Code Block Length Research Articles

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.

A Study of FqR-Cyclic Codes and Their Applications in Constructing Quantum Codes

Let R = F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> + uF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> + vF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> + uvF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> , with u <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = u, v <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = v, uv = vu, where q = p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> for a positive integer m and an odd prime p. We study the algebraic structure of F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> R-cyclic codes of block length (r, s). These codes can be viewed as R[x]-submodules of F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> [x]/(x <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> - 1) × R[x]/(x <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sup> - 1). For this family of codes we discuss the generator polynomials and minimal generating sets. We study the algebraic structure of separable codes. Further, we discuss the duality of this family of codes and determine their generator polynomials. We obtain several optimal and near-optimal codes from this study. As applications, we discuss a construction of quantum error-correcting codes (QECCs) from F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> R-cyclic codes and construct some good QECCs.

An Efficient Polar Coding Scheme for Uplink Data Transmission in Narrowband Internet of Things Systems

Narrowband Internet of Things (NB-IoT) is an emerging IoT cellular-based wireless technology that builds based on the existing LTE standard to extend its network coverage suited for Low Power Wide Area Network (LPWAN) connectivity. In the NB-IoT system, LTE turbo codes and Cyclic Redundancy Check (CRC) codes are adopted as the main channel coding technique for Narrowband Physical Uplink Shared Channel (NPUSCH). However, turbo codes require iterative decoding algorithm at the expense of high computation complexity of decoding hence is crucial to achieving the LPWAN requirement of NB-IoT systems. Polar codes are best suited in this regard due to its capacity approaching and complexity reduction in short block length code. In this paper, we proposed an efficient polar coding technique using the Belief Propagation (BP) decoding algorithm for uplink data transmission on the NPUSCH channel. Furthermore, the BP algorithm is incorporated with the CRC stoppage criterion to decrease the number of decoding iteration and reduce computational complexity. In this scheme, single-tone numerology of NPUSCH using 3.75 kHz and 15 kHz subcarrier spacing is adopted. Then, the encoded data is generated with different NPUSCH resources. The theoretical formulation and simulation demonstrate that the proposed scheme provides better error rate performance over the adopted LTE turbo codes and other polar decoding algorithms while reducing the computational complexity.

Cyclic Properties and Pipeline Implementation of the Fletcher Checksum

The Fletcher checksum (FC) is a means of error detection that is analogous to cyclic redundancy checking but easier to implement in software. Now FC actually has two versions, one is Fletcher's original paper version termed as FC and the other is RFC1146 version termed as FC-RFC. This paper shows that the FC is a cyclic code. This is done by introducing a cyclic code known as the cyclic Fletcher code (CFC) and then showing that the CFC is equivalent to the FC. The clear algebraic structure of cyclic codes is used to analyze the code block length and code distance, and then the single error correction, double error detection, and burst error detection of the CFC are analyzed. Also given is the mathematical relationship between the CFC and a modified FC. Finally, the issue of implementation is considered, and a new scheduling for the CFC is proposed to prevent data hazards. A simulation shows that the proposed scheduling offers improvements of at least 46% in throughput for the CFC and FC-RFC.

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.

Simple Streaming Codes for Reliable, Low-Latency Communication

Streaming codes offer reliable recovery under decoding-delay constraint $\tau $ , of packets transmitted over a burst-and-random-erasure channel. Prior rate-optimal code constructions had field size quadratic in $\tau $ and employed diagonal embedding of a scalar block code of length $n$ within the packet stream. It is shown here that staggered diagonal embedding (SDE) under which the $n$ code symbols are dispersed across a span of $N \ge n$ successive packets leads to a simpler, low-complexity construction of rate-optimal streaming codes having linear field size. The limits of the SDE approach under the restriction $N \leq \tau +1$ are explored. Some binary streaming codes that are rate-optimal under this restriction are identified.

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.

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.

