Decoding Algorithm Research Articles

Spatially Coupled PLDPC-Hadamard Convolutional Codes

We propose a new type of ultimate-Shannon-limit-approaching codes called spatially coupled protograph-based low-density parity-check Hadamard convolutional codes (SC-PLDPCH-CCs), which are constructed by spatially coupling PLDPC-Hadamard block codes. We develop an efficient decoding algorithm that combines pipeline decoding and layered scheduling for the decoding of SC-PLDPCH-CCs, and analyze the latency and complexity of the decoder. To estimate the decoding thresholds of SC-PLDPCH-CCs, we first propose a layered protograph extrinsic information transfer (PEXIT) algorithm to evaluate the thresholds of spatially coupled PLDPC-Hadamard terminated codes (SC-PLDPCH-TDCs) with a moderate coupling length. With the use of the proposed layered PEXIT method, we develop a genetic algorithm to find good SC-PLDPCH-TDCs in a systematic way. Then we extend the coupling length of these SC-PLDPCH-TDCs to form good SC-PLDPCH-CCs. Results show that our constructed SC-PLDPCH-CCs can achieve comparable thresholds to the block code counterparts. Simulations illustrate the superiority of the SC-PLDPCH-CCs over the block code counterparts and other state-of-the-art low-rate codes in terms of error performance. For the rate-0.00295 SC-PLDPCH-CC, a bit error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−5</sup> is achieved at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E_{b}/N_{0} = -1.465$ </tex-math></inline-formula> dB, which is only 0.125 dB from the ultimate Shannon limit.

Integrating LoRa Collision Decoding and MAC Protocols for Enabling IoT Massive Connectivity

One major goal of Beyond 5G and 6G networks is to provide connectivity for a massive number of Internet-of-Things devices. Towards that goal, Long Range (LoRa) is a promising physical layer technology which features low data-rates and large communication ranges, while requiring only low power. However, as the number of devices increases, more and more collisions occur, hence severely degrading LoRa system performances. To cope with this critical drawback, several LoRa collision decoding algorithms and MAC protocols have been proposed. The purpose of this article is to present how collision decoding algorithms interact with MAC layer protocols, and to discuss the potential of such integrated approaches. To do so, we first classify the collision decoding algorithms according to their principles and distinctive features, and compare some reference algorithms in a single simulation setup, using a Software Defined Radio hardware. Then, we analyze how each class of MAC protocols can benefit from each category of collision decoding algorithms. Finally, we discuss long-term perspectives and open issues in this active research area.

Decoding Quadratic Residue Codes Using Deep Neural Networks

In this paper, a low-complexity decoder based on a neural network is proposed to decode binary quadratic residue (QR) codes. The proposed decoder is based on the neural min-sum algorithm and the modified random redundant decoder (mRRD) algorithm. This new method has the same asymptotic time complexity as the min-sum algorithm, which is much lower than the difference on syndromes (DS) algorithm. Simulation results show that the proposed algorithm achieves a gain of more than 0.4 dB when compared to the DS algorithm. Furthermore, a simplified approach based on trapping sets is applied to reduce the complexity of the mRRD. This simplification leads to a slight loss in error performance and a reduction in implementation complexity.

Effects of Low Mental Energy from Long Periods of Work on Brain-Computer Interfaces.

Brain-computer interfaces (BCIs) provide novel hands-free interaction strategies. However, the performance of BCIs is affected by the user’s mental energy to some extent. In this study, we aimed to analyze the combined effects of decreased mental energy and lack of sleep on BCI performance and how to reduce these effects. We defined the low-mental-energy (LME) condition as a combined condition of decreased mental energy and lack of sleep. We used a long period of work (>=18 h) to induce the LME condition, and then P300- and SSVEP-based BCI tasks were conducted in LME or normal conditions. Ten subjects were recruited in this study. Each subject participated in the LME- and normal-condition experiments within one week. For the P300-based BCI, we used two decoding algorithms: stepwise linear discriminant (SWLDA) and least square regression (LSR). For the SSVEP-based BCI, we used two decoding algorithms: canonical correlation analysis (CCA) and filter bank canonical correlation analysis (FBCCA). Accuracy and information transfer rate (ITR) were used as performance metrics. The experimental results showed that for the P300-based BCI, the average accuracy was reduced by approximately 35% (with a SWLDA classifier) and approximately 40% (with a LSR classifier); the average ITR was reduced by approximately 6 bits/min (with a SWLDA classifier) and approximately 7 bits/min (with an LSR classifier). For the SSVEP-based BCI, the average accuracy was reduced by approximately 40% (with a CCA classifier) and approximately 40% (with a FBCCA classifier); the average ITR was reduced by approximately 20 bits/min (with a CCA classifier) and approximately 19 bits/min (with a FBCCA classifier). Additionally, the amplitude and signal-to-noise ratio of the evoked electroencephalogram signals were lower in the LME condition, while the degree of fatigue and the task load of each subject were higher. Further experiments suggested that increasing stimulus size, flash duration, and flash number could improve BCI performance in LME conditions to some extent. Our experiments showed that the LME condition reduced BCI performance, the effects of LME on BCI did not rely on specific BCI types and specific decoding algorithms, and optimizing BCI parameters (e.g., stimulus size) can reduce these effects.

