Weight vs magnetization enumerator for Gallager codes

We propose a method to determine the critical noise level for decoding Gallager type low density parity check error correcting codes. The method is based on the magnetization enumerator (¸M), rather than on the weight enumerator (¸W) presented recently in the information theory literature. The interpretation of our method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. Our results are more optimistic than those derived via the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.

Spatio-temporal intensity dynamics of passively mode-locked fiber laser

We present recent results on measurements of intensity spatio-temporal dynamics in passively mode-locked fibre laser. We experimentally uncover distinct, dynamic and stable spatio-temporal generation regimes of various stochasticity and periodicity properties in though-to-be unstable laser. We present a method to distinguish various types of generated coherent structures, including rogue and shock waves, within the radiation by means of introducing of intensity ACF evolution map. We also discuss how the spectral dynamics could be measured in fiber lasers generating irregular train of pulses of quasi-CW generation via combination of heterodyning and intensity spatio-temporal measurement concept.

Slow deterministic vector rogue waves

For an erbium-doped fiber laser mode-locked by carbon nanotubes, we demonstrate experimentally and theoretically a new type of the vector rogue waves emerging as a result of the chaotic evolution of the trajectories between two orthogonal states of polarization on the Poincare sphere. In terms of fluctuation induced phenomena, by tuning polarization controller for the pump wave and in-cavity polarization controller, we are able to control the Kramers time, i.e. the residence time of the trajectory in vicinity of each orthogonal state of polarization, and so can cause the rare events satisfying rogue wave criteria and having the form of transitions from the state with the long residence time to the state with a short residence time.