Decoding Algorithm Research Articles

From 2D to 3D

Mid-air text entry on virtual keyboards suffers from the lack of tactile feedback, which brings challenges to both tap detection and input prediction. In this paper, we explored the feasibility of single-finger typing on virtual QWERTY keyboards in mid-air. We first conducted a study to examine users' 3D typing behavior on different sizes of virtual keyboards. Results showed that the participants perceived the vertical projection of the lowest point on the keyboard during a tap as the target location and inferring taps based on the intersection between the finger and the keyboard was not applicable. Aiming at this challenge, we derived a novel input prediction algorithm that took the uncertainty in tap detection into a calculation as probability, and performed probabilistic decoding that could tolerate false detection. We analyzed the performance of the algorithm through a full-factorial simulation. Results showed that the SVM-based probabilistic touch detection together with a 2D elastic probabilistic decoding algorithm (elasticity = 2) could achieve the optimal top-5 accuracy of 94.2%. In the evaluation user study, the participants reached a single-finger typing speed of 26.1 WPM with 3.2% uncorrected word-level error rate, which was significantly better than both tap-based and gesture-based baseline techniques. Also, the proposed technique received the highest preference score from the users, proving its usability in real text entry tasks.

A myoelectric digital twin for fast and realistic modelling in deep learning

Muscle electrophysiology has emerged as a powerful tool to drive human machine interfaces, with many new recent applications outside the traditional clinical domains, such as robotics and virtual reality. However, more sophisticated, functional, and robust decoding algorithms are required to meet the fine control requirements of these applications. Deep learning has shown high potential in meeting these demands, but requires a large amount of high-quality annotated data, which is expensive and time-consuming to acquire. Data augmentation using simulations, a strategy applied in other deep learning applications, has never been attempted in electromyography due to the absence of computationally efficient models. We introduce a concept of Myoelectric Digital Twin - highly realistic and fast computational model tailored for the training of deep learning algorithms. It enables simulation of arbitrary large and perfectly annotated datasets of realistic electromyography signals, allowing new approaches to muscular signal decoding, accelerating the development of human-machine interfaces.

Deep Learning Algorithms for BCH Decoding in Satellite Communication

Deep learning is widely used in various fields due to the advancement of algorithms, the enrichment of high-efficiency databases, and the increase in computing power. Especially in the satellite communication, the learning and parallel computing capabilities of neural networks make them ideal for decoding. Many researchers have recently applied deep learning neural networks to decode high-density parity check (HDPC) codes (such as BCH and RS code), improving the decoder’s performance. This review aims to provide general insights on applying neural network decoders to satellite communications. Due to the neural network’s learning ability, the neural network-based decoder can be trained to change the weights, thereby reducing the influence of non-white noise in satellite communications, such as the influence between the satellite and the terrestrial network and the mutual interference within the satellites. To compensate for non-white noise, shortest circles in Tanner graph and unreliable information, a decoder system model for satellite communication constructed by three neural networks is presented.

Linear Diophantine equation (LDE) decoder: A training‐free decoding algorithm for multifrequency SSVEP with reduced computation cost

AbstractMultifrequency steady‐state visual evoked potentials (SSVEPs) have been developed to extend the capability of SSVEP‐based brain‐machine interfaces (BMIs) to complex applications that have large numbers of targets. Even though various multifrequency stimulation methods have been introduced, the decoding algorithms for multifrequency SSVEP are still in early development. The recently developed multifrequency canonical correlation analysis (MFCCA) was shown to be a feasible training‐free option to use in decoding multifrequency SSVEPs. However, the time complexity of MFCCA is shown to be , which will lead to long computation time as grows, where represents the input size in decoding. In this paper, a novel decoding algorithm is proposed with the aim to reduce the time complexity. This algorithm is based on linear Diophantine equation solvers and has a reduced computation cost while remaining training‐free. Our simulation results demonstrated that linear Diophantine equation (LDE) decoder run time is only one fifth of MFCCA run time under respective optimal settings on 5‐s single‐channel data. This reduced computation cost makes it easier to implement multifrequency SSVEP in real‐time systems. The effectiveness of this new decoding algorithm is validated with nine healthy participants when using dry electrode scalp electroencephalography (EEG).

