Decoding Complexity Research Articles

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.

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.

Efficient Decoding Algorithm for Binary Quadratic Residue Codes Using Reduced Permutation Sets

The Quadratic Residue (QR) codes have a rich mathematic structure. Unfortunately, their Algebraic Decoding (AD) is not generalizable for all QR codes. In this study, an efficient hard decoding algorithm is proposed to generalize the decoding of the binary systematic Quadratic Residue (QR) codes. The proposed decoder corrects t erroneous bits or less, in the received word, based on a reduced set of permutations derived from the large automorphism group of QR codes. This set of permutations is applied to the received word to move the error positions and trap all of them in redundancy. Then, to evaluate the proposed method, we applied it to many binary QR codes of moderate code length starting with 17 until 113 with reducible and irreducible generator polynomials. The proposed decoder was validated by inserting all possible error patterns, that have t or less erroneous positions, as input of the proposed decoder and the output is always a correct codeword. The complexity study, in terms of the number of operations used, reveals that the light permutation decoding LPD algorithm significantly decreases decoding complexity without performance loss. So, it is qualified to be a good competitor to decode QR codes with lower lengths but is the best for QR codes with higher lengths.

On the improvements of successive cancellation Creeper decoding for polar codes

In this paper, an improvement for successive cancellation (SC) decoding is presented for polar codes. This improvement is based on applying Creeper approach that was used to decode convolutional codes. The proposed decoder combines a stack and a Fano approaches, allowing to significantly decrease complexity of Successive Cancellation Fano decoder at the cost of a slight increase in space complexity. We also show how to combine the SC-Creeper decoding with a bit-flipping approach to further improve the performance of SC-Creeper due to introducing additional decoding attempts.Simulation results show that the proposed SC-Creeper and SC-Creeper Flip decoders with carefully selected parameters have the same performance as both CRC-aided Successive Cancellation List decoder with list size 8 and Fano decoder, while having much smaller complexity.

NOMA-Based VLC Systems: A Comprehensive Review.

The enhanced proliferation of connected entities needs a deployment of innovative technologies for the next generation wireless networks. One of the critical concerns, however, is the spectrum scarcity, due to the unprecedented broadcast penetration rate nowadays. Based on this, visible light communication (VLC) has recently emerged as a viable solution to secure high-speed communications. VLC, a high data rate communication technology, has proven its stature as a promising complementary to its radio frequency (RF) counterpart. VLC is a cost-effective, energy-efficient, and secure technology that exploits the current infrastructure, specifically within indoor and underwater environments. Yet, despite their appealing capabilities, VLC systems face several limitations which constraint their potentials such as LED's limited bandwidth, dimming, flickering, line-of-sight (LOS) requirement, impact of harsh weather conditions, noise, interference, shadowing, transceiver alignment, signal decoding complexity, and mobility issue. Consequently, non-orthogonal multiple access (NOMA) has been considered an effective technique to circumvent these shortcomings. The NOMA scheme has emerged as a revolutionary paradigm to address the shortcomings of VLC systems. The potentials of NOMA are to increase the number of users, system's capacity, massive connectivity, and enhance the spectrum and energy efficiency in future communication scenarios. Motivated by this, the presented study offers an overview of NOMA-based VLC systems. This article provides a broad scope of existing research activities of NOMA-based VLC systems. This article aims to provide firsthand knowledge of the prominence of NOMA and VLC and surveys several NOMA-enabled VLC systems. We briefly highlight the potential and capabilities of NOMA-based VLC systems. In addition, we outline the integration of such systems with several emerging technologies such as intelligent reflecting surfaces (IRS), orthogonal frequency division multiplexing (OFDM), multiple-input and multiple-output (MIMO) and unmanned aerial vehicles (UAVs). Furthermore, we focus on NOMA-based hybrid RF/VLC networks and discuss the role of machine learning (ML) tools and physical layer security (PLS) in this domain. In addition, this study also highlights diverse and significant technical hindrances prevailing in NOMA-based VLC systems. We highlight future research directions, along with provided insights that are envisioned to be helpful towards the effective practical deployment of such systems. In a nutshell, this review highlights the existing and ongoing research activities for NOMA-based VLC systems, which will provide sufficient guidelines for research communities working in this domain and it will pave the way for successful deployment of these systems.

