Generalized EXIT chars for irregular LDPC codes

It is well-known that irregular Low-Density Parity-Check (LDPC) code ensembles can have performance approaching the capacity of binary memoryless channels as opposed o regular LDPC codes. Recently, an asymptotic analysis tool named Generalized Extrinsic Information Transfer (GEXIT) chart has been proposed for regular LDPC codes that can be used as a substitution o density evolution (DE), the main asympotic analysis tool for LDPC codes. GEXIT charts can be seen as an extension of formerly introduced EXIT charts which have an extensive use in analysis and design of many iterative schemes including LDPC codes. EXIT charts provide exactly the same analysis results as DE for the Binary Erasure Channel. However, they can only be seen as an approximation o DE for other channel types. GEXIT charts have only been derived for regular LDPC codes. To be able o use GEXIT chars in code design and in particular, to devise capacity approaching ensembles, they have to be obtained for irregular codes. In this paper we derive GEXIT charts for irregular LDPC codes and show that a similar relationship which exists between EXIT charts of irregular and regular LDPC code also holds for the case of GEXIT charts.