Linear Decoding Research Articles

Nonlinear sparse partial least squares: an investigation of the effect of nonlinearity and sparsity on the decoding of intracranial data

Objective. Partial Least Squares (PLS) regression is a suitable linear decoder model for correlated and high dimensional neural data. This algorithm has been widely used in the application of brain–computer interface (BCI) for the decoding of motor parameters. PLS does not consider nonlinear relations between brain signal features. The nonlinear version of PLS that considers a nonlinear relationship between the latent variables has not been proposed for the decoding of intracranial data. This nonlinear model may cause overfitting in some cases due to a larger number of free parameters. In this paper, we develop a new version of nonlinear PLS, namely nonlinear sparse PLS (NLS PLS) and test it in BCI applications. Approach. In motor related BCI systems, improving the decoding accuracy of both kinetic and kinematic parameters of movement is crucial. To do this, two BCI datasets were chosen to decode the force amplitude and position of hand trajectory using the nonlinear and sparse versions of PLS algorithm. In our new NLS PLS method, we considered a polynomial relationship between the latent variables and used the lasso penalization in the latent space to avoid overfitting and to improve the decoding accuracy. Main results. Some linear and nonlinear based PLS models and our new proposed method, NLS PLS, were applied to the two datasets. According to our results, significant improvement from the NLS PLS method is confirmed over other methods. Our results show that nonlinear PLS outperforms generic PLS in the force decoding but it has lower accuracy in the hand trajectory decoding because of high dimensional feature space. By using lasso penalization, we presented a sparse nonlinear PLS-based model that outperforms generic PLS in both datasets and improves the coefficient of determination, 34% in the force decoding and 10% in the hand trajectory decoding. Significance. We constructed a simple PLS-based model that considers a nonlinear relationship between features and it is also robust to overfitting because of using the lasso penalty in the latent space. This model is suitable for a high dimensional and correlated datasets, like intracranial data and can improve the accuracy of estimation.

Full-rate Space-time Block Code for Four Transmit Antennas with Linear Decoding

Full-rate Space-time Block Code for Four Transmit Antennas with Linear Decoding

State-Based Decoding of Force Signals From Multi-Channel Local Field Potentials

The functional use of brain-machine interfaces (BMIs) in everyday tasks requires the accurate decoding of both movement and force information. In real-word tasks such as reach-to-grasp movements, a prosthetic hand should be switched between reaching and grasping modes, depending on the detection of the user intents in the decoder part of the BMI. Therefore, it is important to detect the rest or active states of different actions in the decoder to produce the corresponding continuous command output during the estimated state. In this study, we demonstrated that the resting and force-generating time-segments in a key pressing task could be accurately detected from local field potentials (LFPs) in rat's primary motor cortex. Common spatial pattern (CSP) algorithm was applied on different spectral LFP sub-bands to maximize the difference between the two classes of force and rest. We also showed that combining a discrete state decoder with linear or non-linear continuous force variable decoders could lead to a higher force decoding performance compared with the case we use a continuous variable decoder only. Moreover, the results suggest that gamma LFP signals (50-100 Hz) could be used successfully for decoding the discrete rest/force states as well as continuous values of the force variable. The results of this study can offer substantial benefits for the implementation of a self-paced, force-related command generator in BMI experiments without the need for manual external signals to select the state of the decoder.

Pilot-Assisted MIMO-V-OFDM Systems: Compressed Sensing and Deep Learning Approaches