List-serial pipelined hardware architecture for SCL decoding of polar codes

For polar codes, the performance of successive cancellation list (SCL) decoding is capable of approaching that of maximum likelihood decoding. However, the existing hardware architectures for the SCL decoding suffer from high hardware complexity due to calculating L decoding paths simultaneously, which are unfriendly to the devices with limited logical resources, such as field programmable gate arrays (FPGAs). In this paper, we propose a list-serial pipelined hardware architecture with low complexity for the SCL decoding, where the serial calculation and the pipelined operation are elegantly combined to strike a balance between the complexity and the latency. Moreover, we employ only one successive cancellation (SC) decoder core without L×L crossbars, and reduce the number of inputs of the metric sorter from 2L to L + 2. Finally, the FPGA implementations show that the hardware resource consumption is significantly reduced with negligible decoding performance loss.

Fast list decoders for polarization‐adjusted convolutional (PAC) codes

AbstractA latest coding scheme named polarization‐adjusted convolutional (PAC) codes is shown to approach the dispersion bound for the code (128,64) under list decoding. However, to achieve the near‐bound performance, the list size of list decoding needs to be excessively large, which leads to insufferable time complexity. In this paper, to improve the speed of list decoding, fast list decoders for PAC codes are proposed. Four types of constituent nodes are defined and fast list decoding algorithms are provided for each of them. Simulation results present that fast list decoding with three types of constituent nodes can yield exactly the same error‐correction performance as list decoding, and reduce more than 50% time steps for the code (128,64). Moreover, fast list decoding with four types of constituent nodes can further reduce decoding complexity with negligible performance degradation.

Tree-Search-Based Optimal and Suboptimal Low Complexity Detectors for Differential Space Shift Keying MIMO System

This article proposes two low complexity decoders for non coherent differential space shift keying (DSSK) multiple input multiple output (MIMO) system by representing the detection problem as a hierarchical tree structure. Such presentation enables yielding the optimal maximum likelihood (ML) performance but with a massive reduction in computational complexity. Attained reduction is accomplished through 1) utilizing the error-repetitive property of DSSK detection to reduce the number of computed error terms and 2) developing two efficient searching strategies that avoid searching the entire alphabet as in ML detectors. These searching strategies enable a trade–off between performance and complexity. Unlike existing sparse recovery (SR) decoders, which require a projection phase to ensure the closure property (i.e., only single transmit antenna is active at each particular time instant and the multiplication of a constellation matrix with another one will produce a matrix from within the set), the new algorithms, inherently, maintain the closure property of DSSK system without additional procedures. Reported results reveal that optimal ML performance is obtained with a huge reduction in complexity by proper adjustment of parameters. It is also shown that the proposed algorithm performs better than state of the art SR algorithms, and the feasibility of massive MIMO configurations with low complexity is demonstrated.

Design and Analysis of Joint Group Shuffled Scheduling Decoding Algorithm for Double LDPC Codes System.

In this paper, a joint group shuffled scheduling decoding (JGSSD) algorithm for a joint source-channel coding (JSCC) scheme based on double low-density parity-check (D-LDPC) codes is presented. The proposed algorithm considers the D-LDPC coding structure as a whole and applies shuffled scheduling to each group; the grouping relies on the types or the length of the variable nodes (VNs). By comparison, the conventional shuffled scheduling decoding algorithm can be regarded as a special case of this proposed algorithm. A novel joint extrinsic information transfer (JEXIT) algorithm for the D-LDPC codes system with the JGSSD algorithm is proposed, by which the source and channel decoding are calculated with different grouping strategies to analyze the effects of the grouping strategy. Simulation results and comparisons verify the superiority of the JGSSD algorithm, which can adaptively trade off the decoding performance, complexity and latency.

