Decoding Error Probability Research Articles

Decoding error probability of random parity-check matrix ensemble over the erasure channel

AbstractIn this paper we carry out an in-depth study on the average decoding error probability of the random parity-check matrix ensemble over the erasure channel under three decoding principles, namely unambiguous decoding, maximum likelihood decoding and list decoding. We obtain explicit formulas for the average decoding error probabilities of the random parity-check matrix ensemble under these three decoding principles and compute the error exponents. Moreover, for unambiguous decoding, we compute the variance of the decoding error probability of the random parity-check matrix ensemble and the error exponent of the variance, which implies a strong concentration result, that is, roughly speaking, the ratio of the decoding error probability of a random linear code in the ensemble and the average decoding error probability of the ensemble converges to 1 with high probability when the code length goes to infinity.

ESTIMATION OF PROBABILISTIC AND STATISTICAL CHARACTERISTICS OF THE INFORMATIONAL STATE OF A COMMUNICATION CHANNEL

The methods for determining the informational state of a communication channel based on the assessment of probabilistic and statistical characteristics of errors at the channel output are presented. Adaptive information protection methods in digital communication systems, where encoder parameters change depending on the channel state, require the use of network quality control methods based on determining the statistical characteristics of the channel. It is shown that the bit error probability in the channel is constant for the presented error generation process and is independent of the method of dividing information into code blocks. The methods for assessing the statistical characteristics of the channel are based on the topological representation of error generation processes over the length of code blocks. It is demonstrated that, with a fixed code sequence length and a constant bit error probability at the output of the information channel, different error distributions correspond to sets of n-sequences. With a known number of states in the likelihood transition matrix, calculation of observation intervals for counting erroneous blocks is proposed. The presented method of researching statistical characteristics, based on the assumption of error independence, allows for the development of algorithms and procedures for assessing the state of discrete communication channels. The evaluation of potential bounds and statistical characteristics for the decoding error probability enables establishing a connection between the topological characteristics of error sequence partitioning and code parameters. The work confirms that the proposed method allows the synthesis of algorithms for determining code parameters, whose numerical values are determined based on minimizing potential decoding error probabilities.

Intelligent Ultra-Reliable and Low Latency Communications: Security and Flexibility

With the prosperity of emerging applications, the 6 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>th</i></sup> Generation mobile communication systems (6G) is coming at an unimaginable speed. It is expected to provide more intelligent, flexible, and secure services. As an essential pillar of 6G networks, ultra-Reliable Low Latency Communication (uRLLC) has promoted the vigorous development of intelligent communications. However, the existing networks cannot fully satisfy the strict and various requirements of uRLLC services, including delay, reliability and security. Considering the interaction between the physical layer and the upper layer, we propose a Cross-layer Flexible Security Solution (CFSS), which includes initiative waiting strategy, flexible transmission time interval scheduling strategy, and flexible pre-backup transmission strategy. While considering secure communication, CFSS could flexibly provide customized services to the users through cross-layer parameters configuration and resource allocation. In addition, we extend the Stochastic Network Calculus (SNC) modeling to the security field, and use Finite Blocklength Coding (FBC) to analyze the service process of uRLLC. Two cases of FBC are considered comprehensively, namely, given decoding error probability and given transmission rate. Finally, Experienced Meta-Asynchronous Advantage Actor-Critic (EM-A3C) algorithm is proposed to solve the complex optimization problem, the establishment of experience pool effectively improves the algorithm efficiency.

Nonbinary LDPC Coded QAM Signals With Optimized Mapping: Bounds and Simulation Results

This paper studies specific properties of nonbinary low-density parity-check (NB LDPC) codes when used in coded modulation systems. The paper is focused on the practically important NB LDPC codes over the Galois extension fields GF(2m) with m ≤ 6 used with QAM signaling. Performance of NB LDPC coded transmission strongly depends on the mapping of nonbinary symbols to signal constellation points. We obtain a random coding bound on the maximum-likelihood decoding error probability for an ensemble of random irregular NB LDPC codes used with QAM signaling for specific symbol-to-signal point mappings. This bound is based on the ensemble average squared Euclidean distance spectra derived for these mappings. The simulation results for the belief-propagation decoding in the coded modulation schemes with the NB quasi-cyclic (QC)-LDPC codes under different mappings are given. Comparisons with the optimized binary QC-LDPC codes in the WiFi and 5G standards, as well as with the new bound, are performed.

