Achievable Error Probability Research Articles

AI-Generated Incentive Mechanism and Full-Duplex Semantic Communications for Information Sharing

The next generation of Internet services, such as Metaverse, rely on mixed reality (MR) technology to provide immersive user experiences. However, limited computation power of MR headset-mounted devices (HMDs) hinders the deployment of such services. Therefore, we propose an efficient information-sharing scheme based on full-duplex device-to-device (D2D) semantic communications to address this issue. Our approach enables users to avoid heavy and repetitive computational tasks, such as artificial intelligence-generated content (AIGC) in the view images of all MR users. Specifically, a user can transmit the generated content and semantic information extracted from their view image to nearby users, who can then use this information to obtain the spatial matching of computation results under their view images. We analyze the performance of full-duplex D2D communications, including the achievable rate and bit error probability, by using generalized small-scale fading models. To facilitate semantic information sharing among users, we design a contract theoretic AI-generated incentive mechanism. The proposed diffusion model generates the optimal contract design, outperforming two deep reinforcement learning algorithms, i.e., proximal policy optimization and soft actor-critic algorithms. Our numerical analysis experiment proves the effectiveness of our proposed methods.

Energy Optimization of a Laser-Powered Hovering-UAV Relay in Optical Wireless Backhaul

Due to their flexibility and low cost deployment, unmanned aerial vehicles (UAV) will most likely act as base stations and backhaul relays in the next generation of wireless communication systems. However, these UAVs—in the untethered mode—can only operate for a finite time due to limited energy they carry in their batteries. In free-space optical communications, one solution is to transport both data and energy from the source to the UAV through the laser beam—a concept known as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">simultaneous lightwave information and power transfer</i> (SLIPT). In this study, we have analyzed the SLIPT scheme for laser-powered decode-and-forward UAV relays in an optical wireless backhaul. The major goal of this study is to optimally allocate the received beam energy between the decoding circuit, the transmitting circuit and the rotor block of the relay in order to maximize a quality-of-service metric such as maximum achievable rate, outage or error probabilities. As expected, we note that the optimal power allocation depends heavily on the source-relay and relay-destination channel conditions. In the final part of this study, we have maximized the operational time of the UAV relay given that the maximum achievable rate stays above a certain threshold in order to meet a minimum quality-of-service requirement.

Performance Analysis of Orthogonal Multiplexing Techniques for PLC Systems with Low Cyclic Prefix Length and Symbol Timing Offset.

This paper investigates the degradation caused by interference resulting from cyclic prefix violation and symbol timing offset in narrowband power line communication systems. In this sense, it presents a unified formulation from which Hermitian symmetric orthogonal frequency division multiplexing (HS-OFDM), orthogonal chirp division multiplexing (OCDM), single-carrier cyclic prefix (SCCP), and orthogonal time-frequency division multiplexing (OTFDM) can be easily derived. The paper then provides closed-form expressions for quantifying the aforementioned interference in the presence of a frequency domain equalizer. The numerical analyses exhibit the performances of these schemes under various data communication conditions, such as the availability of channel state information, the presence or absence of interference, modeling of additive noise as a white or colored Gaussian random process, frequency domain equalizer type, and the use of bit and power allocation techniques. The closed-form expressions and performance analyses regarding achievable data rate and bit error probability provide guidance for dealing with distinct constraints in narrowband power line communication (PLC) systems using the HS-OFDM, OCDM, SCCP, or OTFDM scheme. Lastly, the unified formulation and results obtained motivate the design of multi-scheme transceivers.

Cooperative Molecular Communication in Drift-Induced Diffusive Cylindrical Channel

A cooperative molecular communication (CMC) system is considered inside a cylindrical-shaped channel where a few cooperative nodes (CNs) are intermediately placed between a transmitter (TX) and a fusion center (FC). The expressions for the maximum achievable rate and probability of error at the FC considering AND and OR rules are derived. Furthermore, the performance of the CMC system in a cylindrical channel is compared with the direct and CN-assisted systems. The CMC system with randomly-placed CNs is also analyzed and compared with the uniformly-placed CNs, and it is found that a lower probability of error is obtained in the case of uniform placement of CNs. Furthermore, the system performance as a function of radial displacement of TX and FC under constant flow is compared with that under laminar flow and a higher probability of error is observed under laminar flow. The increased probability of error under laminar flow occurs due to the fact that the drift velocity decreases towards the walls of the cylindrical channel. The analytical expressions are verified using Monte-Carlo simulations.