Neuro-Inspired Reinforcement Learning to Improve Trajectory Prediction in Reward-Guided Behavior.

Hippocampal pyramidal cells and interneurons play a key role in spatial navigation. In goal-directed behavior associated with rewards, the spatial firing pattern of pyramidal cells is modulated by the animal's moving direction toward a reward, with a dependence on auditory, olfactory, and somatosensory stimuli for head orientation. Additionally, interneurons in the CA1 region of the hippocampus monosynaptically connected to CA1 pyramidal cells are modulated by a complex set of interacting brain regions related to reward and recall. The computational method of reinforcement learning (RL) has been widely used to investigate spatial navigation, which in turn has been increasingly used to study rodent learning associated with the reward. The rewards in RL are used for discovering a desired behavior through the integration of two streams of neural activity: trial-and-error interactions with the external environment to achieve a goal, and the intrinsic motivation primarily driven by brain reward system to accelerate learning. Recognizing the potential benefit of the neural representation of this reward design for novel RL architectures, we propose a RL algorithm based on [Formula: see text]-learning with a perspective on biomimetics (neuro-inspired RL) to decode rodent movement trajectories. The reward function, inspired by the neuronal information processing uncovered in the hippocampus, combines the preferred direction of pyramidal cell firing as the extrinsic reward signal with the coupling between pyramidal cell-interneuron pairs as the intrinsic reward signal. Our experimental results demonstrate that the neuro-inspired RL, with a combined use of extrinsic and intrinsic rewards, outperforms other spatial decoding algorithms, including RL methods that use a single reward function. The new RL algorithm could help accelerate learning convergence rates and improve the prediction accuracy for moving trajectories.

Morphing Quantum Codes

We introduce a morphing procedure that can be used to generate new quantum codes from existing quantum codes. In particular, we morph the 15-qubit Reed-Muller code to obtain a $[\![10,1,2]\!]$ code that is the smallest known stabilizer code with a fault-tolerant logical $T$ gate. In addition, we construct a family of hybrid color-toric codes by morphing the color code. Our code family inherits the fault-tolerant gates of the original color code, implemented via constant-depth local unitaries. As a special case of this construction, we obtain toric codes with fault-tolerant multi-qubit control-$Z$ gates. We also provide an efficient decoding algorithm for hybrid color-toric codes in two dimensions, and numerically benchmark its performance for phase-flip noise. We expect that morphing may also be a useful technique for modifying other code families such as triorthogonal codes.

Improved encoding structure and decoding algorithms for spinal codes

To improve the error correction performance, an innovative encoding structure with tail-biting for spinal codes is designed. Furthermore, an adaptive forward stack decoding (A-FSD) algorithm with lower complexity for spinal codes is proposed. In the A-FSD algorithm, a flexible threshold parameter is set by a variable channel state to narrow the scale of nodes accessed. On this basis, a new decoding method of AFSD with early termination (AFSD-ET) is further proposed. The AFSD-ET decoder not only has the ability of dynamically modifying the number of stored nodes, but also adopts the early termination criterion to curtail complexity. The complexity and related parameters are verified through a series of simulations. The simulation results show that the proposed spinal codes with tail-biting and the AFSD-ET decoding algorithms can reduce the complexity and improve the decoding rate without sacrificing correct decoding performance.

