EXIT Charts of LDPC Codes over BIAWGN Channels with Imperfect Channel Estimation

To efficiently design LDPC code ensembles that perform well in the presence of channel estimation error (also referred to as "SNR mismatch"), it is necessary to generate extrinsic information transfer (EXIT) charts. We have previously observed that the variable node (check node) EXIT curve in the presence of mismatch lies below (above) the original variable node curve in the absence of mismatch in such a way that it makes the tunnel between the two curves tighter. In this paper, we analytically prove this fact for variable node curves.