Zero-Error Capacity of a Class of Timing Channels

We analyze the problem of zero-error communication through timing channels that can be interpreted as discrete-time queues with bounded waiting times. The channel model includes the following assumptions: 1) Time is slotted, 2) at most $N$ "particles" are sent in each time slot, 3) every particle is delayed in the channel for a number of slots chosen randomly from the set $\{0, 1, \ldots, K\}$, and 4) the particles are identical. It is shown that the zero-error capacity of this channel is $\log r$, where $r$ is the unique positive real root of the polynomial $x^{K+1} - x^{K} - N$. Capacity-achieving codes are explicitly constructed, and a linear-time decoding algorithm for these codes devised. In the particular case $N = 1$, $K = 1$, the capacity is equal to $\log \phi$, where $\phi = (1 + \sqrt{5}) / 2$ is the golden ratio, and the constructed codes give another interpretation of the Fibonacci sequence.Comment: 5 pages (double-column), 3 figures. v3: Section IV.1 from v2 is replaced with Remark 1, and Section IV.2 is removed. Accepted for publication in IEEE Transactions on Information Theor

Methodological Basis for Macroeconomic Projections in Countries Exposed to Pressures and Shocks: Example of Serbia

The presented Macroeconomic Projections Model is based on a “pre-established” model for projecting the balance of payment linked with the balance of gross domestic product use. Such a model is the “authentic! one, designed by authors, i.e. based on a no theoretical concept of modelling the macroeconomic equilibrium, but it has a “heuristic” (experiential) character. The idea for designing such a model comes from the fact that theoretical models involve numerous equations that are to be solved, with numerous parameters to be estimated, including also the problem of linearity (smoothness) of longterm analytical curves, as well as the problem of an undeveloped market, a closed economy or an economy that is fragile in its relations with foreign countries, the problem of “turning” points, different internal or external shocks, etc.Macroeconomic projections, GDP deflators, Modelling, Sustainability.