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IEEE Access

Constellation Optimization for Phase-Shift Keying Coherent States With Displacement Receiver to Maximize Mutual Information

Rahul Kumar Bhadani, Ivan B. Djordjević

Published Jan 1, 2020• 7 citations
Publisher

Abstract

An important problem in quantum information theory is finding the best possible capacity of the optical communication channel employing suitable codewords, receiver design, and constellation optimization techniques. In this paper, we derive an alternative channel capacity, CG, of phase-shift keying coherent state with a realizable displacement receiver by maximizing mutual information over symbol priors and pre-detection displacement. We find that CGis higher than the capacity achieved by maximizing mutual information over symbol prior but with zero displacement. The overall scheme demonstrates designing an improved, yet easy-to-implement receiver for better communication performance by tuning it at different photon number regime. Further, we present a comparative analysis of CGwith existing receiver designs. We extend our study to account for detector imperfections.imperfections.

DOI
10.1109/access.2020.3044086

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An important problem in quantum information theory is finding the best possible capacity of the optical communication channel employing suitable codewords, receiver design, and constellation optimization techniques. In this paper, we derive an alternative channel capacity, CG, of phase-shift keying coherent state with a realizable displacement receiver by maximizing mutual information over symbol priors and pre-detection displacement. We find that CGis higher than the capacity achieved by maximizing mutual information over symbol prior but with zero displacement. The overall scheme demonstrates designing an improved, yet easy-to-implement receiver for better communication performance by tuning it at different photon number regime. Further, we present a comparative analysis of CGwith existing receiver designs. We extend our study to account for detector imperfections.imperfections.
An important problem in quantum information theory is finding the best possible performance of the optical communication channel employing suitable codewords, receiver design, and constellation optimization techniques. Many receiver designs have been studied in the past to discriminate Phase-Shift Keying (PSK) quantum states that are used to encode information before transmitting over the communication channel. Among many types of quantum states, there has been significant work on the use of coherent states for encoding information. Previous work has sought to improve the communication performance in terms of various metrics such as error probability of state discrimination and capacities by employing a number of quantum states such as coherent states and squeezed-displaced states. In this thesis, we provide optimal receiver design employing coherent states and squeezed-displaced states to maximize the mutual information and lower the error probability of state discrimination. In the case of pure coherent states, we derive an alternative channel capacity of phase-shift keying coherent state with a realizable displacement receiver by maximizing mutual information over symbol priors and pre-detection displacement. We find that the capacity is higher than the capacity achieved by maximizing mutual information over symbol prior but with zero displacements. The overall scheme demonstrates designing an improved, yet easy-to-implement receiver for better communication performance by tuning it at different photon number regime. We also explore the use of squeezing operations with a displacement receiver for state discrimination. Our calculation demonstrates that we see no performance improvement in terms of the probability of error of state discrimination or mutual information using displacement receivers when optimal squeezing on the transmitter side is used. In addition, we also study the receiver design scheme for QPSK modulation where squeezing is employed at the receiver side. We find that using the squeezing operation on the receiver side provides an advantage in terms of increased mutual information for the low-photon number regime compared to when no squeezing is used. In the later part of the thesis, we study entanglement-assisted communication using two-mode squeezing vacuum. The use of pre-shared entanglement in entanglement-assisted communication provides a superior alternative to classical communication specifically in the low brightness regime and highly noisy environment. In this thesis, we analyze the performance of a few low-complexity receivers that employ optical parametric amplifiers. In the simulation, we demonstrate that receiver designs with an entanglement-assisted scheme using phase-shift-keying modulation can outperform classical capacities. We describe a newly proposed 2x2 optical hybrid receiver for entanglement-assisted communication whose performance is roughly 10% better in terms of error probability as compared to previously proposed optical parametric amplifier-based receivers. Further, we find that using unequal priors for BPSK provides approximately three times the advantage over equal priors in terms of information rate.
