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International Symposium on Information Theory and its Applications

On Optimal Ternary Signal Constellation Maximizing Capacity Under Energy Constraints

Shion Kitamura, Tiancheng Wang, Souichi Takahira, Tsuyoshi Sasaki Usuda

Published Nov 10, 2024• 0 citations
Publisher

Abstract

For efficient use of energy in quantum communication, it is best to use discrete signals that approach the classical capacity achieved by a continuous input of coherent states. Analytical treatment of the classical communication channel requires discretization, and among such discrete signals, using signals as close as possible to the quantum channel capacity is ideal. The class of binary phase shift keying (BPSK) coherent-state signals has been proven to be optimal in the case of binary discretization; however, for multiary discretization with three or more signals, the optimal signals are unknown. In this study, we consider the case of ternary discretization. We numerically show that 3PSK is the optimal signal constellation in two dimensions.

DOI
10.23919/isita60732.2024.10858207

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For efficient use of energy in quantum communication, it is best to use discrete signals that approach the classical capacity achieved by a continuous input of coherent states. Analytical treatment of the classical communication channel requires discretization, and among such discrete signals, using signals as close as possible to the quantum channel capacity is ideal. The class of binary phase shift keying (BPSK) coherent-state signals has been proven to be optimal in the case of binary discretization; however, for multiary discretization with three or more signals, the optimal signals are unknown. In this study, we consider the case of ternary discretization. We numerically show that 3PSK is the optimal signal constellation in two dimensions.
The optimal distributions on a channel input that yield the random coding exponent, the expurgation exponent, and the zero-rate reliability function for a discrete classical-quantum channel with M-ary Phase Shift Keying (PSK) coherent state signal are analytically derived. In each case, the optimal distributions are given by a uniform distribution over the channel input alphabet. As a result, the expressions of the error exponents for M-ary PSK coherent state signal are simplified. By using this result, typical behavior of the error exponents is sketched in the case of M = 16.
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.
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.
It has been reported that error-free quantum reading of a classical digital memory is possible when the entangled coherent state |a〉 |a〉– |– a〉|–a〉 is used as the probe state for quantum reading with binary phase shift keying format under the assumption that the channel is noiseless [quant-ph/1108.4163v2]. In this paper, the theoretical performance limits of the minimum error probability and classical capacity of quantum reading with binary phase shift keying entangled coherent state signal are investigated in the presence of channel loss.