Simplified Ordered Statistic Decoding for Short-Length Linear Block Codes

The ordered statistic decoding (OSD) algorithm for short-length linear block codes provides an attractive ML-approaching performance, expected to be used for the ultra-reliable low latency communication (URLLC) at the next-generation wireless solutions. To find the corrected codeword among numerous candidates, however, the decoding process requires a considerable amount of computational costs, which need to be simplified to achieve low-latency processing. In this letter, we present several schemes that relax the overall complexity of the state-of-the-art segmentation discarding algorithm. Without degrading the error-correcting power, our method approximate the internal steps for computing the segment sizes and the stopping bounds at the run time, reducing the average processing costs by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.6\times 10 ^{4}$ </tex-math></inline-formula> times for achieving the low-BLER performance.

Adaptive Belief Propagation Decoding of CRC Concatenated NR LDPC and Polar Codes

In this paper, we propose a modified adaptive belief propagation (ABP) algorithm, which is referred to as the random ABP (R-ABP) algorithm, for decoding short channel codes adopted in the fifth generation (5G) New Radio (NR) wireless systems. Based on the cyclic redundancy check (CRC) concatenation structure of 5G channel codes, we can take partial or even all CRC bits into iterative R-ABP decoding to improve the error correction performance, while the error detection capability can still be guaranteed by the remaining CRC bits and a proposed threshold-based acceptance criterion. We call this improved R-ABP decoding the threshold-and-CRC-aided R-ABP (TCA-R-ABP) decoding. The simulation results show that our proposed TCA-R-ABP algorithm outperforms the state-of-the-art decoding algorithms for many 5G low-density parity-check (LDPC) and polar codes. Moreover, the proposed TCA-R-ABP algorithm leads to a unified decoder for LDPC and polar codes, which has the potential to be a lower-complexity decoder over the combination of the belief propagation (BP) and CRC-aided successive cancellation list (CA-SCL) decoders.

Multiple-Layer Integrated Interleaved Codes: A Class of Hierarchical Locally Recoverable Codes

The traditional definition of Integrated Interleaved (II) codes generally assumes that the component nested codes are either Reed-Solomon (RS) or shortened Reed-Solomon codes. By taking general classes of codes, we present a recursive construction of Extended Integrated Interleaved (EII) codes into multiple layers, a problem that brought attention in literature for II codes. The multiple layer approach allows for a hierarchical scheme where each layer of the code provides for a different locality. In particular, we present the erasure-correcting capability of the new codes and we show that they are ideally suited as Locally Recoverable codes (LRC) due to their hierarchical locality and the small finite field required by the construction. Properties of the multiple layer EII codes, like their minimum distance and dimension, as well as their erasure decoding algorithms, parity-check matrices and performance analysis, are provided and illustrated with examples. Finally, we will observe that the parity-check matrices of high layer EII codes have low density.

Performance Enhanced of Geometrically Shaped 64-QAM With LDPC in UOWC System

In this letter, to mitigate the decrease of the received optical power caused by scattering, attenuation and reflection in underwater optical wireless communication (UOWC) system, geometrically shaped (GS) 64-ary quadrature amplitude modulation (QAM) based orthogonal frequency division multiplexing (OFDM) is proposed and experimentally demonstrated in UOWC system. And low-density parity-check codes (LDPC) are employed. By using soft decoding algorithm of LDPC, the complexity of demodulation for GS 64-QAM is the same as the uniform 64-QAM. The experimental results show that, the data rate of GS 64-QAM OFDM signal can achieve 3.33Gbps after transmission over 4.2m underwater and 5m free space channel. Compared with the uniform 64-QAM scheme, the proposed scheme can improve the receiver sensitivity of 0.8dB at the bit-error rate (BER) of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.8\times 10^{-3}$ </tex-math></inline-formula> .

Generic Decoding in the Sum-Rank Metric

We propose the first non-trivial generic decoding algorithm for codes in the sum-rank metric. The new method combines ideas of well-known generic decoders in the Hamming and rank metric. For the same code parameters and number of errors, the new generic decoder has a larger expected complexity than the known generic decoders for the Hamming metric and smaller than the known rank-metric decoders. Furthermore, we give a formal hardness reduction, providing evidence that generic sum-rank decoding is computationally hard. As a by-product of the above, we solve some fundamental coding problems in the sum-rank metric: we give an algorithm to compute the exact size of a sphere of a given sum-rank radius, and also give an upper bound as a closed formula; and we study erasure decoding with respect to two different notions of support.

