Quantum noise ultimately restricts the transmission distance in fiber communication systems using optical amplifiers. This paper investigates the quantum-noise-limited performance of optical binary phase-shift keying transmission using gain-saturated phase-sensitive amplifiers (PSAs) as optical repeaters. It is shown that coherent state transmission, where ultimately clean light in the classical sense is transmitted, and endless transmission, where the transmission distance is not restricted, are theoretically achievable under certain system conditions owing to the noise suppression effects of the gain-saturated PSA.