PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Finite Blocklength Analysis of Energy Harvesting Channels
K. G. Shenoy and V. Sharma
pp. 1–32

Abstract—We consider additive white Gaussian noise channels and discrete memoryless channels where the transmitter harvests energy from the environment. These can model wireless sensor networks as well as Internet of Things. By providing a unifying framework that works for any energy harvesting channel, we study these channels assuming an infinite energy buffer and provide the corresponding achievability and converse bounds on the channel capacity in the finite blocklength regime. We additionally provide moderate deviation asymptotic bounds.

Trade-off for Heterogeneous Distributed Storage Systems between Storage and Repair Cost
K. G. Benerjee and M. K. Gupta
pp. 33–53

Abstract—We consider heterogeneous distributed storage systems (DSSs) having flexible reconstruction degree, where each node in the system has nonuniform repair bandwidth and nonuniform storage capacity. In particular, a data collector can reconstruct the file using some $k$ nodes in the system and, for a node failure, the system can be repaired by some set of active nodes. Using min-cut bound, we investigate the fundamental trade-off between storage and repair costs for our model of the heterogeneous DSS. Further, the problem is formulated as bi-objective optimization linear programing problem for various heterogeneous DSSs. For some DSSs, it is shown that the calculated min-cut bound is tight.

The $f$-Divergence and Coupling of Probability Distributions
V. V. Prelov
pp. 54–69

Abstract—We consider the problem of finding the minimum and maximum values of $f$-divergence for discrete probability distributions $P$ and $Q$ provided that one of these distributions and the value of their coupling are given. An explicit formula for the minimum value of the $f$-divergence under the above conditions is obtained, as well as a precise expression for its maximum value. This precise expression is not explicit in the general case, but in many special cases it allows us to write out both explicit formulas and simple upper bounds, which are sometimes optimal. Similar explicit formulas and upper bounds are also obtained for the Kullback–Leibler and $\chi^2$ divergences, which are the most important cases of the $f$-divergence.

On the Generalized Concatenated Construction for Codes in $L_1$ and Lee Metrics
V. A. Zinoviev and D. V. Zinoviev
pp. 70–83

Abstract—We consider a generalized concatenated construction for error-correcting codes over the $q$-ary alphabet in the modulus metric $L_1$ and Lee metric $L$. Resulting codes have arbitrary length, arbitrary distance (independently of the alphabet size), and can correct both independent errors and error bursts in both metrics. In particular, for any length $2^m$ we construct codes over $\mathbb{Z}_4$ with Lee distance $4$ which under the Gray mapping yield extended binary perfect codes of length $2^{m+1}$ (with code distance $4$). We construct codes over $\mathbb{Z}_4$ of length $n$ with Lee distance $n$ which under the Gray mapping yield Hadamard matrices of order $2n$ (under the additional condition that an Hadamard matrix of order $n$ exists). The constructed new codes in the Lee metric are often better in their parameters than previously known ones; in particular, they are essentially better than previously constructed Astola codes.

Affine Variety Codes over a Hyperelliptic Curve
N. Patanker and S. K. Singh
pp. 84–97

Abstract—We estimate the minimum distance of primary monomial affine variety codes defined from a hyperelliptic curve $x^5+x-y^2$ over $\mathbb{F}_7$. To estimate the minimum distance of the codes, we apply symbolic computations implementing the techniques suggested by Geil and Özbudak. For some of these codes, we also obtain the symbol-pair distance. Furthermore, lower bounds on the generalized Hamming weights of the constructed codes are obtained. The proposed method to calculate the generalized Hamming weights can be applied to any primary monomial affine variety codes.