Intelligent Resource Allocation for Edge-Cloud Collaborative Networks: A Hybrid DDPG-D3QN Approach

Mobile edge computing (MEC) has recently emerged as an effective paradigm for computation-intensive and delay-critical applications supported by Internet of Things (IoT) devices. However, the computational resources at MEC servers are normally much smaller compared with the remote cloud server (CS). To handle the ever-increasing IoT devices and applications, the collaborative edge and cloud computing should be jointly exploited. Further, with finite block length (FBL) utilized in URLLC-supported networks, the coding error probability cannot be ignored. On these grounds, this paper investigates the dynamic offloading of FBL packets in an edge-cloud collaborative MEC system consisting of multi-mobile IoT devices (MIDs) with energy harvesting (EH), multi-edge servers, and one CS in a dynamic environment. The optimization problem is formulated to minimize the average long-term service cost defined as the weighted sum of MID energy consumption and service delay (including the uploading transmission delay, the handover cost, and the execution delay for the partial offloaded part, the local execution delay for the local processing part), with the constraints of the available resource, the energy causality, the allowable service delay, and the maximum decoding error probability. To address the problem involving both discrete and continuous variables, we propose a multi-device hybrid decision-based deep reinforcement learning (DRL) solution, named DDPG-D3QN algorithm, where the deep deterministic policy gradient (DDPG) and dueling double deep Q networks (D3QN) are invoked to tackle continuous and discrete action domains, respectively. Specifically, we improve the actor-critic structure of DDPG by combining D3QN. It utilizes the actor part of DDPG to search for the optimal offloading rate and power control of local execution. Meanwhile, it combines the critic part of DDPG with D3QN to select the optimal server for offloading. Simulation results demonstrate the proposed DDPG-D3QN algorithm has better stability and faster convergence while achieving higher rewards than the existing DRL-based methods. Furthermore, the edge-cloud collaboration has been proven to attain improved performance when compared with other offloading schemes with no collaboration between edge and cloud.

Average age upon decisions with truncated HARQ and optimization in the finite blocklength regime

We consider an update-and-decide IoT-based wireless network, where information packets generated from dual sources are co-stored in the transmitter’s buffer, while decisions are made at the destination. Two practical assumptions about the communications between the transmitter and destination are taken into account: the communications are operating with finite blocklength (FBL) codes, and truncated hybrid automatic repeat request (HARQ) schemes are exploited to improve the FBL reliability, i.e., the number of allowed rounds of (re)transmissions is finite. For the first time, this paper characterizes the timeliness of status updates, namely age upon decisions (AuD) (which highlights the timeliness of the information at decisions in comparison to the concept of age of information), for such truncated HARQ-assisted wireless network. First, we characterize the inter-arrival time between two adjacent successfully transmitted packets, while taking into consideration the preemption policy and the randomness of the number of preempted packets from the same source. In particular, the probability density function, statistical performance of such inter-arrival time are derived. Following these characterizations, we propose a new approach to determine the average AuD and obtain a closed-form expression accordingly. Subsequently, a joint blocklength and arrival rate optimization problem is considered to minimize the obtained average AuD. Before addressing the formulated problem, we prove the convexity of decoding error probability in CC-HARQ and IR-HARQ with respect to blocklength. Then, we prove the convexity of average AuD with respect to blocklength and arrival rate, respectively. By an efficient alternating algorithm, we obtain a efficient solution. Via simulations, we evaluate the performance and conclude a set of guidelines for designs on the considered network.

Irregular repetition slotted Aloha with multiuser detection: A density evolution analysis

Irregular repetition slotted Aloha (IRSA) has shown significant advantages as a modern technique for uncoordinated random access with massive number of users due to its capability of achieving theoretically a throughput of 1 packet per slot. When the receiver has also the multi-packet reception of multi-user (MUD) detection property, by applying successive interference cancellation, IRSA also obtains very low packet loss probabilities at low traffic loads, but is unable in general to achieve a normalized throughput close to 1. In this paper, we reconsider the case of IRSA with k-MUD receivers and derive the general density evolution equations for the non-asymptotic analysis of the packet loss rate, for arbitrary frame lengths and two operational variants: frame-structured and frameless transmissions. The first one defers transmission attempts until the beginning of the next frame of slots, while the second allows transmission immediately after a packet arrival. Next, using the potential function, we give new capacity bounds on the capacity of the system, showing the threshold arrival rate for zero decoding error probability. Our numerical results illustrate performance in terms of throughput and average delay for k-MUD IRSA with finite memory at the receiver, and also with bounded maximum delay.

