Problems of Information Transmission
Problems of Information Transmission is a peer-reviewed journal devoted to the studies and development of mathematical aspects of information theory and communication systems. This quarterly journal features coverage of statistical information theory; coding theory and techniques; noisy channels, error detection and correction; signal detection, extraction, and analysis; analysis of communication networks; optimal processing and routing; the theory of random processes; and bionics. Previously focused on translation, the journal now has the aim to become an international publication and accepts manuscripts originally submitted in English from all countries, along with translated works.
- Official Journal of the Russian Academy of Sciences
- Investigates all aspects of communication systems research and development
- Covers statistical information theory; coding theory and techniques; noisy channels; error detection and correction; signal detection, extraction, and analysis; etc.
- English translation of Problemy Peredachi Informatsii
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Том 55, № 4 (2019)
- Год: 2019
- Статей: 5
- URL: https://journal-vniispk.ru/0032-9460/issue/view/10161
Information Theory
The Augustin Capacity and Center
Аннотация
For any channel, the existence of a unique Augustin mean is established for any positive order and probability mass function on the input set. The Augustin mean is shown to be the unique fixed point of an operator defined in terms of the order and the input distribution. The Augustin information is shown to be continuously differentiable in the order. For any channel and convex constraint set with finite Augustin capacity, the existence of a unique Augustin center and the associated van Erven-Harremoes bound are established. The Augustin-Legendre (A-L) information, capacity, center, and radius are introduced, and the latter three are proved to be equal to the corresponding Rényi-Gallager quantities. The equality of the A-L capacity to the A-L radius for arbitrary channels and the existence of a unique A-L center for channels with finite A-L capacity are established. For all interior points of the feasible set of cost constraints, the cost constrained Augustin capacity and center are expressed in terms of the A-L capacity and center. Certain shift-invariant families of probabilities and certain Gaussian channels are analyzed as examples.
299-342
Coding Theory
On the Cardinality Spectrum and the Number of Latin Bitrades of Order 3
Аннотация
By a (Latin) unitrade of order k, we call a subset of vertices of the Hamming graph H(n, k) that intersects any maximal clique at either 0 or 2 vertices. A bitrade is a bipartite unitrade, i.e., a unitrade that can be split into two independent subsets. We study the cardinality spectrum of bitrades in the Hamming graph H(n, k) with k = 3 (ternary hypercube) and the growth of the number of such bitrades as n grows. In particular, we determine all possible small (up to 2.5·2n) and large (from 14·3n−3) cardinalities of bitrades of dimension n and prove that the cardinality of a bitrade takes only values equivalent to 0 or 2n modulo 3 (this result can be treated in terms of a ternary Reed-Muller type code). A part of the results are valid for an arbitrary k. For k = 3 and n → ∞ we prove that the number of nonequivalent bitrades is not less than 2(2/3−o(1))n and not greater than \(2^{\alpha^n}\), α < 2 (the growth order of the double logarithm of this number remains unknown). Alternatively, the studied set Bn of bitrades of order 3 can be defined as follows: B0 consists of three rationals - 1, 0, 1; Bn consists of ordered triples (a, b, c) of elements from Bn−1 such that a + b + c = 0.
343-365
366-375
Large Systems
On a Frankl-Wilson Theorem
Аннотация
We derive an analog of the Frankl-Wilson theorem on independence numbers of some distance graphs. The obtained results are applied to the problem of the chromatic number of a space ℝn with a forbidden equilateral triangle and to the problem of chromatic numbers of distance graphs with large girth.
376-395
Search for a Moving Element with the Minimum Total Cardinality of Tests
Аннотация
We consider the moving element search problem with the minimum total cardinality of tests. As a search space, we consider the set of integer points of a segment of length n. We prove that the total test cardinality of an asymptotically optimal adaptive strategy is \(n + 2\sqrt n \).
396-400