Finite Blocklength Codes Research Articles

Exact Equivocation Expressions for Wiretap Coding Over Erasure Channel Models

Traditional security analysis of wiretap codes requires evaluation of equivocation in the asymptote as the code blocklength tends to infinity. Finite blocklength codes, however, require exact expressions for equivocation so as to allow for comparison of parameterized codes across different code constructions or within the same construction. In this letter, we present two exact equivocation expressions for coset coding over the wiretap channel model with binary erasure channels (BECs) for both the main channel and the eavesdropper’s channel. The expressions are functions of the algebraic structure of the binary wiretap codes, and they also hold for the special case when the main channel is noiseless.

Power-Time Splitting-Based Non-Linear Energy Harvesting in FD Short-Packet Communications

This paper investigates the reliability, goodput and energy efficiency (EE) performance of a energy harvesting (EH) based full-duplex (FD) cooperative internet-of-things (IoT) network for short-packet communications. We derive approximate closed-form expressions for the block error rate (BLER) and outage probability considering hybrid power-time splitting (PTS)-based practical non-linear EH model having the characteristics of sensitivity and threshold. Based on the derived results, we compare the performance of the considered FD non-linear EH based system with linear one. Moreover, we provide the system goodput and EE analysis using finite blocklength codes. Our analysis reveals key insights related to the impact of blocklength, packet size, self-interference and EH parameters on the reliability and EE performance of the considered IoT network.

Statistical Delay and Error-Rate Bounded QoS Provisioning Over mmWave Cell-Free M-MIMO and FBC-HARQ-IR Based 6G Wireless Networks

As a new and dominating 6G mobile-networks’ service class for time-sensitive traffics, massive ultra-reliable and low latency communications (mURLLC) has received tremendous attention. One of key 6G enabling-techniques for achieving mURLLC lies in how to efficiently support statistical delay and error-rate bounded quality-of-services (QoS) provisioning for real-time data-transmissions over time-varying wireless networks. Towards this end, several emerging wireless techniques, including finite blocklength coding (FBC), hybrid automatic repeat request with incremental redundancy (HARQ-IR) protocol, millimeter wave (mmWave), cell-free (CF) massive multiple-input multiple-output (m-MIMO), etc., have been shown to be 6G promising enablers to significantly improve various QoS performances. However, integrating these techniques with the statistical delay and error-rate bounded QoS provisioning theory for mURLLC has imposed many new difficulties not encountered before. To overcome these challenges, in this paper we propose the statistical delay-and-error-rate-bounded QoS provisioning system architecture over mmWave user-centric CF m-MIMO and FBC-HARQ-IR based 6G wireless networks. First, we establish the comprehensive system models by accurately characterizing the integrations of above-described 6G promising techniques with statistical QoS provisioning theory. Then, we integrate FBC with HARQ-IR protocol to derive the channel capacity as a function of error probability. Finally, we obtain the closed-form expressions for effective capacities under our proposed schemes. We also conduct a set of simulations to validate and evaluate our proposed FBC-HARQ-IR based mmWave user-centric CF m-MIMO schemes.

Optimal Resource Allocation in Ground Wireless Networks Supporting Unmanned Aerial Vehicle Transmissions

We consider a fully-loaded ground wireless network supporting unmanned aerial vehicle (UAV) transmission services. To enable the overload transmissions to a ground user (GU) and a UAV, two transmission schemes are employed, namely non-orthogonal multiple access (NOMA) and relaying, depending on whether or not the GU and UAV are served simultaneously. Under the assumption of the system operating with infinite blocklength (IBL) codes, the IBL throughputs of both the GU and the UAV are derived under the two schemes. More importantly, we also consider the scenario in which data packets are transmitted via finite blocklength (FBL) codes, i.e., data transmission to both the UAV and the GU is performed under low-latency and high reliability constraints. In this setting, the FBL throughputs are characterized again considering the two schemes of NOMA and relaying. Following the IBL and FBL throughput characterizations, optimal resource allocation designs are subsequently proposed to maximize the UAV throughput while guaranteeing the throughput of the cellular user. Moreover, we prove that the relaying scheme is able to provide transmission service to the UAV while improving the GU's performance, and that the relaying scheme potentially offers a higher throughput to the UAV in the FBL regime than in the IBL regime. On the other hand, the NOMA scheme provides a higher UAV throughput (than relaying) by slightly sacrificing the GU's performance.

