Optimization of the Bit Mapping for LDPC-Coded Faster-Than-Nyquist Systems

This letter focuses on the analysis and optimization of the bit mapping for low-density parity-check (LDPC) coded faster-than-Nyquist (FTN) systems with high-order modulation. We propose the extrinsic information transfer (EXIT) chart analysis for LDPC-coded FTN systems based on the Ungerboeck observation model, where the vector-input and vector-output mutual information of the FTN detector is approximated using a suitably trained neural network (NN). Leveraging the EXIT chart, we optimize the bit mapping, i.e., the assignment of coded bits to the binary labeled constellation points, specifically for FTN systems. Through threshold analysis and simulations, it is shown that for an FTN system using a variant of the LDPC codes specified in the 5G standard, coded bits with highly reliable positions (information bits) in the Tanner graph preferentially to be transmitted over bit-wise sub-channels with higher capacity, while low-degree bits preferentially to be transmitted over bit-wise sub-channels with lower capacity. Numerical results show that: 1) the LDPC-coded FTN system with the optimized mapping outperforms those with random mappings, consistent with the proposed EXIT chart analysis; 2) under the same spectral efficiency, the LDPC-coded FTN system with optimized mapping also outperforms its 5G LDPC-coded Nyquist counterpart.