Generalized Partial Orders for Polar Code Bit-Channels

We study partial orders (POs) for the synthesized bit-channels of polar codes. First, we give an alternative proof of an existing PO for bit-channels with the same Hamming weight and use the underlying idea to extend the bit-channel ordering to some additional cases. In particular, the bit-channel ordering for a given code block length is used to generate additional bit-channel ordering relationships for larger block lengths, generalizing previously known POs. Next, we consider POs especially for the binary erasure channel (BEC). We identify a symmetry property of the Bhattacharyya parameters of complementary bit-channel pairs on the BEC and provide a condition for the alignment of polarized sets of bit-channels for the BEC and general binary-input memoryless symmetric (BMS) channels. Numerical examples and further properties about the POs for the bit-channels with different Hamming weights are provided to illustrate the new POs. The bit-channels with universal ordering positions, which are independent of the channel erasure probability, are verified for all of the code block lengths. Finally, we show the threshold behavior of the Bhattacharyya parameters of some bit-channels by approximating the threshold values. The corresponding value for a bit-channel can be used to determine whether it is good or bad when the underlying channel is known.

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.

Opportunistic Spectrum Sharing for D2D-Based URLLC

A device-to-device (D2D) ultra-reliable low latency communications network is investigated in this paper. Specifically, a D2D transmitter opportunistically accesses the radio resource provided by a cellular network and directly transmits short packets to its destination. A novel performance metric is adopted for finite block-length code. We quantify the maximum achievable rate for the D2D network, subject to a probabilistic interference power constraint based on imperfect channel state information. First, we perform a convexity analysis that reveals that the finite block-length rate for the D2D pair in short-packet transmission is not always concave. To address this issue, we propose two effective resource allocation schemes using the successive convex approximation based iterative algorithm. To gain more insights, we exploit the monotonicity of the average finite block-length rate. By capitalizing on this property, an optimal power control policy is proposed, followed by closed-form expressions and approximations for the optimal average power and the maximum achievable average rate in the finite block-length regime. Numerical results are provided to confirm the effectiveness of the proposed resource allocation schemes and validate the accuracy of the derived theoretical results.

On the Throughput of Channels That Wear Out

This paper investigates the fundamental limits of communication over a noisy discrete memoryless channel that wears out, in the sense of signal-dependent catastrophic failure. In particular, we consider a channel that starts as a memoryless binary-input channel and when the number of transmitted ones causes a sufficient amount of damage, the channel ceases to convey signals. Constant composition codes are adopted to obtain an achievability bound, and the left-concave right-convex inequality is then refined to obtain a converse bound on the log-volume throughput for channels that wear out. Since infinite blocklength codes will always wear out the channel for any finite threshold of failure, and therefore cannot convey information at positive rates, we analyze the performance of finite blocklength codes to determine the maximum expected transmission volume at a given level of average error probability. We show that this maximization problem has a recursive form and can be solved by dynamic programming. Numerical results demonstrate that a sequence of block codes is preferred to a single block code for streaming sources.

Construction of Polar Codes With Sublinear Complexity

Consider the problem of constructing a polar code of block length $N$ for a given transmission channel $W$ . Previous approaches require one to compute the reliability of the $N$ synthetic channels and then use only those that are sufficiently reliable. However, we know from two independent works by Schurch and by Bardet et al. that the synthetic channels are partially ordered with respect to degradation. Hence, it is natural to ask whether the partial order can be exploited to reduce the computational burden of the construction problem. We show that, if we take advantage of the partial order, we can construct a polar code by computing the reliability of roughly a fraction $1/\log ^{3/2} N$ of the synthetic channels. In particular, we prove that $N/\log ^{3/2} N$ is a lower bound on the number of synthetic channels to be considered and such a bound is tight up to a multiplicative factor $\log \log N$ . This set of roughly $N/\log ^{3/2} N$ synthetic channels is universal, in the sense that it allows one to construct polar codes for any $W$ , and it can be identified by solving a maximum matching problem on a bipartite graph. Our proof technique consists of reducing the construction problem to the problem of computing the maximum cardinality of an antichain for a suitable partially ordered set. As such, this method is general, and it can be used to further improve the complexity of the construction problem, in case a refined partial order on the synthetic channels of polar codes is discovered.