Exploiting Short Block and Concatenated Codes for Reliable Communications Within the Coexistence of 5G-NR-U and WiFi

Unlicensed spectrum offers opportunities for cellular mobile network operators, where traffic can be offloaded from licensed to unlicensed bands. Modern heterogeneous technologies such as 5G and WiFi can simultaneously operate on ISM and UNII bands under strict coexistence rules. While satisfying harmonious coexistence has largely been studied in LTE/4G, an emerging issue for future deployment is to reduce latency and to guarantee reliable communications, in the direction of achieving URLLC. This work mainly focuses on the critical issues arising in the coexistence of LBT systems, sharing common infrastructure of 5G NR-U and WiFi when operating under imperfect energy detection sensing. We consider the application of short, concatenated and product erasure correcting codes to recover missing data due to collisions in LBT-based systems. The goal is to enhance spectrum utilization with reduced delay and to achieve reliable communications under various sensing impairments, with code parameters such as block length, rate and minimum distance. Using concatenation, we construct a series of sophisticated erasure block codes with less decoding complexity. Furthermore, we derive a closed-form expression using Gaussian approximation of spectrum utilization efficiency. The results are compared with the various LDPC correcting ensembles under various levels of user activities. We provide detailed comparisons of global throughput and failure probability of codes under varied number of coexisting users. Our results show that the proposed codes can achieve over 20% higher efficiency at 0.1 false alarm probability and 30% less failure probability under high contention scenarios.

A low complexity distributed differential scheme based on orthogonal space time block coding for decode-and-forward wireless relay networks

<span lang="EN-US">This work proposes a new differential cooperative diversity scheme with high data rate and low decoding complexity using the decode-and-forward protocol. The proposed model does not require either differential encoding or channel state information at the source node, relay nodes, or destination node where the data sequence is directly transmitted and the differential detection method is applied at the relay nodes and the destination node. The proposed technique enjoys a low encoding and decoding complexity at the source node, the relay nodes, and the destination node. Furthermore, the performance of the proposed strategy is analyzed by computer simulations in quasi-static Rayleigh fading channel and using the decode-and-forward protocol. The simulation results show that the proposed differential technique outperforms the corresponding reference strategies.</span>

Latency Optimization for Luby Transform Coded Computation in Wireless Networks

Luby transform (LT) code has attracted a significant attention due to its rateless property and low decoding complexity in distributed computing networks. However, for wireless networks, the frequent interaction in LT coded computation can give rise to the latency bottleneck considering the communication overhead of interaction. In this letter, we study a novel LT coded computation scheme for heterogeneous wireless networks. Considering nodes with the disparate computation and transmission capabilities, we propose a block-design based wireless LT coded computation (BD-WLTCC) scheme to balance both computation and transmission latency. First, we pre-allocate the maximum transmission rounds due to the limited bandwidth of wireless channel. Then, we design the sub-block size for each node by formulating a nonconvex optimization problem to avoid the frequent interaction. Finally, the sub-optimal sub-block size is obtained by solving the relaxed problem iteratively. And the optimized results provably reveal the generalization of existing works. Simulation results show the superiority of our scheme.

A Novel Polar-Coded Probabilistic Shaping Scheme for Optical DMT Interconnection

A novel bit-oriented probabilistic shaping (PS) scheme based on polar-coded bit weight reconstruction (BWR) is proposed and experimentally demonstrated in an intensity modulation and direct-detection optical discrete multi-tone (DMT) interconnection. The BWR is utilized to enhance the weight of bit ‘0’ by dynamic frozen bits shaping in a systematic-like polar encode processing. Compared with the probability-oriented PS schemes employing distribution matcher (DM) with high computational complexity and PS redundancy, and the symbol-oriented ones based on many-to-one mapping with overlapped symbol demapping difficulty, the proposed bit-oriented PS scheme is with the advantages of relatively lower complexity decoder and shaping redundancy-free profile. The experimental results show that 1.34-dB improvement for receiver power sensitivity and 2.52-dB enhancement for systematic tolerance to optical fiber nonlinear effect can be obtained by the polar-coded PS-16QAM DMT signals compared with the unshaped ones in a 5-km optical DMT interconnection system.

