On Merits of Faster-than-Nyquist Signaling in the Finite Blocklength Regime

Abstract: We identify potential merits of faster-than-Nyquist (FTN) signaling in the finite blocklength (FBL) regime. A unique aspect of FTN signaling is that it can increase the blocklength by packing more data symbols within the same time and frequency to yield strictly higher number of independent signaling dimensions than that of Nyquist rate signaling. Using the finite-blocklength information theory, we provide tight bounds on the maximum channel coding rate (MCCR) of FTN signaling for any finite time-bandwidth product. The merits are categorized into two operating regions of FTN, i.e., when the time-acceleration factor of FTN, $\tau$, is above or below a certain threshold $\tau_{0}$. When $\tau > \tau_{0}$, FTN has both higher channel capacity and MCCR than that of Nyquist rate signaling, when the utilized pulse shape is non-sinc. Since the issues associated with the ideal sinc pulse only get exacerbated when packets are short, the benefit of FTN becomes more significant in the FBL regime. On the other hand, when $\tau < \tau_{0}$, the channel capacity is fixed but MCCR of FTN can continue to increase to a certain degree, thereby reducing the gap between the capacity and MCCR. This benefit is present regardless of the utilized pulse shape, including the ideal sinc-pulse, and is unique to the FBL regime. Instead of increasing MCCR for fixed block error rates, FTN can alternatively lower the block error rates for fixed channel coding rates. These results imply that FTN can lower the penalty from limited channel coding over short blocklength and can improve the performance and reliability of short packet communications.