Autoencoder-Based Unequal Error Protection Codes

We present a novel autoencoder-based approach for designing codes that provide unequal error protection (UEP) capabilities. The proposed approach, based on a generalization of an autoencoder loss function, provides a versatile framework for the design of message-wise and bit-wise UEP codes. Using an associated weight vector, the generalized loss function can be used to trade off error probabilities corresponding to different importance classes and to explore the region of achievable error probabilities. For message-wise UEP, we compare the proposed autoencoder-based UEP codes with a union of random coset codes. For bit-wise UEP, the proposed codes are compared with UEP rateless spinal codes and the superposition of random Gaussian codes. In all cases, the autoencoder-based codes show superior performance while providing design simplicity and flexibility in trading off error protection among different importance classes.

Average Rate and Error Probability Analysis in Short Packet Communications Over RIS-Aided URLLC Systems

In this paper, the average achievable rate and error probability of a reconfigurable intelligent surface (RIS) aided systems is investigated for the finite blocklength (FBL) regime. The performance loss due to the presence of phase errors arising from limited quantization levels as well as hardware impairments at the RIS elements is also discussed. First, the composite channel containing the direct path plus the product of reflected channels through the RIS is characterized. Then, the distribution of the received signal-to-noise ratio (SNR) is matched to a Gamma random variable whose parameters depend on the total number of RIS elements, phase errors and the channels' path loss. Next, by considering the FBL regime, the achievable rate expression and error probability are identified and the corresponding average rate and average error probability are elaborated based on the proposed SNR distribution. Furthermore, the impact of the presence of phase error due to either limited quantization levels or hardware impairments on the average rate and error probability is discussed. The numerical results show that Monte Carlo simulations conform to matched Gamma distribution to received SNR for sufficiently large number of RIS elements. In addition, the system reliability indicated by the tightness of the SNR distribution increases when RIS is leveraged particularly when only the reflected channel exists. This highlights the advantages of RIS-aided communications for ultra-reliable and low-latency systems. The difference between Shannon capacity and achievable rate in FBL regime is also discussed. Additionally, the required number of RIS elements to achieve a desired error probability in the FBL regime will be significantly reduced when the phase shifts are performed without error.

Bit Error Probability Performance of Binary Dimmable Visible Light Communication Systems

This paper evaluates the practically achievable best error performance obtained from a dimmable visible light communication (VLC) system that conveys information using binary modulations, such as on-off keying (OOK). As compared to previous studies that address the ideal performance of dimmable VLC systems only over reliable channels with arbitrarily small error probability, this paper presents the best achievable error probability of various configurations with the dimming targets, signal quality, and data rate. The numerical results establish the ultimate decoding error performance targeted for dimmable VLC systems and are expected to provide a practical guideline for the enhanced VLC system design.

Bounds on amplitude-damping-channel discrimination

Amplitude-damping (AD) channels are good models for many physical scenarios, and so the development of protocols to discriminate between them is an important task in quantum information science. It is therefore important to bound the performance of such protocols. Since adaptivity has been shown to improve the performance of discrimination protocols, bounds on the distinguishability of AD channels must take this into account. In this paper, we use both channel simulation and a bound based on the diamond norm to significantly tighten the upper bound on the trace norm between the possible outputs of binary channel discrimination protocols acting on AD channels (and hence the lower bound on the error probability of such protocols). The diamond norm between any two AD channels is found analytically, giving the optimal error probability for a one-shot discrimination protocol. We also present a tighter lower bound on the achievable trace norm between protocol outputs (and a corresponding upper bound on the achievable error probability). The upper and lower bounds are compared with existing bounds and then applied to quantum hacking and biological quantum sensing scenarios.

