In this paper we derive a general expression for the Extrinsic
Mutual Information at the Output of a MAP decoder.
Using this expression we are able to compute the EXIT function for
single parity-check codes over all binary input, discrete, memoryless
channels. By defining another decoder which coincides with the MAP decoder
over the Binary Erasure Channel (BEC) we are able to give an
expression for the EXIT function of a block code over the BEC and
an approximation of the EXIT function over the Gaussian channel
for some block codes, using the EXIT functions of these block
codes over the BEC channel.

Finally, we use the expressions for the EXIT functions of
single parity-check and repetition codes over the Gaussian channel, in
order to analyze the performance of LDPC codes under Belief
Propagation decoding. We suggest an improvement over standard EXIT 
function

method that allows us to obtain more accurate approximation of Density
Evolution.