Searcharxiv⌕ Search

arXiv subjects

Marat Burnashev

Publications and source records attributed to Marat Burnashev.

3 recordsLinked to original sources
arXiv2013

Thresholds of Spatially Coupled Systems via Lyapunov's Method

The threshold, or saturation phenomenon of spatially coupled systems is revisited in the light of Lyapunov's theory of dynamical systems. It is shown that an application of Lyapunov's direct method can be used to quantitatively describe the threshold phenomenon, prove convergence, and compute threshold values. This provides a general proof methodology for the various systems recently studied. Examples of spatially coupled systems are given and their thresholds are computed.

cs.IT↗
arXiv2012

Tracking a Random Walk First-Passage Time Through Noisy Observations

Given a Gaussian random walk (or a Wiener process), possibly with drift, observed through noise, we consider the problem of estimating its first-passage time $τ_\ell$ of a given level $\ell$ with a stopping time $η$ defined over the noisy observation process. Main results are upper and lower bounds on the minimum mean absolute deviation $\inf_η\ex|η-τ_\ell|$ which become tight as $\ell\to\infty$. Interestingly, in this regime the estimation error does not get smaller if we allow $ η$ to be an arbitrary function of the entire observation process, not necessarily a stopping time. In the particular case where there is no drift, we show that it is impossible to track $τ_\ell$: $\inf_η\ex|η-τ_\ell|^p=\infty$ for any $\ell>0$ and $p\geq1/2$.

math.ST↗