EXIT Functions for Randomly Punctured Systematic Codes

In this paper, the extrinsic information transfer (EXIT) functions of randomly punctured systematic codes (RP-SCs) are analyzed. We 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. We 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.