Trade Reliability for Security: Leakage-Failure Probability Minimization for Machine-Type Communications in URLLC

How to provide information security while fulfilling ultra reliability and low-latency requirements is one of the major concerns for enabling the next generation of ultra-reliable and low-latency communications service (xURLLC), specially in machine-type communications. In this work, we investigate the reliability-security tradeoff by defining the leakage-failure probability, a metric that jointly characterizes both reliability and security performances for short-packet transmissions. We discover that the system performance can be enhanced, counter-intuitively, by allocating fewer resources for the transmission with finite blocklength (FBL) codes. In order to solve the corresponding optimization problem for the joint resource allocation, we propose an optimization framework, that leverages lower-bounded approximations for the decoding error probability in the FBL regime. We characterize the convexity of the reformulated problem and establish an efficient iterative searching method, the convergence of which is guaranteed. To show the extendability of the framework, we further discuss the blocklength allocation schemes with practical requirements of reliable-secure performance, as well as the transmissions with the statistical channel state information (CSI). Numerical results verify the accuracy of the proposed approach and demonstrate the reliability-security tradeoff under various setups.

Secure Finite Blocklength Coding Schemes for Reconfigurable Intelligent Surface Aided Wireless Channels With Feedback

Ultra-reliable low-latency communication (URLLC) and reconfigurable intelligent surface (RIS) aided communication are two key technologies in future wireless communications. However, secure URLLC over RIS-adied communication channels receives little attention in the literature. In this paper, we propose finite blocklength (FBL) coding schemes for RIS aided SISO/SIMO/MIMO systems in the presence of an eavesdropper (no direct link between the transceiver), which are based on an existing coding scheme for the point-to-point white Gaussian channel with noiseless feedback. Then, we show that the proposed schemes are self-secure when the blocklengths are larger than certain thresholds. Finally, numerical results show that for given decoding error probability and secrecy level, the required coding blocklengths of our proposed schemes are extremely short, and the secrecy capacities of the RIS-aided systems without channel feedback are significantly enhanced by our feedback schemes.

Conditional Entropy-Based Construction of Multilevel Polar-Coded Modulation With Probabilistic Shaping

Code construction is a critical issue for polar-coded systems to ensure competitive performance. In this letter, we propose a conditional entropy-based method to construct multilevel polar-coded modulation (MLC-PCM) with probabilistic shaping. More specifically, we allocate the bit positions in accordance with their conditional entropies induced by channel and source polarization. We show that a surrogate channel can be used to determine the frozen set in each component polar code efficiently. The remaining positions are assigned to the information and shaping bits by the source Bhattacharyya parameter, where the shaping bits are used to achieve non-uniform channel inputs. Approximate bounds are also derived to evaluate the decoding error probability of the probabilistically shaped MLC-PCM.

Implications of Power Allocation Factors on the Performance of Ergodic Sum Rate in Cooperative Device-to-Device Systems with NOMA

The power allocation issue for cooperative device-to-device (D2D) systems with non-orthogonal multiple access (NOMA) is examined in this paper. In cooperative device-to-device (D2D) NOMA systems, communication occurs in two phases: the direct transmission slot, or the path from the base station to user destinations, and the relaying slot, or the path from the relay (near the user), with different power allocation factors to improve the ergodic sum rate. It is suggested that power allocation considerations affect how well the ergodic sum rate performs with different decoding techniques. The decoding techniques include Reed Solomon's (RS) encoded single signal decoding technique and Reed Solomon's (RS) encoded maximum ratio combining (MRC) decoding technique. The error probability of successive decoding will increase if any errors occur during the successive interference cancellation (SIC) procedure at any user. In order to detect and correct multiple symbol errors in a Rayleigh fading environment, RS codes are used in the system architecture for error detection and correction. Through the results of the simulation, it is demonstrated that the proposed approach performs much better than the existing work for the fixed values of the power allocation parameters.

Power and rate control in wireless communication systems with energy harvesting and rateless codes

In this paper, for a wireless communication system with energy harvesting and rateless error correction codes, the joint optimization of transmit power, modulation scheme and code rate to maximize the long-term average achievable transmission rate under the constraint of available energy is studied. The method is given first to determine the codeword length (or code rate) for a signal-to-noise ratio (SNR) under the constraint of a pre-defined decoding error probability. Then the formula of the actual transmission rate is deduced with a specific modulation and code rate, and the optimization problem to maximize the long-term average actual transmission rate is constructed under the constraints of available harvested energy and the decoding complexity of the rateless code. Since energy harvesting and channel fading are both stochastic processes, the optimization problem is difficult to solve. By using the Lyapunov optimization framework, the original long-term optimization problem is transformed into a per time slot one. Then an efficient numerical method is proposed to obtain the solution to the problem. The proposed algorithm is verified by simulation, and the results show that the proposed algorithm can achieve a higher average actual transmission rate than the comparison algorithms aiming at optimizing the channel capacity.

