Statistical physics of irregular low-density parity-check codes

Low-density parity-check codes with irregular constructions have recently been shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulation results. We compare the performance of irregular codes with that of regular codes and discuss the factors that contribute to the improvement in performance.

Networking - a statistical physics perspective

Networking encompasses a variety of tasks related to the communication of information on networks; it has a substantial economic and societal impact on a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption requires new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with nonlinear large-scale systems. This review aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications. © 2013 IOP Publishing Ltd.

Physics and mathematics of dispersion-managed optical solitons

We review the main physical and mathematical properties of dispersion-managed (DM) optical solitons. Theory of DM solitons can be presented at two levels of accuracy: first, simple, but nevertheless, quantitative models based on ordinary differential equations governing evolution of the soliton width and phase parameter (the so-called chirp); and second, a comprehensive path-average theory that is capable of describing in detail both the fine structure of DM soliton form and its evolution along the fiber line. An analogy between DM soliton and a macroscopic nonlinear quantum oscillator model is also discussed. © 2003 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. All rights reserved.