EXIT functions for binary memoryless symmetric channels

Use of extrinsic information transfer (EXIT) functions characterizing mutual information between the input and output of constituent decoders significantly facilitates performance analysis of iterative decoding schemes. Previously EXIT functions derived for binary erasure channel (BEC) were used as an approximation for other binary memoryless symmetric (BMS) Channels. Here we improve on this approach by introducing a more accurate method to compute EXIT functions of some block codes for BMS channels. A general expression is derived for the extrinsic mutual information at the output of MAP decoder. Using this expression we are able to compute EXIT functions for single parity-check codes over all BMS channels. Application of this result to analysis of convergence thresholds of LDPC codes is described. Using an alternative decoder coinciding with MAP decoder over BEC, we derive an expression for EXIT function over BEC, and based on it approximation to the EXIT function over AWGN channel for some block codes.