Concatenated Permutation Codes under Chebyshev Distance

Permutation codes are error-correcting codes over symmetric groups. We focus on permutation codes under Chebyshev (ℓ∞) distance. A permutation code invented by Kløve et al. is of length n, size 2n-d and, minimum distance d. We denote the code by φn,d. This code is the largest known code of length n and minimum Chebyshev distance d > n/2 so far, to the best of the authors knowledge. They also devised efficient encoding and hard-decision decoding (HDD) algorithms that outperform the bounded distance decoding. In this paper, we derive a tight upper bound of decoding error probability of HDD. By factor graph formalization, we derive an efficient maximum a-posterior probability decoding algorithm for φn,d. We explore concatenating permutation codes of φn,d=0 with binary outer codes for more robust error correction. A naturally induced pseudo distance over binary outer codes successfully characterizes Chebyshev distance of concatenated permutation codes. Using this distance, we upper-bound the minimum Chebyshev distance of concatenated codes. We discover how to concatenate binary linear codes to achieve the upper bound. We derive the distance distribution of concatenated permutation codes with random outer codes. We demonstrate that the sum-product decoding performance of concatenated codes with outer low-density parity-check codes outperforms conventional schemes.

Proximal Decoding for LDPC Codes

This paper presents a novel optimization-based decoding algorithm for LDPC codes. The proposed decoding algorithm is based on a proximal gradient method for solving an approximate maximum a posteriori (MAP) decoding problem. The key idea of the proposed algorithm is the use of a code-constraint polynomial to penalize a vector far from a codeword as a regularizer in the approximate MAP objective function. A code proximal operator is naturally derived from a code-constraint polynomial. The proposed algorithm, called proximal decoding, can be described by a simple recursive formula consisting of the gradient descent step for a negative log-likelihood function corresponding to the channel conditional probability density function and the code proximal operation regarding the code-constraint polynomial. Proximal decoding is experimentally shown to be applicable to several non-trivial channel models such as LDPC-coded massive MIMO channels, correlated Gaussian noise channels, and nonlinear vector channels. In particular, in MIMO channels, proximal decoding outperforms known massive MIMO detection algorithms, such as an MMSE detector with belief propagation decoding. The simple optimization-based formulation of proximal decoding allows a way for developing novel signal processing algorithms involving LDPC codes.

Efficient MP Decoding via Fast G-BADMM Approach for Binary LDPC Codes

Mathematical programming (MP) decoding based on the alternate direction method of multipliers (ADMM) algorithm is a promising approach for low-density parity-check (LDPC) codes in recent years. For this kind of decoding, the convergence characteristic has been considered as a key factor to enhance its advantage in practice. In this letter, we propose an efficient decoding algorithm based on generalized Bregman ADMM (G-BADMM) technique to improve the convergence speed of ADMM-based MP decoding for binary LDPC codes. The G-BADMM algorithm is established by adding additional Bregman divergences to the ADMM iterations of MP decoding. Moreover, the resulted G-BADMM iterations are solved efficiently. Furthermore, we theoretically analyze the proposed G-BADMM algorithm including its decoding performance analysis and computational complexity. Simulations demonstrate the efficiency of the proposed G-BADMM-based decoding algorithm.

Orbit Structure of Grassmannian G2,m and a Decoder for Grassmann Code C(2, m).

In this article, we consider decoding Grassmann codes, linear codes associated to the Grassmannian and its embedding in a projective space. We look at the orbit structure of Grassmannian arising from the multiplicative group in . We project the corresponding Grassmann code onto these orbits to obtain a subcode of a -ary Reed-Solomon code. We prove that some of these projections contain an information set of the parent Grassmann code. By improving the decoding capacity of Peterson's decoding algorithm for the projected subcodes, we prove that one can correct up to errors for Grassmann code, where is the minimum distance of Grassmann code.

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.

A Flexible Encoding/Decoding Procedure for 6G SCMA Wireless Networks via Adversarial Machine Learning Techniques

5 G networks may not be competent in fully supporting the high data rates, system capacity, and spectral efficiency expected in the upcoming 6 G networks. An enabling factor to achieve these requirements is the adoption of the Sparse Code Multiple Access (SCMA), which is one of the most promising code-domain Non-Orthogonal Multiple Access (NOMA) techniques. Nowadays, there are two major challenges for the implementation of SCMA in practical networks. First, the design of a near-optimal codebook set at the transmitter, that heavily impacts the network performance. Second, an efficient decoding algorithm at the receiver, that dominates the computational complexity of the system. The two aspects are not independent from each other; therefore the optimization of an SCMA network should address jointly both the Encoder and the Decoder side. Moreover, such solution is far from optimal when designed for general purpose use, since it does not exploit the channel statistical information known at the transmitter and the receiver side. However, most of the works available in the literature address only one aspect and also are not tailored for a given radio channel. In this paper, we design an end-to-end SCMA en/deconding structure based on the integration between a state-of-the-art AutoEncoder (AE) architecture and a novel Wasserstein Generative Adversarial Network (WGAN). The aim is to jointly create a near-optimal codebook design and a non-computationally heavy Decoder that are robust to the given channel statistics. Finally, we trained our model to be flexible to support different channel conditions and compared its performance against the state-of-the-art AE and the best conventional Decoders. The simulation results show that our innovative design exhibits decoding performance very similar to conventional Decoders with a reduced decoding latency.

