Short Block Length Research Articles

Improved PEG-Based Construction of Analog Fountain Codes.

This paper proposes an improved progressive edge-growth (PEG) construction of analog fountain codes (AFCs). During edge selection, it simultaneously allocates weight coefficients in descending order. Analysis shows that our proposed construction reduces the probability of large weight coefficients involved in harmful short cycles. Simulation results indicate that it has good block error rate (BLER) in short block length regime.

A path splitting and pruning strategy on list decoder for PAC codes

AbstractRecently, Arıkan proposed a polarization‐adjusted convolutional (PAC) codes, demonstrating their superior error correction performance over polar codes at short block lengths. It was confirmed that PAC codes approached the optimal performance achievable with limited code length. This paper proposes a novel low‐complexity list decoding algorithm for PAC codes, incorporating path splitting and pruning strategies based on a set of highly reliable information bits. Simulation results reveal that the proposed algorithm significantly reduces sorting complexity and average list size, all while incurring negligible performance loss. Unlike previous pruning algorithms designed for polar codes, the proposed strategy eliminates the need to individually assess the reliability of decoding paths in each decoding process. Instead, the algorithm minimizes redundant decoding paths through a high‐reliability information bit set, constructed using Monte Carlo experiments.

Performance of Spectral and Energy Efficiency in Cell-Free Massive MIMO-Aided URLLC System With Short Blocklength Communications

Performance of Spectral and Energy Efficiency in Cell-Free Massive MIMO-Aided URLLC System With Short Blocklength Communications

A Study on Determining the Optimal Feedback Rate in Distributed Block Diagonalization with Limited Feedback for Dense Cellular Networks

In this study, we explore a downlink cellular network where each base station (BS) engages in simultaneous communication with multiple users through spatial division multiple access (SDMA). The positions of both BSs and users are established through independent random point processes, effectively representing the cellular network. SDMA utilizes block diagonalization (BD) at each BS, employing multiple receive antennas for each user. To implement BD, users quantize and provide feedback on their downlink channels to their respective BSs. The net spectral efficiency, measuring the effective rate accounting for both downlink and uplink resource usage, serves as a performance metric. In prior research, the optimal feedback rate in terms of maximizing net spectral efficiency has been approximated in this scenario. The corresponding approximations effectively illustrate the asymptotic behavior of the optimal number as a function of the length of the coherent channel block. However, the accuracy of the approximation diminishes when the length of the coherent channel block is relatively small. Given that the length of the coherent channel block can assume relatively small values depending on wireless environments, achieving a precise estimate across the entire range of the coherent block length holds significant importance. Consequently, this paper focuses primarily on enhancing the accuracy of the approximation for the optimal feedback rate. In order to achieve a more precise estimation, we analyze the derivative of the net spectral efficiency, which encompasses two functions that demonstrate distinct growth rates. In contrast to prior studies, both functions are rigorously approximated through mathematical analysis. As a result, the proposed approximation significantly improves the accuracy compared to previous studies, particularly when dealing with short coherent channel block lengths. Moreover, this approximation generally achieves near-optimal performance, regardless of system parameters.

CRC-Aided High-Rate Convolutional Codes With Short Blocklengths for List Decoding

CRC-Aided High-Rate Convolutional Codes With Short Blocklengths for List Decoding

Joint Optimization of Frame Structure and Power Allocation for URLLC in Short Blocklength Regime

Joint Optimization of Frame Structure and Power Allocation for URLLC in Short Blocklength Regime

Parity Check Codes for Second Order Diversity

Short block length “block” codes are typically not used in wireless standards as soft decision decoding is computationally intensive and hard decision decoding results in performance loss. However, short block lengths are of interest to massive machine-type communications (mMTC) and ultra-reliable low-latency communications (URLLC). In this paper, we propose a diversity preserving enhanced hard-decision decoding scheme for parity check codes (PCC) over Rayleigh fading channels. The proposed flip decoding scheme has linear complexity in the block length. Theoretical analysis and simulation results verify the correctness of the proposed detection scheme.

Resource allocation and energy trading in the short blocklength regime for radio access networks

AbstractWith the large‐scale deployment of communication and computation units, the conventional radio access network has been gradually transformed into a sophisticated Cyber‐Physical System. Since the access network is put forward higher expectations for ultra‐reliable and low‐latency services, Short‐Packet Communications (SPC) based on Finite Blocklength Codes can be adopted to further decrease network latency and enhance communication reliability. Considering the interaction among the service provider, the network operator, and users, a three‐stage Stackelberg game is constructed to dynamically arrange communication and computation resources. In this paper, the tripartite interaction problem is modelled as a generalized Nash equilibrium problem, and the reverse induction method is employed to achieve the sub‐game equilibrium. To solve the problem of maximizing tripartite utilities, the authors propose an iterative algorithm for jointly managing resource allocation and tripartite pricing. Simulation results show that compared with the benchmark, the proposed scheme can effectively improve the utilities of users, the service provider, and the network operator and achieve a win–win situation.