Decoding Merged Color-Surface Codes and Finding Fault-Tolerant Clifford Circuits Using Solvers for Satisfiability Modulo Theories

Universal fault-tolerant quantum computers will require the use of efficient protocols to implement encoded operations necessary in the execution of algorithms. In this work, we show how solvers for satisfiability modulo theories (SMT solvers) can be used to automate the construction of Clifford circuits with certain fault-tolerance properties and we apply our techniques to a fault-tolerant magic-state-preparation protocol. Part of the protocol requires converting magic states encoded in the color code to magic states encoded in the surface code. Since the teleportation step involves decoding a color code merged with a surface code, we develop a decoding algorithm that is applicable to such codes.

Single-exposure height-recovery structured illumination microscopy based on deep learning.

Modulation-based structured illumination microscopy (SIM) is performed to reconstruct three-dimensional (3D) surface topography. Generally speaking, modulation decoding algorithms mainly include a phase-shift (PS) method and frequency analysis technique. The PS method requires at least three images with fixed PSs, which leads to low efficiency. Frequency methods could decode modulation from a single image, but the loss of high-frequency information is inevitable. In addition, these methods all need to calculate the mapping relationship between modulation and height to recover the 3D shape. In this paper, we propose a deep learning enabled single-exposure surface measurement method. With only one fringe image, this method can directly restore the height information of the object. Processes such as denoising, modulation calculation, and height mapping are all included in the neural network. Compared with traditional Fourier methods, our method has higher accuracy and efficiency. Experimental results demonstrate that the proposed method can provide accurate and fast surface measurement for different structures.

Joint parameter estimation and decoding in a distributed receiver

SummaryThis paper presents an algorithm for iterative joint channel parameter (carrier phase, Doppler shift, and Doppler rate) estimation and decoding of transmission over channels affected by Doppler shift and Doppler rate using a distributed receiver. This algorithm is derived by applying the sum‐product algorithm (SPA) to a factor graph representing the joint a posteriori distribution of the information symbols and channel parameters given the channel output. In this paper, we present two methods for dealing with intractable messages of the SPA. In the first approach, we use particle filtering with sequential importance sampling for the estimation of the unknown parameters. We also propose a method for fine‐tuning of particles for improved convergence. In the second approach, we approximate our model with a random walk phase model, followed by a phase tracking algorithm and polynomial regression algorithm to estimate the unknown parameters. We derive the Weighted Bayesian Cramer‐Rao Bounds for joint carrier phase, Doppler shift, and Doppler rate estimation, which take into account the prior distribution of the estimation parameters and are accurate lower bounds for all considered signal‐to‐noise ratio values. Numerical results (of bit error rate and the mean‐square error of parameter estimation) suggest that phase tracking with the random walk model slightly outperforms particle filtering. However, particle filtering has a lower computational cost than the random walk model‐based method.

Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound

Quantum error correction has recently been shown to benefit greatly from specific physical encodings of the code qubits. In particular, several researchers have considered the individual code qubits being encoded with the continuous variable GottesmanKitaev-Preskill (GKP) code, and then imposed an outer discrete-variable code such as the surface code on these GKP qubits. Under such a concatenation scheme, the analog information from the inner GKP error correction improves the noise threshold of the outer code. However, the surface code has vanishing rate and demands a lot of resources with growing distance. In this work, we concatenate the GKP code with generic quantum low-density parity-check (QLDPC) codes and demonstrate a natural way to exploit the GKP analog information in iterative decoding algorithms. We first show the noise thresholds for two lifted product QLDPC code families, and then show the improvements of noise thresholds when the iterative decoder – a hardware-friendly min-sum algorithm (MSA) – utilizes the GKP analog information. We also show that, when the GKP analog information is combined with a sequential update schedule for MSA, the scheme surpasses the well-known CSS Hamming bound for these code families. Furthermore, we observe that the GKP analog information helps the iterative decoder in escaping harmful trapping sets in the Tanner graph of the QLDPC code, thereby eliminating or significantly lowering the error floor of the logical error rate curves. Finally, we discuss new fundamental and practical questions that arise from this work on channel capacity under GKP analog information, and on improving decoder design and analysis.