Designing an XAI interface for BCI experts: A contextual design for pragmatic explanation interface based on domain knowledge in a specific context

Domain experts utilize a decision-support system depending on an artificial intelligence (AI) algorithm. Likewise, researchers in brain-computer interface (BCI) have recently employed deep learning (DL) algorithms for decoding and analyzing neural signals. Despite its outstanding performance, the BCI technology with the DLs has pointed out that it has a potential problem of low transparency due to algorithmic complexity of the models. On this problem, explainable artificial intelligence (XAI) can be a solution to make an AI algorithm and its decisions more interpretable. However, the explanation from the XAI has been emphasized that it should be designed corresponding with the user's different expectations which are contextually variable. Thus, our study aims to propose an explanation interface for the BCI expert under Pragmatism structuralizing an explanation with scientific knowledge in a contrastive manner. For this work, we conduct a contextual design process with five BCI experts, specifically conducting a contextual inquiry and work modeling to extract design requirements from their expertise in their work environment; next, designing and evaluating an interactive prototype of the explanation interface. The results indicated that our prototype has the advantages of increasing contextual understanding and intuitive interface design. Yet, there were also challenges on the explanation for novice users without prior knowledge on the XAI and objective understanding of the AI model with enough interpretability. This study contributes to providing a theoretical framework based on Pragmatism and designing a user-centered XAI system for domain experts in a specific context.

Complexity‐reduced maximum‐likelihood hybrid detection for MIMO systems

AbstractFor wireless communications, the multiple‐input multiple‐output (MIMO) system efficiently makes use of the spectrum and enhances the transmission throughput. In this work, the maximum‐likelihood (ML) detection for the MIMO system is studied, and two ML detection algorithms are first considered for the MIMO system, including the sphere decoding (SD) algorithm and an algorithm based on differential metrics (DMs). Each of the two algorithms has its advantages and disadvantages. The two algorithms are first modified such that they are based on the same signal model. Then, a new ML detection algorithm is proposed for the MIMO system based on the hybrid operation of the two modified algorithms on the tree search process, in which both the branch‐and‐bound principle and indicative functions are applied to remove unnecessary searches. The proposed algorithm can attain the ML detection with lower average complexity over low and high ranges of signal‐to‐noise ratio (SNR), as the authors verify by simulations. The proposed ML detection can also generate soft output, and anti‐phase sequences are exploited to further reduce the complexity.

Identifying cortical areas that underlie the transformation from 2D retinal to 3D head-centric motion signals

Accurate motion perception requires that the visual system integrate the 2D retinal motion signals received by the two eyes into a single representation of 3D motion. However, most experimental paradigms present the same stimulus to the two eyes, signaling motion limited to a 2D fronto-parallel plane. Such paradigms are unable to dissociate the representation of 3D head-centric motion signals (i.e., 3D object motion relative to the observer) from the associated 2D retinal motion signals. Here, we used stereoscopic displays to present separate motion signals to the two eyes and examined their representation in visual cortex using fMRI. Specifically, we presented random-dot motion stimuli that specified various 3D head-centric motion directions. We also presented control stimuli, which matched the motion energy of the retinal signals, but were inconsistent with any 3D motion direction. We decoded motion direction from BOLD activity using a probabilistic decoding algorithm. We found that 3D motion direction signals can be reliably decoded in three major clusters in the human visual system. Critically, in early visual cortex (V1-V3), we found no significant difference in decoding performance between stimuli specifying 3D motion directions and the control stimuli, suggesting that these areas represent the 2D retinal motion signals, rather than 3D head-centric motion itself. In voxels in and surrounding hMT and IPS0 however, decoding performance was consistently superior for stimuli that specified 3D motion directions compared to control stimuli. Our results reveal the parts of the visual processing hierarchy that are critical for the transformation of retinal into 3D head-centric motion signals and suggest a role for IPS0 in their representation, in addition to its sensitivity to 3D object structure and static depth.

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.

Application of Tensor Decomposition to Reduce the Complexity of Neural Min-Sum Channel Decoding Algorithm

Channel neural decoding is very promising as it outperforms the traditional channel decoding algorithms. Unfortunately, it still faces the disadvantage of high computational complexity and storage complexity compared with the traditional decoding algorithms. In this paper, we propose that low rank decomposition techniques based on tensor train decomposition and tensor ring decomposition can be utilized in neural offset min-sum (NOMS) and neural scale min-sim (NSMS) decoding algorithms. The experiment results show that the proposed two algorithms achieve near state-of-the-art performance with low complexity.

