Faster than Nyquist signaling with limited computational resources

Abstract This paper focuses on performance analysis of Faster than Nyquist (FTN) signaling schemes that employ low-density parity-check (LDPC) codes, trellis-based detector and turbo equalization decoding principle. We propose an optimization procedure for shaping pulse design, that takes into account number of trellis states used for equalization. By using proposed numerical procedure, we identify information rate limits, achievable by FTN signaling technique, with identically and uniformly distributed (i.u.d.) inputs, from a discrete constellation. Furthermore, based on EXIT chart analysis, we provide a numerical upper bound on achievable information rate (AIR) of FTN communication systems with i.u.d. inputs, finite number of turbo decoding iterations or code complexity limitations. Additionally, we derive a tighter upper bound on AIR and demonstrate its usefulness by showing that it is possible to design irregular repeat accumulate LDPC codes that operate within 0.2 dB of the proposed bound for a wide range of code rates.