Performance of polar codes with low complexity cyclic redundancy check aided bit‐flipping for successive cancellation list decoding over power line channels

SummaryPower lines have complex transmission characteristics and noise interference when used as information transmission channel, thus limiting their data‐carrying rate and reliability. Impulsive noise is the most dominant factor degrading the performance of communication systems over power lines. To combat the impulsive noise, polar codes are introduced into the orthogonal frequency division multiplexing (OFDM)‐based power line communication (PLC) system. Because the successive cancelation list bit‐flip (SCLF) decoding algorithm of polar codes has high decoding complexity, a low complexity segmented cyclic redundancy check (CRC)‐aided SCLF decoding is proposed to improve the decoding performance. The decoding process can be terminated early with segmented CRC, which can reduce the bit‐flip decoding complexity significantly with short and medium block lengths. Experimental results demonstrate that for various configurations, the proposed decoder outperforms the traditional CRC‐aided SCL decoder in terms of decoding performance and complexity, and the suggested polar codes‐based OFDM‐based PLC system can reduce the bit error rate of the system in the presence of impulsive noise.

Analytical Bounds for the Optimal Code Over the Reconfigurable Intelligent Surface at a Short Blocklength

Analytical Bounds for the Optimal Code Over the Reconfigurable Intelligent Surface at a Short Blocklength

Application of the method of equivalent message encoding structures to simplify coding complexity

Formulation of the problem. Modern telecommunication technologies make it possible to transmit data over long distances with limitations in the form of low power consumption and low error rate using error correction codes. The use of such codes plays an important role and is necessary to detect and correct errors caused by signal distortion and noise in the communication channel. According to Shannon's channel coding theorem, the probability of error can be arbitrarily small or close to zero if the encoding rate of transmission R is less than or equal to the bandwidth of channel C. Assuming that the bandwidth C is achievable, we can calculate the minimum signal-to-noise power ratio (SNR) to achieve zero error, or an arbitrarily small error called the Shannon limit, while maintaining R ≤ C. This article discusses a method of applying equivalent message encoding structures to construct low-density parity-checking (LDPC) codes. Low-density parity-checking (LDPC) codes are a class of linear block codes in which the complexity of iterative decoding increases linearly with increasing block length. Standard LDPC codes without modifications are considered to demonstrate the effectiveness of the proposed method, which is expected to provide high encoding speed when transmitting messages with a short block length. The method of obtaining equivalent structures allows: to reduce the computational complexity of encoding and decoding; to provide the possibility of finding a new encoding scheme and evaluating its effectiveness. The validity of the method for obtaining equivalent message encoding structures is evaluated by modeling the bit error rate (BER) of LDPC codes. Purpose. to show the effectiveness of the use of equivalent structures for various methods of compression of transmitted information, to minimize the complexity of encoding, while maintaining energy efficiency, correcting ability and data transfer rate. Results. A method is considered for obtaining equivalent message element encoding structures that can be used to create more LDPC codes for data transmission applications with a short block length. The cascade principle of constructing an equivalent generator and a parity check matrix was analyzed, which also leads to minimizing the computational complexity of the encoder and decoder. An equivalent structure G can be obtained from cascading two (or more) matrices by modifying the second matrix so that it has a unit matrix with the size of the parity check length and a shift to the right by k bits. On the other hand, the equivalent structure H can be obtained by simply cascading directly the second matrix and shifting to the right by k bits. According to the simulation results, the proposed method is adequate, since LDPC codes have the same BER characteristics as codes based on the low density generator matrix (LDGM). During the simulation, it was concluded that the SPC codes (single parity check (single parity check (SPC)) are the most efficient codes (for a given block length), since SPC codes have the smallest interval up to the Shannon limit. Practical significance. The results presented in this article will give a new insight into the development of simple channel coding of LDPC codes of short block length with high encoding speed for future applications with lower power consumption.

Low-Rate and Short-Block-Length Random Permutation-Coded Modulations Achieve Finite-Length Bounds

Ultra-reliable low-latency communication (URLLC) is an important feature brought by 5G New Radio (NR). By using a block code, the low-latency requirement in general requires a short block length in order to reduce the latency of transmitting the entire code block. The ultra-reliable communication requires a low-rate code to achieve high decoding reliability even under low signal-to-noise ratios (SNRs). This paper proposes a new class of coding and modulation schemes, termed permutation-coded modulations, for low-rate and short-block-length applications, such as URLLC. We show that permutation-coded modulations under maximum-likelihood (ML) decoding have remarkable performance levels that achieve the dispersion bounds with normal approximation (NA) for short block lengths. However, their encoding and ML-decoding complexities are prohibitive if the number of message bits transmitted per code block increases. To reduce the encoding and decoding complexities, we propose a trapezoidal permutation-coded modulation scheme which can be decoded efficiently by successive cancellation list (SCL) decoders. We also show that the trapezoidal permutation-coded modulations under SCL decoding can achieve the dispersion bounds with NA for short block lengths.

