in infinite-server queues of type M|G|∞ (at a given time and in a stationary regime). The following cases for the arrival flow rate are considered: (1) time-independent, (2) given by a function of time, (3) given by a random process. As examples of service time distributions, we consider exponential, hyperexponential, Pareto, and uniform distributions. In the case of a constant rate, we study effects that arise when the average service time is infinite (for power-law distribution tails). We find the extremal index of the sequence of maximum remaining service times. The results are extended to queues of type MX|G|∞, including those with dependent service times within a batch.
176-190
Information-Theoretic Approach to Estimating the Capacity of Distributed Memory Systems
Аннотация
Systems with cash memory (or more generally, with distributed memory) are very widely used in information technologies. Such are content delivery networks (CDN) of various types, which deliver digital movies, books, and similar content; peer-to-peer (P2P) networks, where millions of members exchange various information; and many other systems and devices of this kind. We introduce the notions of capacity and entropy efficiency for distributed memory systems, propose methods for estimating these quantities, and give an example of their application.
191-198