A translation of Problemy Peredachi Informatsii

Volume 35, Number 4, October–December, 1999
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New Lower Bounds for Contact Numbers in Small Dimensions
V. A. Zinoviev and T. Ericson
pp. 287–294

Abstract—We consider several new constructions for spherical codes. As an example of their application, we obtain two new spherical codes for dimensions 13 and 14, which improve known lower bounds for contact numbers in these dimensions.


To the Theory of Low-Density Convolutional Codes. I
K. Engdahl and K. Sh. Zigangirov
pp. 295–310

Abstract—In this paper (which is the first part in a series of three), a formal theory and construction methods for low-density convolutional (LDC) codes (including turbo-codes) are presented. Principles of iterative decoding of LDC codes are formulated and an iterative algorithm for the decoding of homogeneous LDC codes is described. Simulation results are also presented. In the following two parts of this work, the authors intend to perform the statistical analysis of LDC codes and theoretical analysis of iterative decoding.


Asymptotic Distance Properties of Binary Woven Convolutional Codes
V. V. Zyablov, R. Johannesson, O. D. Skopintsev, and S. Höst
pp. 311–326

Abstract—Two constructions of binary concatenated convolutional codes are considered. In our previous work [Proc. 4th Int. Symp. Commun. Theory Appl., Lake District, UK (1997)] such codes were called woven convolutional codes. In the present paper, asymptotic lower bounds on active distances of woven convolutional codes are investigated. It is shown that these distances can be bounded from below by linearly growing functions with a strictly positive slope for all rates of concatenated codes, and the construction complexity of woven convolutional codes grows as an exponent of the memory of these codes.


On the Decoding of Preparata Codes
I. M. Boyarinov
pp. 327–337

Abstract—A decoding algorithm for extended Preparata codes is considered. This algorithm is close to the decoding algorithm of binary BCH codes with distance 6. It is shown that, together with the correction of independent single and double errors, Preparata codes can also correct single error bytes of length 4. An algorithm for correcting independent and byte errors is presented.


On Algebraic Decoding of Some Maximal Quaternary Codes and the Binary Golay Code
S. M. Dodunekov, V. A. Zinoviev, and J. E. M. Nilsson
pp. 338–345

Abstract—The quaternary codes devised in [Probl. Inf. Trans., 14, No. 2, 174–181 (1978)] have minimum distance $d=5$. As was shown there, they can be decoded using a standard syndrome decoding algorithm. In the present paper, we derive a simple algebraic criterion to determine the number of errors occurred and reformulate the earlier decoding algorithm described in the paper mentioned. Since a $[12,6,6]$ quaternary code yields a cascade description of a binary extended $[24,12,8]$ Golay code, this description provides a new method for decoding binary Golay codes.


On Variations of Designs
V. A. Yudin
pp. 346–350

Abstract—Properties of spherical $s$-schemes (designs) under movements of their parts along the sphere are studied. Two configurations are considered: an icosahedron in $\mathbb{R}^3$ and a configuration in $\mathbb{R}^7$ that consists of $56$ points of a quadratic-residue code.


A Posteriori Probability Decoding of Convolutional Codes
A. N. Trofimov and K. Sh. Zigangirov
pp. 351–358

Abstract—A new algorithm of the so-called a posteriori probability decoding for convolutional codes is proposed. Its modification for tail-biting codes is considered. For infinite trellises, the algorithm makes delayed decisions. The decoding delay is determined by the parameters of the algorithm.


Determination of a State of a Quantum System from Results of Measurements
L. I. Rozonoer
pp. 359–368

Abstract—It is shown that for determining a pure state of a quantum system (in a finite- or infinite-dimensional case), it suffices to measure four certain observables, and any two of them are not sufficient. Another problem considered is the determination of a compound state in the finite-dimensional case where the space dimension $N$ is not a prime number.


Efficient Method of Adaptive Arithmetic Coding for Sources with Large Alphabets
B. Ya. Ryabko and A. N. Fionov
pp. 369–380

Abstract—We consider the problem of constructing an adaptive arithmetic code for the case of a large source alphabet. We propose a method with encoding/decoding time, which is an order less than that for known methods. We also propose an implementation of the method with the use of a data structure called an “imaginary sliding window,” which makes it possible to essentially decrease the encoder/decoder memory capacity.


pp. 381–387