Bifurcations and Chaos in Turbo Decoding Algorithms

Abstract

The turbo decoding algorithm is a high-dimensional dynamical system parameterized by a large number of parameters (for a practical realization the turbo decoding algorithm has more than 10³ variables and is parameterized by more than 10³ parameters). In this chapter we treat the turbo decoding algorithm as a dynamical system parameterized by a single parameter that closely approximates the signal-to-noise ratio (SNR). A whole range of phenomena known to occur in nonlinear systems, like the existence of multiple fixed points, oscillatory behavior, bifurcations, chaos and transient chaos are found in the turbo-decoding algorithm. We develop a simple technique to control transient chaos in turbo decoding algorithm and improve the performance of the standard turbo codes.