相关论文: Strange Attractor in Density Evolution

We study critical random Boolean networks with two inputs per node that contain only canalyzing functions. We present a phenomenological theory that explains how a frozen core of nodes that are frozen on all attractors arises. This theory…

In this paper, density evolution-based construction methods to design good polar codes on impulsive noise channels for single-carrier and multi-carrier systems are proposed and evaluated. For a single-carrier system, the tight bound of the…

The paper introduces a new 3D strange attractor topologically different from any other known chaotic attractors. The intentionally constructed model of three autonomous first-order differential equations derives from the coupling-induced…

This work contains the results from a comprehensive study of a new class of attractors. The attractors in this class are characterized by strong local instability, but they are not uniformly hyperbolic. Rigorous results on their dynamical,…

Attractors of cooperative dynamical systems are particularly simple; for example, a nontrivial periodic orbit cannot be an attractor. This paper provides characterizations of attractors for the wider class of coherent systems, defined by…

Constructing a polar code is all about selecting a subset of rows from a Kronecker power of $[^1_1{}^0_1]$. It is known that, under successive cancellation decoder, some rows are Pareto-better than the other. For instance, whenever a user…

Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which \textit{unstable…

Polar codes were recently introduced by Ar\i kan. They achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels under a low complexity successive cancellation decoding strategy. The original polar code…

Strength of attractor is studied by the return rate to itself after perturbations, for a multi-attractor state of a globally coupled map. It is found that fragile (Milnor) attractors have a large basin volume at the partially ordered phase.…

Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized…

In this paper, we study the connection between polar codes and product codes. Our analysis shows that the product of two polar codes is again a polar code, and we provide guidelines to compute its frozen set on the basis of the frozen sets…

This paper presents a new chaotic system having four attractors, including two fixed point attractors and two symmetrical chaotic strange attractors. Dynamical properties of the system, viz. sensitive dependence on initial conditions,…

We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or…

Current deterministic algorithms for the construction of polar codes can only be argued to be practical for channels with small input alphabet sizes. In this paper, we show that any construction algorithm for channels with moderate input…

The long-term behaviour of solutions to a model for acoustic-structure interactions is addressed; the system is comprised of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of…

Strange correlators are useful tools for diagnosing symmetry-protected topological states from their bulk wave functions. We study strange correlators for one-dimensional fermionic symmetry-protected topological states using fixed-point…

In the vicinity of a phase transition, the order parameter starts fluctuating before vanishing at the critical point. The fluctuation regime, i.e. the way the ordered phase disappears, is a characteristics of a transition, and determines…

Product codes are widespread in optical communications, thanks to their high throughput and good error-correction performance. Systematic polar codes have been recently considered as component codes for product codes. In this paper, we…

The inherent nature of polar codes being channel specific makes it difficult to use them in a setting where the communication channel changes with time. In particular, to be able to use polar codes in a wireless scenario, varying…

Stochastic encoders for channel coding and lossy source coding are introduced with a rate close to the fundamental limits, where the only restriction is that the channel input alphabet and the reproduction alphabet of the lossy source code…