A translation of Problemy Peredachi Informatsii

Volume 49, Number 4, October–December, 2013
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Multiple-Access Hyperchannel
L. A. Bassalygo and V. V. Rykov
pp. 299–307

Abstract—We derive an asymptotic upper bound on the decoding failure probability for an MDS code in a $q$-ary multiple access channel.


On the User Capacity for a Multiple-Access System in a Vector Disjunctive Channel with Errors
D. S. Osipov, A. A. Frolov, and V. V. Zyablov
pp. 308–321

Abstract—We consider a multiple-access system in which each user is given $q$ out of $Q$ available subchannels ($q \ll Q$). We investigate capacities of two channels emerging in the system under consideration in the case of single-user reception. These channels can be considered as modifications of the A-channel. In the first case we assume that a signal transmitted by a certain user is always registered by the receiver. Thus, activity of other users is the only obstacle to correct reception of information transmitted by a certain user in the multiple-access system. In the second case we assume that the output of each subchannel is inverted with probability $p$. Analytical expressions (both asymptotic and nonasymptotic) are derived and investigated.


Investigation of Binary Orthogonal Arrays via Their Distance Distributions
P. Boyvalenkov and H. Kulina
pp. 322–332

Abstract—We show how one can use polynomial techniques to compute all possible distance distributions of binary orthogonal arrays (OAs) of relatively small lengths and strengths. Then we exploit certain connections between OAs and their derived OAs. Having all distance distributions of OAs under consideration, we are able to test them aimed at classification results.


Low-Density Parity-Check Codes Based on Steiner Systems and Permutation Matrices
F. I. Ivanov and V. V. Zyablov
pp. 333–347

Abstract—An algorithm for generating parity-check matrices of regular low-density parity-check codes based on permutation matrices and Steiner triple systems $S(v,3,2)$, $v=2^m-1$, is proposed. Estimations of the rate, minimum distance, and girth for obtained code constructions are presented. Results of simulation of the obtained code constructions for an iterative “belief propagation” (Sum-Product) decoding algorithm applied in the case of transmission over a binary channel with additive Gaussian white noise and BPSK modulation are presented.


A New Subclass of Cyclic Goppa Codes
S. V. Bezzateev and N. A. Shekhunova
pp. 348–353

Abstract—We propose a subclass of cyclic Goppa codes given by separable self-reciprocal Goppa polynomials of degree two. We prove that this subclass contains all reversible cyclic codes of length $n$, $n\mid(q^m\pm 1)$, with a generator polynomial $g(x)$, $g(\alpha^{\pm i})=0$, $i=0,1$, $\alpha^n=1$, $\alpha\in\mathop{\textit{GF}}(q^{2m})$.


The Laplace Method for Gaussian Measures and Integrals in Banach Spaces
V. R. Fatalov
pp. 354–374

Abstract—We prove results on tight asymptotics of probabilities and integrals of the form $$ \mathop{\bf{P}}\nolimits_A(uD)\qquad \text{and}\qquad J_u(D) =\int\limits_D f(x)\exp\{-u^2F(x)\}\,d \mathop{\bf{P}}\nolimits_A(ux), $$ where $\mathop{\bf{P}}\nolimits_A$ is a Gaussian measure in an infinite-dimensional Banach space $B$, $D=\{x\in B:\: Q(x)\ge 0\}$ is a Borel set in $B$, $Q$ and $F$ are continuous functions which are smooth in neighborhoods of minimum points of the rate function, $f$ is a continuous real-valued function, and $u\to\infty$ is a large parameter.


Group Testing Problem with Two Defectives
C. Deppe and V. S. Lebedev
pp. 375–381

Abstract—We consider the classical $(2,N)$ group testing problem, i.e., the problem of finding two defectives among $N$ elements. We propose a new adaptive algorithm such that for $N=\bigl\lfloor 2^{\frac {t+1}2}-t\cdot2^{\frac t4}\bigr\rfloor$ the problem can be solved in $t$ tests.


On the Number of Nonzero Permanents over a Finite Field of Odd Characteristic
L. A. Bassalygo
pp. 382–383

Abstract—This note is a comment to [1], where it was proved that, over a field of odd characteristic, the number of square matrices of order $n$, $n\ge 3$, with nonzero permanent is greater than the number of square matrices of the same order with nonzero determinant.


New Estimates in the Problem of the Number of Edges in a Hypergraph with Forbidden Intersections
E. I. Ponomarenko and A. M. Raigorodskii
pp. 384–390

Abstract—We improve the Frankl–Wilson upper bound on the maximal number of edges in a hypergraph with forbidden cardinalities of edge intersections.


Individual Redundancy of Adaptive and Weighted Source Coding
Yu. M. Shtarkov
pp. 391–395

Abstract—We define individual redundancy of adaptive codes. We propose a method of weighted coding asymptotically optimal with respect to the maximal average and maximal individual redundancy criteria for universal and adaptive codes.