Shannon Meets von Neumann: A Minimax Theorem for Channel Coding in the Presence of a Jammer

We study the setting of channel coding over a family of channels whose state is controlled by an adversarial jammer by viewing it as a zero-sum game between a finite blocklength encoder-decoder team, and the jammer. The encoder-decoder team choose stochastic encoding and decoding strategies to minimize the average probability of error in transmission, while the jammer chooses a distribution on the state-space to maximize this probability. The min-max value of the game is equivalent to channel coding for a compound channel - we call this the Shannon solution of the problem. The max-min value corresponds to finding a mixed channel with the largest value of the minimum achievable probability of error. When the min-max and max-min values are equal, the problem is said to admit a saddle-point or von Neumann solution. While a Shannon solution always exists, the communicating team’s problem is nonconvex for finite blocklengths, whereby a von Neumann solution may not exist. Despite this, we show that the min-max and max-min values become equal asymptotically in the large blocklength limit, for all but finitely many rates. We explicitly characterize this limiting value as a function of the rate and obtain tight finite blocklength bounds on the min-max and max-min value. As a corollary we get an explicit expression for the $\epsilon $ -capacity of a compound channel under stochastic codes - the first such result, to the best of our knowledge. Our results demonstrate a deeper relation between the compound channel and mixed channel than was previously known. They also show that the conventional information-theoretic viewpoint, articulated via the Shannon solution, coincides asymptotically with the game-theoretic one articulated via the von Neumann solution. Key to our results is the derivation of new finite blocklength upper bounds on the min-max value of the game via a novel achievability scheme, and lower bounds on the max-min value obtained via the linear programming relaxation based approach we introduced in [2] .

On the Performance of Splitting Receiver With Joint Coherent and Non-Coherent Processing

In this paper, we revisit a recently proposed receiver design, named the splitting receiver, which jointly uses coherent and non-coherent processing for signal detection. By considering an improved signal model for the splitting receiver as compared to the original study in the literature, we conduct a performance analysis on the achievable data rate under Gaussian signaling and obtain a fundamentally different result on the performance gain of the splitting receiver over traditional receiver designs that use either coherent or non-coherent processing alone. Specifically, the original study ignored the antenna noise and concluded on a 50% gain in achievable data rate in the high signal-to-noise ratio (SNR) regime. In contrast, we include the antenna noise in the signal model and show that the splitting receiver improves the achievable data rate by a constant gap in the high SNR regime. This represents an important correction of the theoretical understanding on the performance of the splitting receiver. In addition, we examine the maximum-likelihood detection and derive a low-complexity detection rule for the splitting receiver for practical modulation schemes. Our numerical results give further insights into the conditions under which the splitting receiver achieves significant gains in terms of either achievable data rate or detection error probability.

Convergence Rates for Empirical Estimation of Binary Classification Bounds

Bounding the best achievable error probability for binary classification problems is relevant to many applications including machine learning, signal processing, and information theory. Many bounds on the Bayes binary classification error rate depend on information divergences between the pair of class distributions. Recently, the Henze–Penrose (HP) divergence has been proposed for bounding classification error probability. We consider the problem of empirically estimating the HP-divergence from random samples. We derive a bound on the convergence rate for the Friedman–Rafsky (FR) estimator of the HP-divergence, which is related to a multivariate runs statistic for testing between two distributions. The FR estimator is derived from a multicolored Euclidean minimal spanning tree (MST) that spans the merged samples. We obtain a concentration inequality for the Friedman–Rafsky estimator of the Henze–Penrose divergence. We validate our results experimentally and illustrate their application to real datasets.

