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

2026-08-08

AI Summary

This work addresses the problem of capacity enhancement for bandlimited additive white Gaussian noise channels under amplitude-constrained inputs. It introduces probabilistic time shaping (PTS) into this setting for the first time, deriving the optimal input distribution under an invertibility constraint that permits at most one data-dependent transition per symbol at Nyquist sampling instants. By formulating a corresponding information-theoretic model, the proposed approach significantly improves the achievable rate lower bound at high signal-to-noise ratios. The full PTS scheme yields a gain of at least 1.94 dB over the current state-of-the-art, while a newly devised simplified sequential PTS implementation still achieves a notable 1.64 dB improvement, offering an attractive balance between performance and practicality.

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.

Problem

• level-constrained signaling
• bandlimited AWGN channels
• capacity lower bounds
• probabilistic temporal shaping

Innovation

• Probabilistic Temporal Shaping
• Level-Constrained Signaling
• Capacity Lower Bound
• Bandlimited AWGN Channel
• Optimal Shaping Density