Uncoded Binary Signaling through Modulo AWGN Channel

Modulo-wrapping receivers have attracted interest in several areas of digital communications, including precoding and lattice coding. The asymptotic capacity and error performance of the modulo AWGN channel have been well established. However, due to underlying assumptions of the asymptotic analyses, these findings might not always be realistic in physical world applications, which are often dimension- or delay-limited. In this work, the optimum ways to achieve minimum probability of error for binary signaling through a scalar modulo AWGN channel is examined under different scenarios where the receiver has access to full or partial information. In case of partial information at the receiver, an iterative estimation rule is proposed to reduce the error rate, and the performance of different estimators are demonstrated in simulated experiments.