Neural decoders with permutation invariant structure

Neural decoders were introduced as a generalization of the classic Belief Propagation (BP) decoding algorithms. In this work, we propose several neural decoders with different permutation invariant structures for BCH codes and punctured RM codes. Firstly, we propose the cyclically equivariant neural decoder which makes use of the cyclically invariant structure of these two codes. Next, we propose an affine equivariant neural decoder utilizing the affine invariant structure of those two codes. Both these two decoders outperform previous neural decoders when decoding cyclic codes. The affine decoder achieves a smaller decoding error probability than the cyclic decoder, but it usually requires a longer running time. Similar to using the property of the affine invariant property of extended BCH codes and RM codes, we propose the list decoding version of the cyclic decoder that can significantly reduce the frame error rate(FER) for these two codes. For certain high-rate codes, the gap between the list decoder and the Maximum Likelihood decoder is less than 0.1 dB when measured by FER.

Concatenated Permutation Codes under Chebyshev Distance

Permutation codes are error-correcting codes over symmetric groups. We focus on permutation codes under Chebyshev (ℓ∞) distance. A permutation code invented by Kløve et al. is of length n, size 2n-d and, minimum distance d. We denote the code by φn,d. This code is the largest known code of length n and minimum Chebyshev distance d > n/2 so far, to the best of the authors knowledge. They also devised efficient encoding and hard-decision decoding (HDD) algorithms that outperform the bounded distance decoding. In this paper, we derive a tight upper bound of decoding error probability of HDD. By factor graph formalization, we derive an efficient maximum a-posterior probability decoding algorithm for φn,d. We explore concatenating permutation codes of φn,d=0 with binary outer codes for more robust error correction. A naturally induced pseudo distance over binary outer codes successfully characterizes Chebyshev distance of concatenated permutation codes. Using this distance, we upper-bound the minimum Chebyshev distance of concatenated codes. We discover how to concatenate binary linear codes to achieve the upper bound. We derive the distance distribution of concatenated permutation codes with random outer codes. We demonstrate that the sum-product decoding performance of concatenated codes with outer low-density parity-check codes outperforms conventional schemes.

Usage of LDPC Codes in a Gilbert Channel

Although low-density parity-check (LDPC) codes in modern communication standards have been extensively studied over a memoryless channel, their burst error correction capacity in channels with memory has yet to be thoroughly analyzed. The conventional approach to transmission in channels with memory uses interleaving within a buffer of several codewords. However, such an approach reduces the efficiency of the redundancy embedded by the error-correcting code. It is known from information theory that considering channel memory during decoding allows the transmission rate to be increased. An evaluation of the decoding error probability of different types of low-density parity-check codes in channels with memory is presented along with estimates of minimum distance and burst error correction capability for the considered codes. The decoding error probability is estimated for conventional decoding with deinterleaving and decoding taking channel memory into account. The decoding error probability is estimated for several parameters of a channel with memory and different buffer lengths. The obtained results reveal the absence of the unique decoding approach for all parameters of the channel with memory. The best decoding error probability is determined by the degree of channel memory correlation.

Optimization of Effective Throughput in NOMA-Based Cognitive UAV Short-Packet Communication

Unmanned aerial vehicles (UAVs) are considered an important component of 6G wireless technology. However, there are many challenges to the employment of UAVs, one of which is spectrum scarcity. To address this challenge, non-orthogonal multiple access (NOMA) and cognitive radio (CR) techniques are employed in UAV short-packet communication systems. In this paper, we consider a NOMA-based cognitive UAV short-packet communication system. Firstly, a mathematical expression for the effective throughput of the secondary users is derived. Then, we aim to maximize the effective throughput of the far secondary user by optimizing the sensing time, power allocation, and information bits under the constraints of the transmission power and effective decoding error probability. A joint optimization algorithm is used to solve this problem, where the bisection method and the one-dimensional linear search algorithm are used to solve the subproblem. The simulation results show that the proposed algorithm has low complexity and similar performance compared to the exhaustive method. In addition, the necessity of joint optimization is shown in the simulation results.