Downlink Transmission With Heterogeneous URLLC Services: Discrete Signaling With Single-User Decoding

The problem of designing downlink transmission schemes for supporting heterogeneous ultra-reliable low-latency communications (URLLC) and/or with other types of services is investigated. We consider the broadcast channel, where the base station sends superimposed signals to multiple users. Under heterogeneous blocklength constraints, strong users who are URLLC users cannot wait to receive the entire transmission frame and perform successive interference cancellation (SIC) due to stringent latency requirements, in contrast to the conventional infinite blocklength cases. Even if SIC is feasible, SIC may be imperfect under finite blocklength constraints. To cope with the heterogeneity in latency and reliability requirements, we propose a practical downlink transmission scheme with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">discrete signaling</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">single-user decoding (SUD), i.e., without SIC</i> . We carefully design the discrete input distributions to enable efficient SUD by exploiting the structural interference. Furthermore, we derive the second-order achievable rate under heterogenous blocklength and error probability constraints and use it to guide the design of channel coding and modulations. It is shown that in terms of achievable rate under short blocklength, the proposed scheme with regular quadrature amplitude modulations and SUD can operate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">extremely close</i> to the benchmark schemes that assume perfect SIC with Gaussian signaling.

Improved Route to Linear Triblock Copolymers by Coupling with Glycidyl Ether-Activated Poly(ethylene oxide) Chains.

Poly(ethylene oxide) block copolymers (PEOz BCP) have been demonstrated to exhibit remarkably high lithium ion (Li+) conductivity for Li+ batteries applications. For linear poly(isoprene)-b-poly(styrene)-b-poly(ethylene oxide) triblock copolymers (PIxPSyPEOz), a pronounced maximum ion conductivity was reported for short PEOz molecular weights around 2 kg mol-1. To later enable a systematic exploration of the influence of the PIx and PSy block lengths and related morphologies on the ion conductivity, a synthetic method is needed where the short PEOz block length can be kept constant, while the PIx and PSy block lengths could be systematically and independently varied. Here, we introduce a glycidyl ether route that allows covalent attachment of pre-synthesized glycidyl-end functionalized PEOz chains to terminate PIxPSy BCPs. The attachment proceeds to full conversion in a simplified and reproducible one-pot polymerization such that PIxPSyPEOz with narrow chain length distribution and a fixed PEOz block length of z = 1.9 kg mol-1 and a Đ = 1.03 are obtained. The successful quantitative end group modification of the PEOz block was verified by nuclear magnetic resonance (NMR) spectroscopy, gel permeation chromatography (GPC) and differential scanning calorimetry (DSC). We demonstrate further that with a controlled casting process, ordered microphases with macroscopic long-range directional order can be fabricated, as demonstrated by small-angle X-ray scattering (SAXS), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). It has already been shown in a patent, published by us, that BCPs from the synthesis method presented here exhibit comparable or even higher ionic conductivities than those previously published. Therefore, this PEOz BCP system is ideally suitable to relate BCP morphology, order and orientation to macroscopic Li+ conductivity in Li+ batteries.

Efficient Decoders for Short Block Length Codes in 6G URLLC

This article reviews the potential channel decoding techniques for ultra-reliable low-latency communications (URLLC). URLLC is renowned for its stringent requirements including ultra-reliability, low end-to-end transmission latency, and packet-size flexibility. These requirements exacerbate the difficulty of the physical-layer design, particularly for the channel coding and decoding schemes. To satisfy the requirements of URLLC, decoders must exhibit superior error-rate performance and low decoding complexity. Also, it is desired that decoders be universal to accommo-date various coding schemes. This article provides a comprehensive review and comparison of different candidate decoding techniques for URLLC in terms of their error-rate performance and computational complexity for structured and random short codes. We further make recommendations of the decoder selections and suggest several potential research directions.

Series Editorial: Mobile Communications and Networks

We are excited to have an unusually large number of articles in this issue of Mobile Communications and Networks series. These articles explore further evolutions of communications and some potentials for 6G, including delivery of high-precision clock sources, next generation connectivity for Railways, integration of terrestrial and non-terrestrial networks, integration of artificial intelligence (AI) into open Radio Access Network (O-RAN), investigation of MIMO channel quantization and channel error models towards 6G, the potential of near-field beam focusing for 6G, enabling rural connectivity by recycling TV towers with massive MIMO, integration of satellite communication systems into 5G networks, efficient decoders for short block length codes for ultra-reliability low-latency communications (URLLC), and the potential benefits of virtualized distributed unit (vDU) standardization in softwarized RAN.

