  In this work, we introduce a framework that enables the use of Syndrome-Based
Neural Decoders (SBND) for high-order Bit-Interleaved Coded Modulations (BICM).
To this end, we extend the previous results on SBND, for which the validity is
limited to Binary Phase-Shift Keying (BPSK), by means of a theoretical channel
modeling of the bit Log-Likelihood Ratio (bit-LLR) induced outputs. We
implement the proposed SBND system for two polar codes $(64,32)$ and
$(128,64)$, using a Recurrent Neural Network (RNN) and a Transformer-based
architecture. Both implementations are compared in Bit Error Rate (BER)
performance and computational complexity.