Large MIMO Detection Schemes Based on Channel Puncturing: Performance and Complexity Analysis

A family of low-complexity detection schemes based on channel matrix puncturing targeted for large multiple-input multiple-output (MIMO) systems is proposed. It is well known that the computational cost of MIMO detection based on QR decomposition is directly proportional to the number of non-zero entries involved in back-substitution and slicing operations in the triangularized channel matrix, which can be too high for low-latency applications involving large MIMO dimensions. By systematically puncturing the channel to have a specific structure, it is demonstrated that the detection process can be accelerated by employing standard schemes, such as chase detection, list detection, nulling-and-cancellation detection, and sub-space detection on the transformed matrix. The performance of these schemes is characterized and analyzed mathematically, and bounds on the achievable diversity gain and probability of bit error are derived. Surprisingly, it is shown that puncturing does not negatively impact the receive diversity gain in hard-output detectors. The analysis is extended to soft-output detection when computing per-layer bit log-likelihood ratios; it is shown that significant performance gains are attainable by ordering the layer of interest to be at the root when puncturing the channel. Simulations of coded and uncoded scenarios certify that the proposed schemes scale up efficiently both in the number of antennas and constellation size, as well as in the presence of correlated channels. In particular, soft-output per-layer sub-space detection is shown to achieve a 2.5 dB signal-to-noise ratio gain at 10−4 bit error rate in 256-quadratic-amplitude modulation $16\times 16$ MIMO, while saving 77% of nulling-and-cancellation computations.

Optimal measurement strategies for the trine states with arbitrary prior probabilities

We investigate the optimal measurement strategy for state discrimination of the trine ensemble of qubit states prepared with arbitrary prior probabilities. Our approach generates the minimum achievable probability of error and also the maximum confidence strategy. Although various cases with symmetry have been considered and solution techniques put forward in the literature, to our knowledge this is only the second such closed form, analytical, arbitrary prior, example available for the minimum-error figure of merit, after the simplest and well-known two-state example.

Tomography of a displacement photon counter for discrimination of single-rail optical qubits

We investigate the performance of a detection strategy composed of a displacement operation and a photon counter, which is known as a beneficial tool in optical coherent communications, to the quantum state discrimination of the two superpositions of vacuum and single photon states corresponding to the eigenstates in the single-rail encoding of photonic qubits. We experimentally characterize the detection strategy in vacuum-single photon two-dimensional space using quantum detector tomography and evaluate the achievable discrimination error probability from the reconstructed measurement operators. We furthermore derive the minimum error rate obtainable with Gaussian transformations and homodyne detection. Our proof-of-principle experiment shows that the proposed scheme can achieve a discrimination error surpassing homodyne detection.

Implementation of a single-shot receiver for quaternary phase-shift keyed coherent states

We experimentally investigate a strategy to discriminate between quaternary phase-shift keyed coherent states based on single-shot measurements that is compatible with high-bandwidth communications. We extend previous theoretical work in single-shot measurements to include critical experimental parameters affecting the performance of practical implementations. Specifically, we investigate how the visibility of the optical displacement operations required in the strategy impacts the achievable discrimination error probability, and identify the experimental requirements to outperform an ideal heterodyne measurement. Our experimental implementation is optimized based on the experimental parameters and allows for the investigation of realistic single-shot measurements for multistate discrimination.

On the integration of crowd knowledge in pattern recognition

This paper is concerned with the fundamentals of integrating crowd knowledge such as ratings, opinions or tags provided by the internet users. As a concrete example, we consider the problem of image recognition based on user-provided tags. Each user is assumed to have certain knowledge about the images, which can be incomplete or only of partial relevance to the recognition task. Each user is also assumed to have his own choice of tag vocabulary, possibly different from the set of prescribed labels for image recognition. We argue that a user’s knowledge can be separated into the structure of the knowledge and the representation of the structure (namely, his tag vocabulary). This perspective advocates a systematic three-step methodology for crowd knowledge integration in such applications, whereby the problem of interest is decoupled into three sub-problems in tandem: knowledge structure aggregation, vocabulary interpretation, and label assignment. We derive a lower bound for the achievable error probability. Using this bound and via Monte-Carlo simulations, we investigate the performance of a knowledge integration system in relation to various parameter settings.

Decoding Performance in Low-Power Wide Area Networks With Packet Collisions

This paper proposes an analytical framework for the prediction of decoding error probabilities in heterogeneous wireless environments, where transmissions from various radio nodes with distinct Poisson-arrival rates and packet lengths populate the channel. Random channel access without feedback is assumed, where partial packet collisions can lead to the loss of packets. The analysis is based on the modeling of the collision length distribution between competing nodes. With recent results from information theory in the finite block length regime, we provide bounds on achievable decoding error probabilities for a given interference scenario. The new framework enables jointly considering inter- and intra-system interference, which is an important aspect in unlicensed radio bands. The framework’s applicability to optimize system designs is demonstrated for a typical low-power wide area network scenario. We study the tradeoff between reliability and code rate for a point-to-point link and present achievable throughput regions. The analysis reveals the superior performance of coded time-hopping spread spectrum systems. They reach very low error probability even under strong interference for wide ranges of practically relevant load regions.

Optimal receiver design for diffusive molecular communication with flow and additive noise.

In this paper, we perform receiver design for a diffusive molecular communication environment. Our model includes flow in any direction, sources of information molecules in addition to the transmitter, and enzymes in the propagation environment to mitigate intersymbol interference. We characterize the mutual information between receiver observations to show how often independent observations can be made. We derive the maximum likelihood sequence detector to provide a lower bound on the bit error probability. We propose the family of weighted sum detectors for more practical implementation and derive their expected bit error probability. Under certain conditions, the performance of the optimal weighted sum detector is shown to be equivalent to a matched filter. Receiver simulation results show the tradeoff in detector complexity versus achievable bit error probability, and that a slow flow in any direction can improve the performance of a weighted sum detector.

Achievable Error Exponents in the Gaussian Channel With Rate-Limited Feedback

We investigate the achievable error probability in communication over an AWGN discrete time memoryless channel with noiseless delayless rate-limited feedback. For the case where the feedback rate RFB is lower than the data rate R transmitted over the forward channel, we show that the decay of the probability of error is at most exponential in blocklength, and obtain an upper bound for increase in the error exponent due to feedback. Furthermore, we show that the use of feedback in this case results in an error exponent that is at least RFB higher than the error exponent in the absence of feedback. For the case where the feedback rate exceeds the forward rate (RFB ≥ R), we propose a simple iterative scheme that achieves a probability of error that decays doubly exponentially with the codeword blocklength n. More generally, for some positive integer L, we show that a L-th order exponential error decay is achievable if RFB ≥ (L-1)R. While the above results are proved under an average feedback rate constraint, we show that all the achievability results for RFB ≥ R hold in a more restrictive case where the feedback constraint is expressed in terms of the per-channel-use feedback rate. Our results show that the error exponent as a function of RFB has a strong discontinuity at R, where it jumps from a finite value to infinity.

Multi-Hop Diversity Aided Multi-Hop Communications: A Cumulative Distribution Function Aware Approach

In this contribution, we propose and study a signal transmission scheme, namely the multihop diversity (MHD) scheme, conceived for transmission of information over multihop links (MHLs). During each time-slot (TS), the MHD scheme activates the specific hop transmission, whose signal-to-noise ratio (SNR) cumulative distribution function (CDF) gives the highest ordinate value amongst all the available hops. The next packet is then transmitted over the selected hop. Our studies show that this CDF-aware MHD scheme represents a generalized MHD scheme suitable for operation in the scenarios, where the different hops may have different distances, hence resulting in different average SNRs, and/or experience different types of fading. This MHD scheme is also capable of achieving the full diversity gain provided by the independent fading experienced by the different hops. In this paper, our attention is dedicated to the error probability, outage probability as well as to the achievable diversity order, when BPSK and M-ary quadrature amplitude modulation (MQAM) are employed. Both the error probability and the outage probability of the MHLs are investigated for transmission over Nakagami-m fading channels, both of which demonstrate a significant diversity gain. Furthermore, the impact of the various system parameters on the achievable error probability and outage performance is characterized.