Computation of Symbol-Wise Mutual Information in Transmis- sion Systems with LogAPP Decoders and Application to EXIT Charts

The symbol-wise mutual information between the binary inputs of a channel encoder and the soft-outputs of a LogAPP decoder, i.e., the a-posteriori log-likelihood ratios (LLRs), is analyzed. This mutual information can be expressed as the expectation of a function of solely the absolute values of the a-posteriori LLRs. This result provides a simple and elegant method for computing the mutual information by simulation. As opposed to the conventional method, explicit measurements of histograms of the soft-outputs are not necessary. In fact, online estimation is possible, and bits having different statistical properties need not be treated separately. As a direct application, the computation of extrinsic information transfer (EXIT) charts is considered.