Bifurcations and EXIT charts for the binary erasure channel

Abstract

In this paper we present an abstraction of the extrinsic information transfer (EXIT) chart as the interconnection of two nonlinear systems in feedback with each other. We present results on the stability of fixed points for such a dynamical system and use this framework to rederive the wellknown stability condition, Connecting this to the one-dimensional dynamical system describing the fractions of erasure for lowdensity parity-check (LDPC) codes on the binary rasure channel (BEC). We observe that the error threshold corresponds to a fixed point bifurcation for this one-dimensional system, and show that this information can be visualized using a well-known tool from control theory; the root locus plot. We further show that these bifurcations can be seen by examining the EXIT chart. Show more