A Critical MTC Resource Allocation Approach for LTE Networks With Finite Blocklength Codes

Critical machine-type communications (cMTC) are targeted as a major use case in the design of the fifth generation (5G) cellular systems. In this regard, the third-generation partnership project (3GPP) has introduced several enhancements to evolve the LTE standard to meet the 5G requirements. Shortened transmission time intervals (sTTIs) are considered one of the most significant improvements proposed to satisfy the stringent latency requirements of cMTC. However, this entails several challenges to the resource allocation and scheduling process. In this paper, we address the resource allocation and scheduling of cMTC in LTE networks. The impact on the conventional human-type communications (HTC) is considered while adopting a puncturing scheduling technique. In addition, the reliability of the cMTC is ensured by utilizing the finite blocklength coding analysis to model the transmission errors and the effective bandwidth and effective capacity concepts to guarantee the queuing delay statistics of the cMTC packets. Moreover, we propose matching theory-based computationally efficient algorithms to solve the formulated optimal resource allocation problems with reduced complexity. The proposed methods are analyzed from a practical perspective. Extensive simulations show a close-to-optimal performance of the proposed schemes while outperforming other scheduling algorithms from the literature.

Performance Analysis of Distributed Antenna System for Downlink Ultrareliable Low-Latency Communications

In this article, we consider a distributed antenna system to enable the downlink ultrareliable and low-latency communications (URLLC) for the industrial Internet of Things. To satisfy the low latency, the short packet length is exploited and accordingly, the achievable rate under the finite blocklength codes is considered in the analysis of the packet loss probability in downlink URLLC distributed antenna system. Specifically, the packet loss probability is approximated as a sum of the channel OP and the finite blocklength coding error probability. By using a stochastic geometry approach, we analytically derive the packet loss probability in terms of the system parameters (i.e., the densities of the DA ports and the receiving sensor nodes, the number of receive antennas, and the packet size/duration, etc.), when the sensor nodes and the DA ports are randomly distributed in a given area. From the analytic results, we show how to optimize the short blocklength coding error probability to minimize the overall packet loss probability. Furthermore, we also derive the required DA port density to satisfy the packet loss probability constraint for a given distributed antenna system parameters, which gives us a useful insight into the design of downlink distributed antenna system for URLLC.

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.

Transmission Energy Minimization for Heterogeneous Low-Latency NOMA Downlink

This paper investigates the transmission energy minimization problem for the two-user downlink with strictly heterogeneous latency constraints. To cope with the latency constraints and to explicitly specify the trade-off between blocklength (latency) and reliability the normal approximation of the capacity of finite blocklength codes (FBCs) is adopted, in contrast to the classical Shannon capacity formula. We first consider the non-orthogonal multiple access (NOMA) based transmission scheme. However, due to heterogeneous latency constraints and channel conditions at receivers, the conventional successive interference cancellation may be infeasible. We thus study the problem by considering heterogeneous receiver conditions under different interference mitigation schemes and solve the corresponding NOMA design problems. It is shown that, though the energy function is not convex and does not have closed form expression, the studied NOMA problems can be globally solved semi-analytically and with low complexity. Moreover, we propose a hybrid transmission scheme that combines the time division multiple access (TDMA) and NOMA. Specifically, the hybrid scheme can judiciously perform bit and time allocation and take TDMA and NOMA as two special instances. To handle the more challenging hybrid design problem, we propose a concave approximation of the FBC rate/capacity formula, by which we obtain computationally efficient and high-quality solutions. Simulation results show that the hybrid scheme can achieve considerable transmission energy saving compared with both pure NOMA and TDMA schemes.

Max-min fairness in downlink non-orthogonal multiple access with short packet communications

In this paper, the performance of non-orthogonal multiple access (NOMA) technique for communication based on finite blocklength (FBL) codes is studied. NOMA, by co-serving multi users has great potential for achieving low-latency and better spectral efficiency rather than conventional orthogonal multiple access (OMA) techniques. Our goal is to have optimal power allocation to attain fair throughput in a DL-NOMA scenario. The optimization problem is formulated and an analytical approach using optimal solution search algorithm is introduced. Performance of the proposed NOMA system is compared with an OMA scheme which is benefiting from optimal power and blocklength allocation as well. Numerical results show that NOMA significantly improves the users’ fair throughput in FBL regime.

Heterogeneous Statistical-QoS Driven Resource Allocation Over mmWave Massive-MIMO Based 5G Mobile Wireless Networks in the Non-Asymptotic Regime

The statistical delay-bounded quality-of-service (QoS) theory has been developed to efficiently support multimedia transmissions over 5G wireless networks. On the other hand, unlike in Shannon’s information-theoretic formalism requiring infinite blocklength, finite blocklength coding (FBC) has recently emerged for error control in the non-asymptotic regime, guaranteeing stringent statistical QoS requirements in terms of both latency and reliability for ultra-reliable low-latency communications (URLLC) in 5G services. Moreover, integrated with FBC, millimeter wave (mmWave) massive multi-input multi-output (m-MIMO) schemes have been designed to significantly improve the performance in guaranteeing delay/error-rate bounded QoS. However, due to the complexity of modeling and solving the optimization problems over mmWave m-MIMO fading channels in the non-asymptotic error-control regime, it is challenging to derive an optimal resource allocation policy for maximizing $\epsilon$ -effective capacity to guarantee statistical delay/error-rate bounded QoS. To overcome the above problems, in this paper we propose heterogeneous statistical-QoS driven resource allocation policies for mmWave m-MIMO based 5G wireless networks in both asymptotic and non-asymptotic regimes. In particular, we develop an mmWave m-MIMO based 5G wireless networks model to optimize the effective capacity for our proposed schemes. Our simulations show that our proposed schemes outperform the existing schemes in guaranteeing heterogeneous statistical delay/error-rate bounded QoS.

