### Article

## О пропускной способности для пользователя системы множественного доступа в векторном дизъюнктивном канале при наличии ошибок

We consider a signal-code construction for a special class of multiple access system over vector-disjunctive channel. This construction is based on interleaved Reed-Solomon codes with collaborative decoding. The considered methods of encoding and decoding on one hand have acceptable complexity for a wide range parameters and on other one a decoding algorithm is able to correct significantly more collisions than bounded-distance decoder. We estimate a maximum achievable relative sum-rate of this construction for fixed number of active users and total number of frequencies to transmit.

Non-orthogonal multiple access schemes are of great interest for next generation wireless systems, as such schemes allow to reduce the total number of resources (frequencies or time slots) in comparison to orthogonal transmission (TDMA, FDMA, CDMA). In this paper we consider an iterative LDPC-based joint decoding scheme suggested in [1]. We investigate the most difficult and important problem where all the users have the same power constraint and the same rate. For the case of 2 users we use a known scheme and analyze it by means of simulations. We found the optimal relation between the number of inner and outer iterations. We further extend the scheme for the case of any number of users and investigated the cases of 3 and 4 users by means of simulations. Finally, we showed, that considered non-orthogonal transmission scheme is more efficient (for 2 and 3 users), than orthogonal transmission.

We consider a signal-code construction for a special class of multiple access system over vector-disjunctive channel when users transmit some vector of bits of finite length L. This construction is based on interleaved Reed-Solomon codes with collaborative decoding. The considered methods of encoding and decoding in one hand have acceptable complexity for a wide range parameters and in other one a decoding algorithm is able to correct significantly more collisions than bounded- distance decoder. We present some simulation results for relative sum-rate of interleaved Reed-Solomon and for frame error rate (FER) in the case of different number of active users and different code constructions. Simulation results we obtained allow us to conclude that our scheme has a good performance even for very short codes.

The volume contains proceedings of the XIII International symposium on problems of redundancy in information and control systems.

This book constitutes the refereed proceedings of the 5th International Workshop on Multiple Access Communications, MACOM 2012, held in Maynooth, Ireland, in November 2012. The 13 full papers and 5 demo and poster papers presented were carefully reviewed and selected from various submissions. The papers are organized in topical sections on network coding, handling interference and localization techniques at PHY/MAC layers, wireless access networks, and medium access control.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Generalized error-locating codes are discussed. An algorithm for calculation of the upper bound of the probability of erroneous decoding for known code parameters and the input error probability is given. Based on this algorithm, an algorithm for selection of the code parameters for a specified design and input and output error probabilities is constructed. The lower bound of the probability of erroneous decoding is given. Examples of the dependence of the probability of erroneous decoding on the input error probability are given and the behavior of the obtained curves is explained.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability