Decoding Error Probability Research Articles

Joint Transmit Power and Placement Optimization for URLLC-Enabled UAV Relay Systems

This letter considers an unmanned aerial vehicle (UAV)-enabled relay communication system for delivering latency-critical messages with ultra-high reliability, where the relay is operating under amplifier-and-forward (AF) mode. We aim to jointly optimize the UAV location and power to minimize decoding error probability while guaranteeing the latency constraints. Both the free-space channel model and three-dimensional (3-D) channel model are considered. For the first model, we propose a low-complexity iterative algorithm to solve the problem, while globally optimal solution is derived for the case when the signal-to-noise ratio (SNR) is extremely high. For the second model, we also propose a low-complexity iterative algorithm to solve the problem. Simulation results confirm the performance advantages of our proposed algorithms.

Joint Pilot and Payload Power Allocation for Massive-MIMO-Enabled URLLC IIoT Networks

The Fourth Industrial Revolution (Industrial 4.0) is coming, and this revolution will fundamentally enhance the way the factories manufacture products. The conventional wired lines connecting central controller to robots or actuators will be replaced by wireless communication networks due to its low cost of maintenance and high deployment flexibility. However, some critical industrial applications require ultra-high reliability and low latency communication (URLLC). In this paper, we advocate the adoption of massive multiple-input multiple output (MIMO) to support the wireless transmission for industrial applications as it can provide deterministic communications similar as wired lines thanks to its channel hardening effects. To reduce the latency, the channel blocklength for packet transmission is finite, and suffers from transmission rate degradation and decoding error probability. Thus, conventional resource allocation for massive MIMO transmission based on Shannon capacity assuming the infinite channel blocklength is no longer optimal. We first derive the closed-form expression of lower bound (LB) of achievable uplink data rate for massive MIMO system with imperfect channel state information (CSI) for both maximum-ratio combining (MRC) and zero-forcing (ZF) receivers. Then, we propose novel low-complexity algorithms to solve the achievable data rate maximization problems by jointly optimizing the pilot and payload transmission power for both MRC and ZF. Simulation results confirm the rapid convergence speed and performance advantage over the existing benchmark algorithms.

Exploiting Randomized Continuous Wave in Secure Backscatter Communications

To enable the low-cost ubiquitous Internet of Things, passive backscatter communication is envisioned as one of the most prominent and promising techniques; however, the underlying security issues associated with practical finite-alphabet signaling from the perspective of physical-layer security (PLS) have not been well studied. Despite several preliminary efforts on improving the eavesdropper’s decoding error probability through PLS approaches, this article comprehensively investigates the secrecy rate performance of a secure multiantenna radio-frequency identification (RFID) system with a finite-alphabet input at the RFID tag. Unlike conventional noise-injection schemes, a randomized continuous wave (CW) signal is exploited at the RFID reader for security enhancement, and an analytical framework is proposed to evaluate the impact of exploiting either full or only statistical knowledge of the randomized CW signal at the reader and the eavesdropper, respectively. The secrecy rate is maximized by designing the transmitted randomized CW signal to tackle the stability–variance tradeoff between balancing legitimate signal reception and eavesdropper mitigation. In particular, we show that the proposed scheme also poses a tradeoff between the received additive and multiplicative noise at the eavesdropper for the special case of a single-antenna eavesdropper. Moreover, the more practical case where the eavesdropper’s instantaneous channel state information is unavailable is studied under different fading conditions. The numerical results verify the accuracy of the proposed approximations and show that introducing a small variance into the CW signal can greatly improve the system secrecy.

Throughput Analysis of Low-Latency IoT Systems With QoS Constraints and Finite Blocklength Codes

Internet of Things (IoT) is a promising paradigm to connect massive number of devices in future wireless communications while satisfying various quality of service (QoS) requirements. In this paper, we consider a QoS-constrained IoT system operating with finite blocklength (FBL) codes to support low latency communications. Two data arrival models are considered, namely, constant-rate arrival and ON-OFF discrete-time Markov arrival. The throughput performance is studied for both arrival models under statistical queuing constraints and deadline limits. For the scenario with instantaneous channel state information (CSI), we derive the QoS-constrained throughput expressions for both arrival models. Subsequently, an instantaneous-CSI-driven optimal power control algorithm is proposed to maximize the throughput, while guaranteeing a certain reliability target. In addition, we consider a scenario with only average CSI being available at the transmitter and propose to apply hybrid automatic repeat request (HARQ) schemes to improve the FBL performance. The decoding error probability and the outage probability are first characterized, following which the distribution of transmission period is derived. Furthermore, the throughput expressions are provided for both types of arrivals. Via numerical analysis, the impact of error probability, fixed transmission rate, coding blocklength, and QoS constraints on the throughput is studied.

Performance Measurement and Optimization of Relays Used for 5G Ultra Reliable Low Latency Communication Network

The objective of this paper is to analyse and optimize the performance parameters of Relay nodes used in the finite block length (FBL) regime. A relaying system with a single Decode and Forward (DF) Relay is used for this purpose. Here using FBL, the performance parameters like coding rate, decoding error probability etc are obtained for different scenarios like without relay, with relay and using cooperative relaying. Effects of SNR and code Block length on performance parameters are analyzed. To enhance the performance of the Relay in URLLC scenario, power distribution between source and Relay node is optimized using evolutionary algorithms such as Multi-Objective Particle Swarm Optimization (MOPSO) and Infeasibility Driven Evolutionary Algorithm (IDEA). Low error probability and high throughput at the desired block length and power were the optimization goals. After using both the algorithms, the optimized Relay has shown improvement in performances like throughput (coding rate) and decoding error probability. It is also observed that IDEA optimization approach is found to be more efficient than MOPSO to provide optimum design parameters.

Joint Power and Blocklength Optimization for URLLC in a Factory Automation Scenario

Ultra-reliable and low-latency communication (URLLC) is one of three pillar applications defined in the fifth generation new radio (5G NR), and its research is still in its infancy due to the difficulties in guaranteeing extremely high reliability (say 10−9 packet loss probability) and low latency (say 1 ms) simultaneously. In URLLC, short packet transmission is adopted to reduce latency, such that conventional Shannon’s capacity formula is no longer applicable, and the achievable data rate in finite blocklength becomes a complex expression with respect to the decoding error probability and the blocklength. To provide URLLC service in a factory automation scenario, we consider that the central controller transmits different packets to a robot and an actuator, where the actuator is located far from the controller, and the robot can move between the controller and the actuator. In this scenario, we consider four fundamental downlink transmission schemes, including orthogonal multiple access (OMA), non-orthogonal multiple access (NOMA), relay-assisted, and cooperative NOMA (C-NOMA) schemes. For all these transmission schemes, we aim for jointly optimizing the blocklength and power allocation to minimize the decoding error probability of the actuator subject to the reliability requirement of the robot, the total energy constraints, as well as the latency constraints. We further develop low-complexity algorithms to address the optimization problems for each transmission scheme. For the general case with more than two devices, we also develop a low-complexity efficient algorithm for the OMA scheme. Our results show that the relay-assisted transmission significantly outperforms the OMA scheme, while the NOMA scheme performs well when the blocklength is very limited. We further show that the relay-assisted transmission has superior performance over the C-NOMA scheme due to larger feasible region of the former scheme.

SigMix: Decoding Superimposed Signals for IoT

The growth of Internet of Things (IoT) is anticipated to accelerate in the coming years. However, the wireless spectrum is insufficient to support the ever-growing IoT applications. A promising solution is to allow concurrent wireless transmissions and decode the superimposed signal. To make this solution practical for IoT systems, dynamic channel conditions and hardware imperfections are the key practical challenges, but not yet be addressed in the past work, leading to a low decoding performance. In this article, we introduce SigMix, aiming to deal with the practical challenges by proposing a solution to decode the superimposed signal, and eventually boost the spectrum efficiency. To this end, we first derive a theoretical expression that reveals the close relationship between phase shifts among concurrently transmitted signals and the error probability in decoding the superimposed signal. Then, based on the theoretical expression, we propose a rotation code and an adaptive decoding scheme to largely reduce the decoding error probability. Extensive experiments have shown that the median bit-error-rate of our scheme is one-order lower than the state-of-the-art.

On Safeguarding Visible Light Communication Systems Against Attacks by Active Adversaries

We consider an indoor visible light communication (VLC) system comprising of a transmitter (Alice) and a receiver (Bob). The communication from Alice to Bob is prone to active attacks by a malicious node (Eve) installed nearby. Specifically, when the VLC channel contains idle slots, Eve launches impersonation attack—thus, the VLC channel becomes orthogonal multiple access (OMA). On the other hand, when the VLC channel remains fully occupied by Alice, Eve is left with no choice other than to transmit simultaneously and this constitutes a jamming attack—thus, the VLC channel becomes non-orthogonal multiple access (NOMA). To thwart the impersonation attack, Bob authenticates the received packets via binary hypothesis testing (BHT) by utilizing the channel gain as the transmit device fingerprint. As for the jamming attack, Bob treats Eve’s interference as Gaussian noise to recover the data sent by Alice. We further study two different physical scenarios: a room and a corridor, respectively. In the former, Bob remains static, while in the latter, Bob is mobile. Thus, for the corridor scenario, Bob tracks Alice’s channel via a linear Kalman filter whose prediction is then fed to the BHT as the ground truth. Simulation results show that: i) for OMA VLC, authentication becomes more effective as Eve’s distance to Bob becomes more dissimilar to Alice’s distance to Bob; ii) for NOMA VLC, the average decoding error probability increases approximately logarithmically with the increase in the interference power of Eve.

On the Secrecy Performance and Power Allocation in Relaying Networks With Untrusted Relay in the Partial Secrecy Regime

Recently, three useful secrecy metrics based on the partial secrecy regime were proposed to analyze secure transmissions on wireless systems over quasi-static fading channels, namely: generalized secrecy outage probability, average fractional equivocation, and average information leakage. These metrics were devised from the concept of fractional equivocation, which is related to the decoding error probability at the eavesdropper, so as to provide a comprehensive insight on the practical implementation of wireless systems with different levels of secrecy requirements. Considering the partial secrecy regime, in this paper we examine the secrecy performance of an amplify-and-forward relaying network with an untrusted relay node, where a destination-based jamming is employed to enable secure transmissions. In this regard, a closed-form approximation is derived for the generalized secrecy outage probability, and integral-form expressions are obtained for the average fractional equivocation and the average information leakage rate. Additionally, equal and optimal power allocation schemes are investigated and compared for the three metrics. From this analysis, we show that different power allocation approaches lead to different system design criteria. The obtained expressions are validated via Monte Carlo simulations.

Low Rank Parity Check Codes: New Decoding Algorithms and Applications to Cryptography

We introduce a new family of rank metric codes: Low Rank Parity Check codes (LRPC), for which we propose an efficient probabilistic decoding algorithm. This family of codes can be seen as the equivalent of classical LDPC codes for the rank metric. We then use these codes to design cryptosystems A la McEliece: more precisely we propose two schemes for key encapsulation mechanism (KEM) and public key encryption (PKE). Unlike rank metric codes used in previous encryption algorithms -notably Gabidulin codes - LRPC codes have a very weak algebraic structure. Our cryptosystems can be seen as an equivalent of the NTRU cryptosystem (and also to the more recent MDPC code-based cryptosystem) in a rank metric context, due to the similar form of the public keys. The present paper is an extended version of the article introducing LRPC codes, with important new contributions. We have improved the decoder thanks to a new approach which allows for decoding of errors of higher rank weight, namely up to $\frac {2}{3}(n-k)$ when the previous decoding algorithm only decodes up to $\frac {n-k}{2}$ errors. Our codes therefore outperform the classical Gabidulin code decoder which deals with weights up to $\frac {n-k}{2}$ . This comes at the expense of probabilistic decoding, but the decoding error probability can be made arbitrarily small. The new approach can also be used to decrease the decoding error probability of previous schemes, which is especially useful for cryptography. Finally, we introduce ideal rank codes, which generalize double-circulant rank codes and allow us to avoid known structural attacks based on folding. To conclude, we propose different parameter sizes for our schemes and we obtain a public key of 3337 bits for key exchange and 5893 bits for public key encryption, both for 128 bits of security.

Achievable Rate Regions for Source Coding with Delayed Partial Side Information

In this paper, we consider a source coding with side information partially used at the decoder through a codeword. We assume that there exists a relative delay (or gap) of the correlation between the source sequence and side information. We also assume that the delay is unknown but the maximum of possible delays is known to two encoders and the decoder, where we allow the maximum of delays to be subject to change by the block length. In this source coding, we give an inner bound and an outer bound on the achievable rate region, where the achievable rate region is the set of rate pairs of encoders such that the decoding error probability vanishes as the block length tends to infinity. Furthermore, we clarify that the inner bound coincides with the outer bound when the maximum of delays for the block length converges to a constant.

Quasi-Optimization of Distance and Blocklength in URLLC Aided Multi-Hop UAV Relay Links

Achieving ultra-high reliability for short packets is a core challenge for future wireless communication systems, as current systems are designed only to transmit long packets based on classical information-theoretic principles. To tackle this challenge, this letter relies on multi-hop unmanned aerial vehicle (UAV) relay links to deliver short ultra-reliable and low-latency (URLLC) instruction packets between ground Internet of Things (IoT) devices. To accomplish this task, we perform non-linear optimization to minimize the overall decoding error probability in order to find the optimal values of the distance and the blocklength. In this vein, a novel, semi-empirical based non-iterative algorithm is proposed to solve the quasi-optimization problem. The algorithm executes in quasilinear time and converges to a globally optimal/sub-optimal solution based on the chosen parameters. Simulation results demonstrate that our algorithm allows operation under the ultra-reliable regime (URR), and yields the same performance as exhaustive search algorithms.

On Data-Processing and Majorization Inequalities for f-Divergences with Applications

This paper is focused on the derivation of data-processing and majorization inequalities for f-divergences, and their applications in information theory and statistics. For the accessibility of the material, the main results are first introduced without proofs, followed by exemplifications of the theorems with further related analytical results, interpretations, and information-theoretic applications. One application refers to the performance analysis of list decoding with either fixed or variable list sizes; some earlier bounds on the list decoding error probability are reproduced in a unified way, and new bounds are obtained and exemplified numerically. Another application is related to a study of the quality of approximating a probability mass function, induced by the leaves of a Tunstall tree, by an equiprobable distribution. The compression rates of finite-length Tunstall codes are further analyzed for asserting their closeness to the Shannon entropy of a memoryless and stationary discrete source. Almost all the analysis is relegated to the appendices, which form the major part of this manuscript.

The Decoding Error Probability of Linear Codes Over the Erasure Channel

In this paper, we study the decoding error probability of linear codes over the erasure channel under the list decoding. The notion of the $q^\ell $ -incorrigible sets of linear codes is introduced to characterize its decoding error probability under the list decoding or the maximum likelihood decoding. By calculating the $q^\ell $ -incorrigible set distributions, the decoding error probability of a linear code over the erasure channel under the list decoding or the maximum likelihood decoding is expressed by its support weight distributions. For the ensemble of all $[n,k]$ linear codes, the average decoding error probability under the maximum likelihood decoding and the average unsuccessful decoding probability under unambiguous decoding are determined. Furthermore, the error exponent of the average unsuccessful decoding probability under the unambiguous decoding is determined for the ensemble of all $[n,nR]$ linear codes.

On Distance Properties of Convolutional Polar Codes

A lower bound on the minimum distance of convolutional polar codes is provided. The bound is obtained from the minimum weight of the generalized cosets of the codes generated by the bottom rows of the polarizing matrix. Moreover, a construction of convolutional polar subcodes is proposed, which provides improved performance under successive cancellation list decoding. For sufficiently large list size, the decoding complexity of convolutional polar subcodes appears to be lower compared with Arikan polar subcodes with the same performance. The error probability of successive cancellation list decoding of convolutional polar subcodes is lower than that of Arikan polar subcodes with the same list size.

Exponential Strong Converse for One Helper Source Coding Problem.

We consider the one helper source coding problem posed and investigated by Ahlswede, Körner and Wyner. Two correlated sources are separately encoded and are sent to a destination where the decoder wishes to decode one of the two sources with an arbitrary small error probability of decoding. In this system, the error probability of decoding goes to one as the source block length n goes to infinity. This implies that we have a strong converse theorem for the one helper source coding problem. In this paper, we provide the much stronger version of this strong converse theorem for the one helper source coding problem. We prove that the error probability of decoding tends to one exponentially and derive an explicit lower bound of this exponent function.

