EXIT Functions for Randomly Punctured Systematic Codes

In this paper, the EXtrinsic Information Transfer (EXIT) functions of Randomly Punctured Systematic Codes (RPSCs) are analyzed. The authors consider the systematic encoder to consist of a Non-systematic Code (NC) and a parallel path for the systematic bits; puncturing of the systematic and the parity bits is then carried out separately. They show that the decoding model for measuring the EXIT characteristics of a RP-SC can be transformed into a decoding model of the underlying NC. For the special case where the a priori/communication channels are modeled by binary erasure channels, it becomes obvious that the EXIT functions of any RP-SC can be analytically derived from the EXIT functions of the underlying NC. This theoretical result is verified by a comparison to simulated EXIT functions.