6G-Oriented LDPC-Coded Faster-Than-Nyquist Signaling: Code Design and Performance Analysis

This paper focuses on the design and performance analysis of faster-than-Nyquist (FTN) signaling employing enhanced 5G low-density parity-check (LDPC) codes, oriented toward the requirements of future 6G systems. We propose the extrinsic information transfer (EXIT) chart analysis for the LDPC-coded FTN system based on the Ungerboeck observation model, where the input-output mutual information function of the detector is approximated using least squares fitting. With the proposed EXIT chart analysis, we explore the thresholds and decoding performance of different LDPC codes (regular codes, irregular codes and protograph codes) in both Nyquist and FTN systems, revealing two important observational findings for FTN signaling: 1) unlike Nyquist systems, where certain 5G New Radio (NR)-like information puncturing can enhance the decoding threshold and performance, we observe that in the FTN setting considered in this paper such puncturing leads to performance degradation; 2) unlike Nyquist systems, the parity-check matrix of LDPC codes optimized for FTN signaling tends to be relatively sparser within comparable ensembles, due to the intentionally introduced inter-symbol interference (ISI). Based on these findings, we develop tailored LDPC codes for FTN signaling by applying the masking operation to the base matrix of the standard 5G LDPC codes, aiming to achieve a lower decoding threshold and thereby better decoding performance. Moreover, the raptor-like structure and rate compatibility are preserved in the proposed LDPC codes, and the encoder and decoder are reused with only minor modifications. Numerical results show that: 1) all simulation results align with the decoding thresholds obtained by the proposed EXIT chart analysis, confirming the effectiveness of the analysis; 2) for the FTN system, the tailored LDPC codes outperform standard 5G LDPC codes, achieving over 0.4 dB coding gain and approaching (slightly exceeding) the constrained Nyquist capacity; 3) under the same spectral efficiency, FTN with tailored LDPC codes performs better than standard 5G LDPC codes with Nyquist signaling, demonstrating a coding gain of up to 0.6 dB; 4) proposed LDPC codes with the FTN signaling achieve better performance compared to existing high-performance codes specifically designed for FTN signaling.