On the feedback capacity of the first-order moving average Gaussian channel

In this paper, we study the discrete-time additive Gaussian noise channel given by \(Y_i=X_i+Z_i\), \(i=1,2,\ldots ,\) where the input signal \(\{X_i\}\) satisfies an average power constraint and the noise \(\{Z_i\}\) is a stationary Gaussian process. We are interested in the capacity of the channel with feedback. Despite numerous lower and upper bounds having been reported, except for some special cases, it is an open problem to find the closed form for the feedback capacity. In the paper, we consider the case where the Gaussian noise \(\{Z_i\}\) is a first-order moving average process defined by \(Z_i=W_i+\alpha W_{i-1}\), \(|\alpha |\le 1\), with white Gaussian innovations \(W_i\), \(i=0,1,2,\ldots\). For this channel, Kim (IEEE Trans Inf Theory 52(7):3063–3079, 2006; IEEE Trans Inf Theory 56(1):57–85, 2010) showed that a modified Schalkwijk–Kailath scheme achieves the feedback capacity and obtained the closed form of the feedback capacity. The main aim of the paper is to give a new proof of the optimality of the coding scheme given by Kim. In our proof, decompositions of the input signal \(X_i\) and the Gaussian innovation \(W_i\) into independent components play important roles. For this channel, the minimum decoding error probability decreases with an exponential order which linearly increases with block length.

A Characterization of Guesswork on Swiftly Tilting Curves

Given a collection of strings, each with an associated probability of occurrence, the guesswork of each of them is their position in a list ordered from most likely to least likely, breaking ties arbitrarily. Guesswork is central to several applications in information theory: Average guesswork provides a lower bound on the expected computational cost of a sequential decoder to decode successfully the transmitted message; the complementary cumulative distribution function of guesswork gives the error probability in list decoding; the logarithm of guesswork is the number of bits needed in optimal lossless one-to-one source coding; and guesswork is the number of trials required of an adversary to breach a password protected system in a brute-force attack. In this paper, we consider memoryless string-sources that generate strings consisting of i.i.d. characters drawn from a finite alphabet, and characterize their corresponding guesswork. Our main tool is the tilt operation. We show that the tilt operation on a memoryless string-source parametrizes an exponential family of memoryless string-sources, which we refer to as the tilted family. We provide an operational meaning to the tilted families by proving that two memoryless string-sources result in the same guesswork on all strings of all lengths if and only if their respective categorical distributions belong to the same tilted family. Establishing some general properties of the tilt operation, we generalize the notions of weakly typical set and asymptotic equipartition property to tilted weakly typical sets of different orders. We use this new definition to characterize the large deviations for all atypical strings and characterize the volume of weakly typical sets of different orders. We subsequently build on this characterization to prove large deviation bounds on guesswork and provide an accurate approximation of its PMF.

The Error Probability of Sparse Superposition Codes With Approximate Message Passing Decoding

Sparse superposition codes, or sparse regression codes (SPARCs), are a recent class of codes for reliable communication over the AWGN channel at rates approaching the channel capacity. Approximate message passing (AMP) decoding, a computationally efficient technique for decoding SPARCs, has been proven to be asymptotically capacity-achieving for the AWGN channel. In this paper, we refine the asymptotic result by deriving a large deviations bound on the probability of AMP decoding error. This bound gives insight into the error performance of the AMP decoder for large but finite problem sizes, giving an error exponent as well as guidance on how the code parameters should be chosen at finite block lengths. For an appropriate choice of code parameters, we show that for any fixed rate less than the channel capacity, the decoding error probability decays exponentially in $n/(\log n)^{2T}$, where $T$, the number of AMP iterations required for successful decoding, is bounded in terms of the gap from capacity.

LDPC Codes Over the BEC: Bounds and Decoding Algorithms

The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. A tightened union-type upper bound on the ML decoding error probability based on the precise coefficients of the average weight spectrum is presented. For LDPC codes from the Gallager ensemble and the Richardson–Urbanke ensemble, new upper bounds on the ML decoding performance based on computing the rank of submatrices of the code parity-check matrix are derived. A new lower bound on the ML decoding threshold followed from the latter error probability bound is obtained. An improved lower bound on the error probability for codes with a known estimate on the minimum distance is presented as well. A new low-complexity near-ML decoding algorithm for quasi-cyclic LDPC codes is proposed and simulated. Its performance is compared to the simulated belief propagation and ML decoding performance and simulated performance of the best known improved iterative decoding techniques, as well as, with the derived upper bounds on the ML decoding performance and with decoding thresholds obtained by the density evolution technique.