Path Selection Strategy of Communication Network Based on Graph Convolutional Neural Network

In order to improve the efficiency of communication network path selection, this paper combines the graph convolutional neural network to formulate the communication network path selection strategy and selects the enhanced decoding algorithm as the fixed-point decoding algorithm. For the quantization scheme based on the enhanced decoding algorithm, the selection of the fixed-point integer bit width of each operation variable in the SISO decoder is analyzed and determined by the method of statistical characteristic analysis. Moreover, this paper calculates the normalized threshold value according to the proposed state metric normalization scheme. In addition, this paper constructs an intelligent communication path selection system. Through research, it can be seen that the communication network path selection system based on graph convolutional neural network proposed in this paper can effectively improve the effect of multicommunication path selection.

Research on Efficient Channel Decoding Algorithm for Memory Channel and Short Packet Transmission in Smart Grid

Many smart factories use the smart grid for power system automation, and its wireless control technology requires low-time-delay and high-reliability communication. Guessing random additive noise decoding algorithm has outstanding short packet error correction performance. In the decoding process, the order of noise parameter combination affects the decoding delay. Aiming at the communication problem of the smart grid in the process of factory power supply and distribution, this study analyzes the characteristics of the original noise parameter ranking algorithm. When the steady-state flip probability is large, more search times are required to obtain the correct combination of noise parameters, which means that greater delay is required for decoding in the time-varying channel. To solve the aforementioned problems, this study optimizes the noise parameter ranking before the noise error mode arrangement and proposes a noise parameter ranking algorithm for predicting the symbol string. First, the channel perception is completed by edge computing. Then, the algorithm uses the obtained soft information to rank the channel noise parameters. Simulation results show that the proposed algorithm has better search performance than the original sorting algorithm, especially when the channel parameter b is greater than 0.5. Finally, by comparing the BM Decoding Algorithm of BCH with different noise parameter ranking algorithms of decoding, the results show that the noise parameter ranking algorithm proposed in this study has better decoding performance in the environmental channel of the smart factory, so as to improve the reliability of the smart grid in the process of factory power supply and distribution.

Bar Code Decoding in a Camera-Based Scanner: Analysis and Algorithm

The goal of this work is to provide a foundational understanding of the resolution requirement for camera-based bar code scanning systems and to develop an effective algorithm for decoding. The main theoretical question we wish to address is how well resolved must the bar code image be for the system to be able to decode it. To facilitate the analysis we consider the UPC bar code, which is widely used in retail and commerce. We further assume that the pixels of the camera are aligned with the bar code, making the problem one-dimensional. We find that if the narrowest bar in the bar code is larger than two-thirds the size of the camera pixel, it is possible to uniquely determine the encoded message in the bar code. The result, which exploits the symbology of the UPC bar code, shows that under-resolved bar code images can be decoded. To further gain insight into the robustness of the decoding process, we perform numerical experiments.

Secrecy Coding Analysis of Short-Packet Full-Duplex Transmissions with Joint Iterative Channel Estimation and Decoding Processes.

This paper studies the secrecy coding analysis achieved by the self-jamming technique in the presence of an eavesdropper by considering a short-packet Full-Duplex (FD) transmission developed based on iterative blind or semi-blind channel estimation and advanced decoding algorithms. Indeed, the legitimate receiver and eavesdropper can simultaneously receive the intended signal from the transmitter and broadcast a self-jamming or jamming signal to the others. Unlike other conventional techniques without feedback, the blind or semi-blind algorithm applied at the legitimate receiver can simultaneously estimate, firstly, the Self-Interference (SI) channel to cancel the SI component and, secondly, estimate the propagation channel, then decode the intended messages by using 5G Quasi-Cyclic Low-Density Parity Check (QC-LDPC) codes. Taking into account the passive eavesdropper case, the blind channel estimation with a feedback scheme is applied, where the temporary estimation of the intended channel and the decoded message are fed back to improve both the channel estimation and the decoding processes. Only the blind algorithm needs to be implemented in the case of a passive eavesdropper because it achieves sufficient performances and does not require adding pilot symbols as the semi-blind algorithm. In the case of an active eavesdropper, based on its robustness in the low region of the Signal-to-Noise Ratio (SNR), the semi-blind algorithm is considered by trading four pilot symbols and only requiring the feedback for channel estimation processes in order to overcome the increase in noise in the legitimate receiver. The results show that the blind or semi-blind algorithms outperform the conventional algorithm in terms of Mean Square Error (MSE), Bit Error Rate (BER) and security gap (). In addition, it has been shown that the blind or semi-blind algorithms are less sensitive to high SI and self-jamming interference power levels imposed by secured FD transmission than the conventional algorithms without feedback.