Probabilistic Temporal Shaping for Level-Constrained Signaling on Bandlimited Additive White Gaussian Noise Channels

Abstract

Level-constraints model one-bit-quantized signaling over real-alphabet continuous-time channels. New lower bounds on the capacity of bandlimited, additive white Gaussian noise channels with level-constrained inputs are derived by using probabilistic temporal shaping (PTS). The optimal shaping density is derived for signals with one data-dependent sign change per Nyquist-rate sample, which ensures they satisfy an invertibility requirement. Calculations show that PTS improves the best existing lower bound by at least 1.94 dB at high signal-to-noise ratio (SNR). A simpler sequential PTS scheme achieves a gain of 1.64 dB at high SNR.