Black hole information recovery in JT gravity

We consider the issue of information recovery for an object carrying energy and entropy into a black hole using the generalized entropy formalism, in the context of JT gravity where the backreaction problem can be solved exactly. We verify the main aspects of the Hayden-Preskill scenario but with some refinements. We show that the information is encoded in the Hawking radiation in a redundant way, as expected for a quantum error correcting code. We show how quantum extremal surfaces associated to information recovery have the form of a python’s lunch and thereby show that the complexity of decoding is exponential in a combination of the entropy shift of the black hole and the entropy of the object. We also show that an infalling observer must have a smooth experience at the horizon and we calculate their endurance proper time inside the black hole before they are radiated out.

Optimal Volumetric Video Streaming With Hybrid Saliency Based Tiling

Volumetric video enables a six-degree-of-freedom (6DoF) immersive viewing experience and has a wide range of applications in entertainment and education, among others. Most existing approaches to volumetric video streaming are extensions of VR video streaming solutions that do not take into account user behavior and the properties of the video during the tiling process, and the complexity of decoding is high. To this end, we study volumetric video streaming in this paper and address the research questions mentioned above. In particular, we first propose a hybrid visual saliency and hierarchical clustering empowered 3D tiling scheme that better matches the user's field of view (FoV). Then, we build a quality of experience (QoE) model considering the volumetric video features as the optimization objective. In addition to the usual encoded version, we introduce the reconstructed version (i.e., decoded version, which allows the user to skip the decoding process and thus reduces the decoding overhead) and propose a joint computational and communication resource allocation scheme to achieve a trade-off between communication and computational resources to maximize the QoE. We perform exhaustive simulations and build a prototype system to verify the performance of the proposed tiling and transmission scheme. The results show that the proposed tiling and transmission scheme performs significantly better than the comparison schemes.

Region-based Template Matching Prediction for Intra Coding.

Copy prediction is a renowned category of prediction techniques in video coding where the current block is predicted by copying the samples from a similar block that is present somewhere in the already decoded stream of samples. Motion-compensated prediction, intra block copy, template matching prediction etc. are examples. While the displacement information of the similar block is transmitted to the decoder in the bit-stream in the first two approaches, it is derived at the decoder in the last one by repeating the same search algorithm which was carried out at the encoder. Region-based template matching is a recently developed prediction algorithm that is an advanced form of standard template matching. In this method, the reference area is partitioned into multiple regions and the region to be searched for the similar block(s) is conveyed to the decoder in the bit-stream. Further, its final prediction signal is a linear combination of already decoded similar blocks from the given region. It was demonstrated in previous publications that region-based template matching is capable of achieving coding efficiency improvements for intra as well as inter-picture coding with considerably less decoder complexity than conventional template matching. In this paper, a theoretical justification for region-based template matching prediction subject to experimental data is presented. Additionally, the test results of the aforementioned method on the latest H.266/Versatile Video Coding (VVC) test model (version VTM-14.0) yield an average Bjøntegaard-Delta (BD) bit-rate savings of -0.75% using all intra (AI) configuration with 130% encoder run-time and 104% decoder run-time for a particular parameter selection.

