Publication

Minimum distance properties of coded modulations based on iterated chaotic maps

Thomas Schimming
2003
Conference Papers

Abstract

In this paper we introduce a method for analyzing the performance of coded modulation schemes based on iterated chaotic maps. In particular, it is known from coding theory that the minimum distance plays an important role, defining the behavior of the error probability performance at sufficiently high signal to noise ratios. We introduce the method and illustrate it for two examples of chaotic maps, the Bernoulli shift map and the tent map. We emphasize that the performance of the map can not be understood by a reasoning in terms of ergodic behavior of the map. The given simulation results confirm the relevance of the minimum distance for describing the performance of such a system.

Official source

https://infoscience.epfl.ch/entities/publication/ee60d752-62af-4c99-861e-366de03f7861

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Thomas Schimming
2003
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/ee60d752-62af-4c99-861e-366de03f7861

About this result

Related concepts (32)

Logistic map

The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations. The map was popularized in a 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation written down by Pierre François Verhulst. Mathematically, the logistic map is written where xn is a number between zero and one, which represents the ratio of existing population to the maximum possible population.

Dyadic transformation

The dyadic transformation (also known as the dyadic map, bit shift map, 2x mod 1 map, Bernoulli map, doubling map or sawtooth map) is the mapping (i.e., recurrence relation) (where is the set of sequences from ) produced by the rule Equivalently, the dyadic transformation can also be defined as the iterated function map of the piecewise linear function The name bit shift map arises because, if the value of an iterate is written in binary notation, the next iterate is obtained by shifting the binary point one bit to the right, and if the bit to the left of the new binary point is a "one", replacing it with a zero.

Baker's map

In dynamical systems theory, the baker's map is a chaotic map from the unit square into itself. It is named after a kneading operation that bakers apply to dough: the dough is cut in half, and the two halves are stacked on one another, and compressed. The baker's map can be understood as the bilateral shift operator of a bi-infinite two-state lattice model. The baker's map is topologically conjugate to the horseshoe map. In physics, a chain of coupled baker's maps can be used to model deterministic diffusion.