Adaptive Decoding Algorithm With Variable Sliding Window for Double SC-LDPC Coding System

In this letter, an adaptive decoding algorithm with a variable sliding window for joint source-channel coding (JSCC) scheme based on double spatially coupled low-density parity-check (DSC-LDPC) codes is investigated. For the traditional sliding window decoding (SWD) algorithm, one or more errors occurring in a decoding window may affect the decoding of the next window, which will trigger error propagation. To mitigate the effects, a window extension algorithm based on average log-likelihood ratios (LLRs) will be proposed, but the implement of extension implies higher decoding complexity. In order to trade-off the error rate performance and complexity, the source and channel threshold that determines the window extension are analyzed. In the simulation, the proposed SWD algorithm with acceptable complexity has better error rate performance in the water fall region and the error floor region.

Design of Implicit Partial Product-LDPC Codes and Low Complexity Decoding Algorithm

In this letter, we are concerned with a recently proposed class of product codes, called implicit partial product low-density parity-check (IP-LDPC) codes, which consist of LDPC codes for rows and Bose-Chaudhuri-Hocquenghem (BCH) codes for columns. Distinguished from the conventional product codes, only partial columns are doubly-protected and the column checks are transmitted implicitly rather than explicitly. For any given LDPC code, we present three heuristic rules to design an IP-LDPC code with the same code rate, showing how to select the number of doubly-protected columns and the BCH code (for columns). The stringent constraint is that the product of the number of doubly-protected columns and the length of syndrome per column must be less than or equal to the product of the number of the rows and the length of extra bits that can be carried reliably and implicitly per row (LDPC codeword). We also propose a simple bit-flipping algorithm for the column decoding in the case when the number of unsuccessfully decoded rows is relatively small, which occurs often especially when the iterative decoding is implemented. The simulation results show that IP-LDPC codes can lower down the word error rate (WER) of a (3,6)-regular LDPC code with length 1024 from 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−6</sup> at the SNR around 2.0 dB but without any code rate loss.

A Low-Complexity RS-SPC Product Coding Scheme for Optical Systems

This paper presents a product coding scheme based on binary images of Reed-Solomon (RS) codes and single-parity-check (SPC) codes for high-speed communications. Utilizing the special selection of components, we propose hybrid soft- and hard-decision iterative decoding (ID) algorithms for these codes, during which many RS component decoders can be early terminated. The proposed hybrid ID only exchanges ternary messages between component decoders and early stops the RS component decoders satisfying a proposed stopping criterion, thus low hardware and computational complexities are guaranteed. The hybrid ID of RS-SPC product codes not only performs comparable to the soft-decision decoding of low-density parity-check (LDPC) codes and block turbo codes (BTCs), but also takes much lower computational complexity and smaller decoder data flow. We also propose semi-analytical methods to estimate the waterfall and error-floor performances of the proposed scheme, which yield relatively accurate estimated results. The simulation results and error-floor estimations indicate that some good RS-SPC product codes have very low error floors that satisfy the requirements of optical systems.

A Low-Complexity Ordered Statistic Decoding of Short Block Codes

This letter is concerned with a generalized ordered statistic decoding (OSD) algorithm, called locally constrained OSD (LC-OSD). Instead of order- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> reprocessing on the most reliable independent bits, the LC-OSD searches for test error patterns using the serial list Viterbi algorithm (SLVA) over a trellis specified by a local parity-check matrix. We derive several early stopping criteria that can be used to reduce the number of searches. Numerical results show that the LC-OSD algorithm with the proposed stopping criteria has much lower time complexity than the original OSD but incurs negligible performance loss.

Single parity check node adapted to polar codes with dynamic frozen bit equivalent to binary linear block codes

&lt;span lang="EN-US"&gt;In the context of decoding binary linear block codes by polar code decoding techniques, we propose in this paper a new optimization of the serial nature of decoding the polar codes equivalent to binary linear block codes. In addition to the special nodes proposed by the simplified successive-cancellation list technique, we propose a new special node allowing to estimate in parallel the bits of its sub-code. The simulation is done in an additive white gaussian noise channel (AWGN) channel for several linear block codes, namely bose–chaudhuri–hocquenghem codes (BCH) codes, quadratic-residue (QR) codes, and linear block codes recently designed in the literature. The performance of the proposed technique offers the same performance in terms of frame error rate (FER) as the ordered statistics decoding (OSD) algorithm, which achieves that of maximum likelihood decoder (MLD), but with high memory requirements and computational complexity.&lt;/span&gt;