Universal Decoding of Quantum Stabilizer Codes via Classical Guesswork

A universal decoding scheme is conceived for quantum stabilizer codes (QSCs) by appropriately adapting the ‘guessing random additive noise decoding’ (GRAND) philosophy of classical domain codes. We demonstrate that the generalized quantum decoder conceived is eminently suitable for different QSC decoding paradigms, namely for both stabilizer-measurement-based as well as the inverse-encoder-based decoding. We then harness the resultant decoder for both quantum Bose-Chaudhuri-Hocquenghem (BCH) codes and quantum polar codes and quantify both their quantum block error rate (QBLER), and QBLER per logical qubits as well as their decoding complexity. Furthermore, we provide a parametric study of the associated design trade-offs and offer design guideline for the implementation of GRAND-based QSC decoders.

ДИНАМІКА ЕЕГ ПІД ЧАС СПРИЙНЯТТЯ ЕМОЦІЙНИХ ВИРАЗІВ ОБЛИЧ ЗА РІЗНОГО ЧАСУ ДЕМОНСТРАЦІЇ: ДОСЛІДЖЕННЯ ПОТЕНЦІАЛІВ, ПОВ'ЯЗАНИХ ІЗ ПОДІЯМИ

The face is one of the most significant elements of non-verbal communication, which allows humans to quickly get various types of information about a specific person. Therefore, understanding facial expressions is crucial for normal social interaction, as it lets us determine the emotional states and intentions of other people. The purpose of this study was to investigate the influence of the time factor on the happy and fearful facial expression processing, reflected in the structure and components of event-related potentials (ERPs). Accordingly, two parallel examinations were conducted with stimulus presentation periods of 500 ms and 100 ms. For the obtained data, two separate analyses (for happy and fearful faces) of the averaged ERP curves corresponding to different stimulus exposure periods were executed. The initial stages of processing (EPN, P3) demonstrated that the difference in the structure and amplitude characteristics of the ERP curve was not that significant, but it demonstrated an increase in attentional resources involvement and a strengthening of the primary emotional analysis. Later ERP components (N400, LPP) showed a more compelling difference, that reflected the complexity of semantic decoding, subsequent conscious evaluation, and processes related to decision-making. Thus, reducing the time of image display from 500 ms to 100 ms created the expected difficulties for the perception and processing of emotional facial expressions and was not sufficient for the normal course of these processes.

Deep learning aided SCL decoding of polar codes with shifted-pruning

Recently, a generalized successive cancellation list (SCL) decoder implemented with shifted-pruning (SP) scheme, namely the SCL-SP-ω decoder, is presented for polar codes, which is able to shift the pruning window at most ω times during each SCL re-decoding attempt to prevent the correct path from being eliminated. The candidate positions for applying the SP scheme are selected by a shifting metric based on the probability that the elimination occurs. However, the number of exponential/logarithm operations involved in the SCL-SP-ω decoder grows linearly with the number of information bits and list size, which leads to high computational complexity. In this paper, we present a detailed analysis of the SCL-SP-ω decoder in terms of the decoding performance and complexity, which unveils that the choice of the shifting metric is essential for improving the decoding performance and reducing the re-decoding attempts simultaneously. Then, we introduce a simplified metric derived from the path metric (PM) domain, and a custom-tailored deep learning (DL) network is further designed to enhance the efficiency of the proposed simplified metric. The proposed metrics are both free of transcendental functions and hence, are more hardware-friendly than the existing metrics. Simulation results show that the proposed DL-aided metric provides the best error correction performance as comparison with the state of the art.

A Weighted Sum Based Construction of PAC Codes

The polarization-adjusted convolutional (PAC) codes concatenate an outer convolutional transform with an inner polar transform to improve the error-correction performance of polar codes. In the short-to-medium codeword length regime, it can approach the normal approximation (NA) bound. However, its optimal rate-profile remains unknown. This letter proposes a new construction for PAC codes based on a weighted sum (WS) metric, which considers both the cutoff rates and the utilizations of the polarized subchannels. In comparison with the existing Reed-Muller (RM) rate-profiles, it can yield a flexible rate. By adjusting the design signal-to-noise ratio (SNR), an appropriate tradeoff between the decoding performance and complexity can be achieved. Simulation results show the designed codes can outperform the ones that are designed by the existing techniques.