Performance Bounds of Concatenated Polar Coding Schemes

A concatenated coding scheme over binary memoryless symmetric (BMS) channels using a polarization transformation followed by outer sub-codes is analyzed. Achievable error exponents and upper bounds on the error rate are derived. The first bound is obtained using outer codes which are typical random linear codes. As a byproduct of this bound, it determines the rates of the outer codes. A lower bound on the error exponent that holds for all BMS channels with a given capacity is then derived. Improved bounds and approximations for finite blocklength codes using channel dispersions (normal approximation), as well as converse and approximate converse results, are also obtained. The bounds are compared with actual simulation results from the literature. For the cases considered, when transmitting over the binary input additive white Gaussian noise channel, there was only a small gap between the channel dispersion-based approximation and the actual error rate of concatenated BCH-polar codes.

Secure Short-Packet Communications for Mission-Critical IoT Applications

In pervasive Internet of Things (IoT) applications, the use of short packets is expected to meet the stringent latency requirement in ultra-reliable low-latency communications; however, the incurred security issues and the impact of finite blocklength coding on the physical-layer security have not been well understood. This paper comprehensively investigates the performance of secure short-packet communications in a mission-critical IoT system with an external multi-antenna eavesdropper. An analytical framework is proposed to approximate the average achievable secrecy throughput of the system with finite blocklength coding. To gain more insight, a simple case with a single-antenna access point (AP) is considered first, in which the secrecy throughput is approximated in a closed form. Based on that result, the optimal blocklengths to maximize the secrecy throughput with and without the reliability and latency constraints, respectively, are derived. For the case with a multi-antenna AP, following the proposed analytical framework, closed-form approximations for the secrecy throughput are obtained under both beamforming and artificial-noise-aided transmission schemes. Numerical results verify the accuracy of the proposed approximations and illustrate the impact of the system parameters on the tradeoff between transmission latency and reliability under the secrecy constraint.

Optimal Memory Order of Memory-Based LT Encoders for Finite Block-Length Codes Over Binary Erasure Channels

Memory-based LT encoders (MBLTEs) have been shown to have better performance than the regular LT encoder in terms of bit error rate (BER) and decoding convergence speed. In this paper, we explore the entire family of MBLTEs for finite block-length codes over the binary erasure channel (BEC). We propose an algorithm to extend the first and second order MBLTE approach to an arbitrary i-th order MBLTE. We analyze the performance of such encoders mathematically by characterizing the expected accumulated number of recovered variable nodes at each decoding round. We define the threshold of the memory-based encoding method (MBEM) and show that the performance of MBLTEs increases as the memory order increases up to the point where this threshold is achieved. Beyond this point, we show that the performance of MBLTEs saturates if the channel erasure probability is zero and degrades otherwise. We formulate an optimization problem to solve for the optimal memory order based on whether or not the MBEM threshold is achieved. We present an extensive set of numerical results. These show agreement between our analysis and computer simulations. They also show that our optimization problem is efficient in determining the optimal memory order of MBLTEs in terms of decoding convergence speed, BER/frame-error-rate, and error floor.

SWIPT-Enabled Relaying in IoT Networks Operating With Finite Blocklength Codes

This paper considers simultaneous wireless information and power transfer (SWIPT) mechanisms in a relaying-assisted ultra-reliable low latency communication network operating with finite blocklength codes. The reliability of the network is maximized by the optimal selection of SWIPT parameters under both a power splitting (PS) protocol and a time switching (TS) protocol. In addition, we propose a protocol to improve the reliability performance by introducing a tradeoff between the PS and TS protocols. To further improve the reliability, a joint design is provided, which aligns the optimal selection of SWIPT parameters together with a blocklength allocation between two relaying hops. Via simulations, we validate our analytical model and show that the proposed algorithm achieves the same performance as that obtained with exhaustive search. In addition, we evaluate the considered network, and characterize the impact of blocklength, transmit power, and packet size on the reliability of the considered SWIPT-enabled relaying network. Finally, the performance advantages of the proposed protocol (in comparison with the PS and TS protocols) and the proposed joint designs are investigated.

