EXIT functions for binary input memoryless symmetric channels

Use of extrinsic information transfer (EXIT) functions, characterizing the amplification of mutual information between the input and output of the maximum a posteriori (MAP) decoder, significantly facilitates analysis of iterative coding schemes. Previously, EXIT functions derived for binary erasure channels (BECs) were used as an approximation for other channels. Here, we improve on this approach by introducing more accurate methods to construct EXIT functions for binary-input memoryless symmetric (BMS) channels. By defining an alternative pseudo-MAP decoder coinciding with the MAP decoder over BEC, we provide an expression for the EXIT functions of block codes over BEC. Furthermore, we draw a connection between the EXIT function over BEC and the EXIT function over the BMS channel under certain conditions. This is used for deriving accurate or approximate expressions of EXIT functions over BMS channels in certain scenarios.