Joint Convexity of Error Probability in Blocklength and Transmit Power in the Finite Blocklength Regime

To support ultra-reliable and low-latency services for mission-critical applications, transmissions are usually carried via short blocklength codes, i.e., in the so-called finite blocklength (FBL) regime. Different from the infinite blocklength regime where transmissions are assumed to be arbitrarily reliable at the Shannon’s capacity, the reliability and capacity performances of an FBL transmission are impacted by the coding blocklength. The relationship among reliability, coding rate, blocklength and channel quality has recently been characterized in the literature, considering the FBL performance model. In this paper, we follow this model, and prove the joint convexity of the FBL error probability with respect to blocklength and transmit power within a region of interest, as a key enabler for designing systems to achieve globally optimal performance levels. Moreover, we apply the joint convexity to general use cases and efficiently solve the joint optimization problem in the setting with multiple users. We also extend the applicability of the proposed approach by proving that the joint convexity still holds in fading channels, as well as in relaying networks. Via simulations, we validate our analytical results and demonstrate the advantage of leveraging the joint convexity compared to other commonly-applied approaches.

Probabilistic Shaping for Trellis-Coded Modulation With CRC-Aided List Decoding

This paper applies probabilistic amplitude shaping (PAS) to cyclic redundancy check (CRC)-aided tail-biting trellis-coded modulation (TCM). CRC-TCM-PAS produces practical codes for short block lengths on the additive white Gaussian noise (AWGN) channel. In the transmitter, equally likely message bits are encoded by a distribution matcher (DM) generating amplitude symbols with a desired distribution. A CRC is appended to the sequence of amplitude symbols, and this sequence is then encoded and modulated by TCM to produce real-valued channel input signals. This paper proves that the sign values produced by the TCM are asymptotically equally likely to be positive or negative. The CRC-TCM-PAS scheme can thus generate channel input symbols with a symmetric capacity-approaching probability mass function. The paper provides an analytical upper bound on the frame error rate of the CRC-TCM-PAS system over the AWGN channel. This FER upper bound is the objective function used for jointly optimizing the CRC and convolutional code. Additionally, this paper proposes a multi-composition DM, which is a collection of multiple constant-composition DMs. The optimized CRC-TCM-PAS systems achieve frame error rates below the random coding union (RCU) bound in AWGN and outperform the short-blocklength PAS systems with various other forward error correction codes studied in Coşkun et al. (2019).

Short Blocklength Wiretap Channel Codes via Deep Learning: Design and Performance Evaluation

We design short blocklength codes for the Gaussian wiretap channel under information-theoretic security guarantees. Our approach consists in decoupling the reliability and secrecy constraints in our code design. Specifically, we handle the reliability constraint via an autoencoder, and handle the secrecy constraint with hash functions. For blocklengths smaller than or equal to 128, we evaluate through simulations the probability of error at the legitimate receiver and the leakage at the eavesdropper for our code construction. This leakage is defined as the mutual information between the confidential message and the eavesdropper’s channel observations, and is empirically measured via a neural network-based mutual information estimator. Our simulation results provide examples of codes with positive secrecy rates that outperform the best known achievable secrecy rates obtained non-constructively for the Gaussian wiretap channel. Additionally, we show that our code design is suitable for the compound and arbitrarily varying Gaussian wiretap channels, for which the channel statistics are not perfectly known but only known to belong to a pre-specified uncertainty set. These models not only capture uncertainty related to channel statistics estimation, but also scenarios where the eavesdropper jams the legitimate transmission or influences its own channel statistics by changing its location.

Short-Block Length Polar-Coded Modulation for the Relay Channel

Short-block length communication is becoming increasingly important for applications such as machine-to-machine communication, among others. This paper studies polar-coded modulation in the short-block length regime for decode-forward, amplify-forward and compress-forward relays. Our work seamlessly combines multi-level signaling, polar coding/decoding, and the requirements of relaying, into encoders and decoders that exhibit excellent performance. Compared with the state of the art in decode-forward, our work demonstrates 2.5 dB improvement (at block length 512). For shorter block lengths 256 and 128, this work is the first reported implementation for any coded modulation and any relaying protocol. In the category of polar-coded full-duplex relaying, this work presents the first implementation at any block length and for any relaying protocol. For decode-forward, we propose and analyze joint iterative belief propagation decoding with polar codes, and successive list decoding with polarization-adjusted convolutional (PAC) codes. For amplify-forward, we utilize PAC codes and successive list decoding. For the three relaying protocols, the respective dispersion bounds are presented for comparison, and the error exponent of the multi-level relaying coded modulations are analyzed to shed light on the results. Extensive simulations verify the performance of the proposed coding schemes.