Many receiver designs have been studied in the past to discriminate Phase-Shift Keying (PSK) quantum states that are used to encode information before transmitting over the communication channel. Among many types of quantum states, there has been significant work on the use of coherent states for encoding information. Previous work has sought to improve the communication performance in terms of various metrics such as error probability of state discrimination and capacities by employing more complex quantum states such as squeezed-displaced states. One of the simplest receivers for state discrimination is the displacement receiver. However, our calculation demonstrates that when we use optimal parameters for a displacement receiver, squeezed-displaced states might not be necessary, and merely using coherent states suffice. We see no performance improvement in terms of probability of error of state discrimination as well as mutual information using displacement receivers when optimal squeezing parameters are used with squeezing operation on the transmitter side for BPSK and QPSK. In addition, we also study the receiver design scheme for QPSK modulation where squeezing is employed at the receiver side. We find that using squeezing operation on the receiver side just before detection provides an advantage in terms of increased mutual information for the low-photon regime compared to when no squeezing is used. For all other cases, squeezing offers no additional advantage.
The quantum receiver is an important tool for overcoming the standard quantum limit (SQL) of discrimination errors in optical communication. We theoretically study the quantum receivers for discriminating ternary and quaternary phase-shift-keying coherent states in terms of average error rate and mutual information. Our receiver consists of on-off--type photon detectors and displacement operations without electrical feedforward operations. We show that for the ternary signals, the receiver shows a reasonable gain from the SQL even without feedforward. This scheme is realizable with the currently available technology. For the quaternary signals feedforward operation is crucial to overcome the SQL with imperfect devices. We also analytically examine the asymptotic limit of the performance of the proposed receiver with respect to the number of feedforward steps.
We present the theory and experimental realization of a quantum polarization-displacement receiver for photonic communications with laser coherent states modulated in their polarization degree of freedom, employing an unconditionally polarization-nulling photon counting scheme. We describe the quantum detection analysis for Polarization Shift Keying (PolSK) modulation formats with laser coherent states, deriving their theoretical performance bounds in error probability and mutual information; and we propose a receiver structure based on a polarization-displacement technique, inspired on the conventional quadrature-displacement schemes employed in the reception of Phase Shift Keying (PSK) modulation formats. Experimentally, we implement our coherent states receiver in a polarization-nulling configuration, employing linear optics for the polarization rotations and displacement, with photon counting at the telecommunications wavelength of 1550 nm, and performing post-detection count–to–voltage operations and logical decision with optimized photon number thresholds; additionally, as a reference, we also implement a quadrature-nulling receiver for a binary PSK format. We perform measurements on the symbol error probability of our receiver, as a function of the photon number of the received photonic signal, finding good agreement with the theoretical estimation at low photon numbers. This receiving structure has advantages over the conventional polarization-splitting and separate photon counting schemes, which is of interest in quantum communications, quantum cryptography and other fields in quantum information.
Abstract The achievable rate of information transfer in optical communications is determined by the physical properties of the communication channel, such as the intrinsic channel noise. Bosonic phase noise channels, a class of non-Gaussian channels, have emerged as a relevant noise model in quantum information and optical communication. However, while the fundamental limits for communication over Gaussian channels have been extensively studied, the properties of communication over Bosonic phase noise channels are not well understood. Here we propose and demonstrate experimentally the concept of optimized communication strategies for communication over phase noise channels to enhance information transfer beyond what is possible with conventional methods of modulation and detection. Two key ingredients are generalized constellations of coherent states that interpolate between standard on-off keying and binary phase-shift keying formats, and non-Gaussian measurements based on photon number resolving detection of the coherently displaced signal. For a given power constraint and channel noise strength, these novel strategies rely on joint optimization of the input alphabet and the measurement to provide enhanced communication capability over a non-Gaussian channel characterized in terms of the error rate as well as mutual information.
This paper proposes a multichannel optimal squeezing-displacement receiver (MOSDR) with photon-number-resolving detectors for discriminating binary phase-shift keying (BPSK) coherent states. Unlike previous squeezing-based receivers whose gain is largely limited to the low photon-number regime, we partition the input signal into multiple channels so that the mean photon number in each channel is reduced, allowing the squeezing operation to be used more effectively in its favorable operating region. In addition, we use displacement feedforward between channels and accumulate the per-channel discrimination outcomes through a sequential decision process, thereby reducing the overall error probability. We analyze MOSDR under an ideal detector as well as under quantum efficiency, dark counts and visibility reduction. The results show that MOSDR outperforms an optimized-displacement multichannel displacement feedforward receiver and remains below the standard quantum limit over a wide photon-number range, exhibiting improved robustness to detection imperfections.