Wireless communications require powerful channel codes and decoders to protect against transmission errors. Turbo product codes (TPCs) are constructed by concatenating short component codes that are decoded iteratively. Traditionally, turbo product decoding passes log-likelihood ratios between the component decoders, thereby inherently losing information when bit correlations exist. Such correlation can arise exogenously from sources such as intersymbol interference and endogenously during component-code decoding.

In this talk, I propose turbo product decoding based on group probabilities to preserve these correlations and quantify the resulting mutual information gains. To translate these theoretical insights to practice, I revisit non-binary TPCs with entries over higher-order fields that naturally support group-probability decoding. I present an iterative decoding framework based on group-probability component decoding and demonstrate its effectiveness via soft-output guessing random additive noise decoding (SOGRAND). Finally, I show that the predicted gains are realized in practice, with SNR improvements of up to 0.7 dB for endogenous correlation and 1.0 dB for exogenous correlation, compared to conventional bit-probability decoding.