PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Strong Converse for the Classical Capacity of the Pure-Loss Bosonic Channel
M. M. Wilde and A. Winter
pp. 117–132

Abstract—This paper strengthens the interpretation and understanding of the classical capacity of the pure-loss bosonic channel, first established in [1]. In particular, we first prove that there exists a trade-off between communication rate and error probability if one imposes only a mean photon number constraint on the channel inputs. That is, if we demand that the mean number of photons at the channel input cannot be any larger than some positive number $N_S$, then it is possible to respect this constraint with a code that operates at a rate $g(\eta N_S/(1-p))$ where $p$ is the code error probability, $\eta$ is the channel transmissivity, and $g(x)$ is the entropy of a bosonic thermal state with mean photon number $x$. Then we prove that a strong converse theorem holds for the classical capacity of this channel (that such a rate-error trade-off cannot occur) if one instead demands for a maximum photon number constraint, in such a way that mostly all of the “shadow” of the average density operator for a given code is required to be on a subspace with photon number no larger than $nN_S$, so that the shadow outside this subspace vanishes as the number $n$ of channel uses becomes large. Finally, we prove that a small modification of the well-known coherent-state coding scheme meets this more demanding constraint.

On the Capacity of a Multiple-Access Vector Adder Channel
A. A. Frolov and V. V. Zyablov
pp. 133–143

Abstract—We investigate the capacity of the $Q$-frequency $S$-user vector adder channel (channel with intensity information) introduced by Chang and Wolf. Both coordinated and uncoordinated types of transmission are considered. Asymptotic (under the conditions $Q\to\infty$, $S=\gamma Q$, $0<\gamma<\infty$) upper and lower bounds on the relative (per subchannel) capacity are derived. The lower bound for the coordinated case is shown to increase with $\gamma$. At the same time, the relative capacity for the uncoordinated case is upper bounded by a constant.

Error Exponents for Nakagami-$m$ Fading Channels
J. Xue, M. Z. I. Sarkar, and T. Ratnarajah
pp. 144–170

Abstract—Along with the channel capacity, the error exponent is one of the most important information-theoretic measures of reliability, as it sets ultimate bounds on the performance of communication systems employing codes of finite complexity. In this paper, we derive an exact analytical expression for the random coding error exponent, which provides significant insight regarding the ultimate limits to communications through Nakagami-$m$ fading channels. An important fact about this error exponent is that it determines the behavior of error probability in terms of the transmission rate and the code length that reflects the coding complexity required to achieve a certain level of reliability. Moreover, from the derived analytical expression, we can easily compute the necessary codeword length without extensive Monte-Carlo simulation to achieve a predefined upper bound for error probability at a rate below the channel capacity. We also improve the random coding bound by expurgating bad codewords from the code ensemble, since random coding error exponent is determined by selecting codewords independently according to the input distribution where good and bad codewords contribute equally to the overall average error probability. Finally, we derive exact analytical expressions for the cutoff rate, critical rate, and expurgation rate and verify the analytical expressions via Monte-Carlo simulation.

Equidistributed Sequences over Finite Fields Produced by One Class of Linear Recurring Sequences over Residue Rings
O. V. Kamlovskii
pp. 171–185

Abstract—We consider the distribution of $r$-patterns in one class of uniformly distributed sequences over a finite field. We establish bounds for the number of occurrences of a given $r$-pattern and prove upper bounds for the cross-correlation function of these sequences.

On One Method for Fast Approximation of Zeta Constants by Rational Fractions
E. A. Karatsuba
pp. 186–202

Abstract—We present a new method for deriving both known and new fast approximations of zeta constants $\zeta(n)$, $n\ge 2$, $n$ is an integer, by rational fractions.