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.

Delay-Sensitive Communications Over IR-HARQ: Modulation, Coding Latency, and Reliability

With the growing popularity of delay-sensitive applications (e.g., real-time conversational video, online gaming, and augmented reality) and future trends toward ultra-reliable low-latency communications such as the tactile Internet, performance analysis of wireless systems under the finite code blocklength constraint becomes extremely important. In this paper, we investigate the maximum achievable throughput of incremental redundancy-hybrid automatic repeat request (IR-HARQ) over the (correlated) Rayleigh fading channel under finite blocklength and delay-violation probability constraints as a function of the modulation scheme. The maximum number of HARQ rounds together with the transport block size specifies the underlying coding latency of the IR-HARQ scheme. A framework, namely the HARQ Markov model (HARQ-MM), is introduced to track the throughput and the probability of error of IR-HARQ over the Rayleigh fading channel as a function of the modulation scheme. The dispersion of parallel additive white Gaussian noise channels with finite input alphabets (e.g., pulse amplitude modulation) is analytically characterized. It is used to identify the state transition probabilities of the underlying HARQ-MM. An algorithm is developed to efficiently compute the steady-state distribution of the HARQ-MM. Extensive performance evaluation is conducted, which shows a good match between the throughput performance characterized by the theoretical framework and that achieved by the practical channel codes.

Repetition‐assisted decoding of polar codes

Error correction performance of finite-length polar codes has been a major concern in the past decade. This Letter presents a method for improving the error correction performance of cyclic redundancy check (CRC)-aided successive cancellation list decoding for polar codes of medium block-lengths with high code rates. In the proposed decoding scheme, a one-time repetition of least reliable bit-channels along with partial protection of the message is employed to correct the error(s) when decoding fails. The results show an improvement of nearly 0.2 dB in error correction performance.

Resource Allocation for Wireless-Powered IoT Networks With Short Packet Communication

Internet-of-Things (IoT) is a promising technology to connect massive machines and devices in the future communication networks. In this paper, we study a wireless-powered IoT network (WPIN) with short packet communication (SPC), in which a hybrid access point (HAP) first transmits power to the IoT devices wirelessly, then the devices in turn transmit their short data packets achieved by finite blocklength codes to the HAP using the harvested energy. Different from the long packet communication in conventional wireless network, SPC suffers from transmission rate degradation and a significant packet error rate. Thus, conventional resource allocation in the existing literature based on Shannon capacity achieved by the infinite blocklength codes is no longer optimal. In this paper, to enhance the transmission efficiency and reliability, we first define effective-throughput and effective-amount-of-information as the performance metrics to balance the transmission rate and the packet error rate, and then jointly optimize the transmission time and packet error rate of each user to maximize the total effective-throughput or minimize the total transmission time subject to the users’ individual effective-amount-of-information requirements. To overcome the non-convexity of the formulated problems, we develop efficient algorithms to find high-quality suboptimal solutions for them. The simulation results show that the proposed algorithms can achieve similar performances as that of the optimal solution via exhaustive search, and outperform the benchmark schemes.

Short Block-Length Codes for Ultra-Reliable Low Latency Communications

This article reviews state of the art channel coding techniques for URLLC. The stringent requirements of URLLC services, such as ultrahigh reliability and low latency, have made it the most challenging feature of 5G of mobile networks. The problem is even more challenging for services beyond the 5G promise, such as tele-surgery and factory automation, which require latencies less than 1ms and packet error rates as low as 10-9. This article provides an overview of channel coding techniques for URLLC and compares them in terms of performance and complexity. Several important research directions are identified and discussed in more detail.

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.

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.