Decoding of linear codes for single error bursts correction based on the determination of certain events

Introduction: In modern systems for communication, data storage and processing the error-correction capability of codes are estimated for memoryless channels. In real channels the noise is correlated, which leads to grouping error in bursts. A traditional method to fight this phenomenon is channel decorrelation, which does not allow developing of coding schemes, mostly utilizing the channel capacity. Thus the development of bursts decoding algorithms for arbitrary linear codes is the actual task. Purpose: To develop a single error burst decoding algorithm for linear codes, to estimate the decoding error probability and computational complexity. Results: Two approaches are proposed to burst error correction. The first one is based on combining the window sliding modification of well-known bit-flipping algorithm with preliminary analysis of the structure of parity check matrix. The second one is based on the recursive procedure of constructing the sequence of certain events which, in the worst case, performs the exhaustive search of error bursts, but in many cases the search may be significantly decreased by using the proposed heuristics. The proposed recursive decoding algorithm allows a guaranteed correction of any single error bursts within burst-correction capability of the code, and in many cases beyond the burst-correction capability. The complexity of this algorithm is significantly lower than that of a bit flipping algorithm if the parity-check matrix of the code is sparse enough. An alternative hybrid decoding algorithm is proposed utilizing the bit-flipping approach and showing the error probability and completion time comparable to the recursive algorithm, however, in this case the possibility of a guaranteed burst correction hardly can be proved. Practical relevance: The proposed decoding methods may be used in modern and perspective communication systems, allowing energy saving and increasing reliability of data transmission by better error performance and computational complexity.

MIND: Maximum Mutual Information Based Neural Decoder

We are assisting at a growing interest in the development of learning architectures with application to digital communication systems. Herein, we consider the detection/decoding problem. We aim at developing an optimal neural architecture for such a task. The definition of the optimal criterion is a fundamental step. We propose to use the mutual information (MI) of the channel input-output signal pair, which yields to the minimization of the a-posteriori information of the transmitted codeword given the communication channel output observation. The computation of the a-posteriori information is a formidable task, and for the majority of channels it is unknown. Therefore, it has to be learned. For such an objective, we propose a novel neural estimator based on a discriminative formulation. This leads to the derivation of the mutual information neural decoder (MIND). The developed neural architecture is capable not only to solve the decoding problem in unknown channels, but also to return an estimate of the average MI achieved with the coding scheme, as well as the decoding error probability. Several numerical results are reported and compared with maximum a-posteriori and maximum likelihood decoding strategies.

Passive Covert Communications Based on Reconfigurable Intelligent Surface

In this letter, a reconfigurable intelligent surface (RIS)-based passive covert communication scheme is proposed, where source node Alice covertly transmits information to receiver Bob by using a RIS and reflecting the incident signals from an ambient radio frequency source. The key idea is to adjust the phase shifts of the RIS to align the phases of the received reflected signals at Bob and meanwhile to adjust the reflection amplitude to satisfy the covert constraint. The detection error probability at warden Willie and the decoding error probability at Bob in Rayleigh fading channels are derived analytically. It is shown that the proposed scheme can enhance transmission reliability while satisfying the covert constraint by increasing RIS’s elements.

Proactive Eavesdropping via Jamming Over Short Packet Suspicious Communications With Finite Blocklength

Short packet communications play key roles in the Internet-of-Things. Conventional Shannon’s coding theorem is not applicable for short packet communications, and the achievable rate in the finite blocklength regime is related to the blocklength and the decoding error probability. Contrary to conventional physical layer security, wireless information surveillance assumes that the communication users are suspicious users and the eavesdroppers are legitimate monitors, and proactive eavesdropping via jamming has been proposed to improve the eavesdropping performance. Existing works on proactive eavesdropping ignored the scenario when the suspicious users adopt the short packet communications. Thus, this paper tries to develop effective proactive eavesdropping schemes suitable for the short packet suspicious communications. Under the truncated channel inversion power allocation and the modified constant power allocation policies at the suspicious source, the problems of jamming power allocation for maximizing the monitoring success probability subject to the average transmit power constraint at the monitor are investigated. Based on the Dinkelbach-type algorithm, the Lagrange duality method and a novel tractable approximate expression for the decoding error probability, we derive suboptimal solutions to the problems. Simulation results demonstrate the effectiveness of the proposed solutions compared to various benchmark algorithms in existing literature.