Fast HARQ Over Finite Blocklength Codes: A Technique for Low-Latency Reliable Communication

This paper studies the performance of delay-constrained hybrid automatic repeat request HARQ protocols. Particularly, we propose a fast HARQ protocol where, to increase the end-to-end throughput, some HARQ feedback signals and successive message decodings are omitted. Considering quasi-static channels and a bursty communication model, we derive closed-form expressions for the message decoding probabilities as well as the throughput, the expected delay and the error probability of the HARQ setups. The analysis is based on recent results on the achievable rates of finite-length codes and shows the effect of the codeword length on the system performance. Moreover, we evaluate the effect of various parameters such as imperfect channel estimation and hardware on the system performance. As demonstrated, the proposed fast HARQ protocol reduces the packet transmission delay considerably, compared to state-of-the-art HARQ schemes. For example, with typical message decoding delay profiles and a maximum of 2,...,5 transmission rounds, the proposed fast HARQ protocol can improve the expected delay, compared to standard HARQ, by 27, 42, 52 and 60%, respectively, independently of the code rate/fading model.

On the Throughput of Large-but-Finite MIMO Networks Using Schedulers

This paper studies the sum throughput of the {multi-user} multiple-input-single-output (MISO) networks in the cases with large but finite number of transmit antennas and users. Considering continuous and bursty communication scenarios with different users' data request probabilities, we derive quasi-closed-form expressions for the maximum achievable throughput of the networks using optimal schedulers. The results are obtained in various cases with different levels of interference cancellation. Also, we develop an efficient scheduling scheme using genetic algorithms (GAs), and evaluate the effect of different parameters, such as channel/precoding models, number of antennas/users, scheduling costs and power amplifiers' efficiency, on the system performance. Finally, we use the recent results on the achievable rates of finite block-length codes to analyze the system performance in the cases with short packets. As demonstrated, the proposed GA-based scheduler reaches (almost) the same throughput as in the exhaustive search-based optimal scheduler, with substantially less implementation complexity. Moreover, the power amplifiers' inefficiency and the scheduling delay affect the performance of the scheduling-based systems significantly.

Resource allocation for ultra-reliable low latency communications in sparse code multiple access networks

In this paper, we propose an optimal resource allocation policy for sparse code multiple access (SCMA) networks supporting ultra-reliable low-latency communications (URLLC). The network is assumed to operate with finite blocklength (FBL) codes, which is opposed to the classical information-theoretic works with infinite blocklength (IBL) codes. In particular, we aim at maximizing the average transmission rate in the FBL regime while guaranteeing the transmission reliability. A joint design is proposed, which combines the power allocation with the codebook assignment. The convexity of the corresponding optimization problem is analyzed and an iterative search algorithm is further provided. We study the impact of reliability and short blocklength constraints on the performance of the proposed optimal resource allocation policy through numerical simulations. In addition, we evaluate the FBL performance of the proposed joint design in comparison to the scenario with an IBL assumption.

Ultra-Reliable Short-Packet Communications: Half-Duplex or Full-Duplex Relaying?

This letter analyzes and compares the performance of full-duplex relaying (FDR) and half-duplex relaying (HDR) for ultra-reliable short-packet communications. Specifically, we derive both approximate and asymptotic closed-form expressions of the block error rate (BLER) for FDR and HDR using short packets with finite blocklength codes. We define and attain a closed-form expression of a critical BLER, which can be used to efficiently determine the optimal duplex mode for ultra-reliable low latency communication scenarios. Our results unveil that FDR is more appealing to the system with relatively lower transmit power constraint, less stringent BLER requirement and stronger loop interference suppression.

Delay-Sensitive Area Spectral Efficiency: A Performance Metric for Delay-Constrained Green Networks

This paper introduces a new metric, referred to as delay-sensitive area spectral efficiency (DASE), to analyze the performance of delay-constrained wireless networks. We study DASE in different point-to-point, spectrum sharing, interference, and Poisson-point process-based dense network configurations and with different levels of channel state information (CSI) at the transmitters. Also, we determine the optimal rates/powers optimizing DASE. Finally, we use some recent results on finite block-length codes to analyze the effect of the codewords length on the network DASE. As demonstrated, DASE is a useful metric for analyzing delay-sensitive green networks. Moreover, adaptive power allocation and partial CSI feedback are powerful tools for performance improvement in green networks.

Delay Minimization in Real-Time Communications With Joint Buffering and Coding

We present a closed-form expression for the minimal delay that is achievable in a setting that combines a buffer and an erasure code, used to mitigate the packet delay variance. The erasure code is modeled according to the recent information-theoretic results on finite block length codes. Evaluations reveal that accurate knowledge of the network parameters is essential for optimal operation. Moreover, it is shown that, when the network packet delay variance is large, the buffer delay becomes negligible. Therefore, in this case, the delay budget should be spent mainly on the erasure code.