We introduce a squeezed-state pulse-position modulation (S-PPM) format, where the empty slots are squeezed vacuum states and the pulse slot is a displaced squeezed state. Based on this property, we propose an inverse-squeezing conditional pulse-nulling (IS-CPN) receiver. In the ideal case, inverse squeezing maps S-PPM into an equivalent coherent-state PPM signal with a large pulse energy, leading to a closed-form expression for the receiver error probability. We further analyze IS-CPN under common phase diffusion using a finite-path MAP formulation with phase-averaged likelihoods. Numerical results show that IS-CPN outperforms conventional CPN under the same energy constraint and remains advantageous under phase noise and finite photon-number resolution. These results demonstrate that combining squeezed-state modulation with inverse-squeezing conditional nulling can improve photon-efficient optical communication.
Optical pulse-position modulation (PPM) is one of the primary modulation formats being investigated for use in deep-space communications, as well as terrestrial fiber optical communications. We consider the problem of demodulating M-ary optical PPM waveforms, and propose a structured receiver whose mean probability of symbol error is smaller than all known receivers, and approaches the Helstrom (quantum) limit of the minimum probability of error (MPE) of discriminating between the coherent-state PPM signals. The receiver uses photodetection coupled with optimized phase-coherent optical feedback control through the PPM pulse slots and a phase-sensitive parametric amplifier. We present a general framework of optical receivers known as the ‘conditional pulse nulling receiver’, and present new results on ultimate limits and achievable regions of the trade-off space between the spectral versus photon efficiency of PPM, for the single-spatial-mode far-field pure-loss optical communication channel.
Quantum receivers which can discriminate phase shift keying (PSK) and pulse position modulation (PPM) signals below the standard quantum limit have been proposed and some have been demonstrated experimentally. But for quadrature amplitude modulation (QAM) signals, few literatures have been reported so far. It is important to reduce the average error probability of QAM signals below the standard quantum limit (SQL), since these modulation have a high spectral efficiency. In this paper, we present a quantum receiver for 16-QAM signals discrimination with hybrid structure, which contains a homodyne receiver and a displacement receiver. By numerical simulation, we prove that the performance of the quantum receiver can outperform the SQL, and it can be improved by an optimized displacement.
Optical pulse position modulation (PPM) places a laser pulse, a.k.a. a coherent state of amplitude
αof mean photon number
N=∣α∣2, in one of
Mconsecutive time slots, Ideal photon detection on each slot achieves a mean probability of error
((M−1)/1M)e−Nof distinguishing the
iMPPM codewords, since
e−Nis the probability the pulse-containing slot does not produce a click, per Poisson-shot-noise photo-detection theory. The quantum (Helstrom) limit of the minimum probability of error is lower than above, has a closed-form expression, and scales as
∼e−2Nwhen
Me−N≪1. The optimal receiver must make a quantum joint measurement on all
Mslots. Even though receiver algorithms exist that achieve the
∼e−2Nscaling in the high
Nregime, none are known that bridge the classical-quantum gap for small
N, the primary regime of interest for optical PPM. It is also not known how close to the Helstrom limit can one get using LOCC. (local operations and classical communications), i.e., a receiver that slices each of the
Mslots into
ntiny slices, makes a measurement on the first slice, and based on the measurement result picks a measurement to apply to the next slice, etc., until all the
Mnslices have been measured. In this paper, we propose an LOCC receiver for demodulating PPM that uses semiclassical coherent feedback control and photon detection, which outperforms all known PPM receivers, including one that employed squeezing, a non-classical operation. To bridge the remaining gap to the Helstrom limit, one might need truly quantum operations within a joint (non-LOCC) receiver.