Existence Proofs of Some EXIT Like Functions

Details Existence Proofs of Some EXIT Like Functions Existence Proofs of Some EXIT Like Functions

2007-04-19

arxiv.org/abs/0704.2544v1

Computer Science

Information Theory

To appear in proc. of ISIT 2007

Scientific paper

The Extended BP (EBP) Generalized EXIT (GEXIT) function introduced in \cite{MMRU05} plays a fundamental role in the asymptotic analysis of sparse graph codes. For transmission over the binary erasure channel (BEC) the analytic properties of the EBP GEXIT function are relatively simple and well understood. The general case is much harder and even the existence of the curve is not known in general. We introduce some tools from non-linear analysis which can be useful to prove the existence of EXIT like curves in some cases. The main tool is the Krasnoselskii-Rabinowitz (KR) bifurcation theorem.

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