In this paper, we investigate the channel estimation and decoding methods exploiting the channel sparsity in pilot-assisted Multiple-Input Multiple-Output (MIMO) Vector Orthogonal Frequency Division Multiplexing (V-OFDM) systems. Based on the sparse multipath channels, we utilize orthogonal and non-orthogonal pilot schemes to design the compressed sensing (CS) measurement process. For the optimization of the sensing matrix, we discuss the influence of pilot search algorithms and evaluation criteria and propose a particle swarm optimization (PSO) based pilot search algorithm with the simplified evaluation criterion to improve the pilot design procedure. Meanwhile, the effect of pilot insertion on the Peak-to-Average Power Ratio (PAPR) is reduced by a particular precoding matrix method without affecting the decoding complexity. Simulation data are used to evaluate the classical sparsity adaptive matching (SAMP) algorithms and the proposed Variable Threshold SAMP (VTSAMP) algorithm, and the results show that the improved method has higher channel estimation accuracy with unknown sparsity. On the other hand, to overcome the complexity of CS-based decoding, we design the fully connected Deep Neural Network (FC-DNN) decoders, which combine the results of channel estimation results with the prevalent neural network technology. We observe that when the sparse channels are estimated accurately by CS methods, the proposed FC-DNN can achieve the same performance as the high-precision linear decoder by using the time-domain pilots and channel estimation results.

Enhanced Sensory Coding in Mouse Vibrissal and Visual Cortex Through TRPA1

Transient Receptor Potential Ankyrin 1 (TRPA1) is a non-selective cation channel, which is broadly expressed throughout the body. Despite its expression in the mammalian cortex, little is known about the contribution of TRPA1 to cortical function. Here we investigate the role of TRPA1 in sensory information processing by performing electrophysiological recording and 2-photon calcium imaging from two sensory areas in mice: the primary vibrissal somatosensory cortex (vS1) and the primary visual cortex (V1). In vS1, local activation of TRPA1 by its agonist AITC significantly increased the spontaneous activity of cortical neurons, their evoked response to vibrissal stimulation, and their response range, consistent with a positive gain modulation. TRPA1 inhibition with HC-030031 reversed these modulations to below initial control gains. The gain modulations were absent in TRPA1 Knockout mice. In V1, TRPA1 activation increased the gain of direction and orientation selectivity similarly to the gain modulations observed in vS1 cortex. Linear decoding analysis of V1 population activity confirmed faster and more reliable encoding of visual signals in the presence of TRPA1 activation. Overall, our findings reveal a physiological role for TRPA1 in enhancing sensory signals in the mammalian cortex.

New Construction of Low-Density Parity-Check Codes Based on Vector Space Over Finite Fields

Low-Density Parity-Check (LDPC) codes have low linear decoding complexity, which is a kind of good codes with excellent performance. Therefore, LDPC codes have great research value. Two kinds of LDPC codes are constructed based on vector space over finite field. The code length, code rate and minimum distance are given. Moreover, the two kinds of codes are compared with the existing codes, and the constructed codes are better than some existing ones in terms of code rate or minimum distance.

A simple linear readout of MT supports motion direction-discrimination performance.

Motion discrimination is a well-established model system for investigating how sensory signals are used to form perceptual decisions. Classic studies relating single-neuron activity in the middle temporal area (MT) to perceptual decisions have suggested that a simple linear readout could underlie motion discrimination behavior. A theoretically optimal readout, in contrast, would take into account the correlations between neurons and the sensitivity of individual neurons at each time point. However, it remains unknown how sophisticated the readout needs to be to support actual motion-discrimination behavior or to approach optimal performance. In this study, we evaluated the performance of various neurally plausible decoders, trained to discriminate motion direction from small ensembles of simultaneously recorded MT neurons. We found that decoding the stimulus without knowledge of the interneuronal correlations was sufficient to match an optimal (correlation aware) decoder. Additionally, a decoder could match the psychophysical performance of the animals with flat integration of up to half the stimulus and inherited temporal dynamics from the time-varying MT responses. These results demonstrate that simple, linear decoders operating on small ensembles of neurons can match both psychophysical performance and optimal sensitivity without taking correlations into account and that such simple read-out mechanisms can exhibit complex temporal properties inherited from the sensory dynamics themselves.NEW & NOTEWORTHY Motion perception depends on the ability to decode the activity of neurons in the middle temporal area. Theoretically optimal decoding requires knowledge of the sensitivity of neurons and interneuronal correlations. We report that a simple correlation-blind decoder performs as well as the optimal decoder for coarse motion discrimination. Additionally, the decoder could match the psychophysical performance with moderate temporal integration and dynamics inherited from sensory responses.

Adaptive Linear Programming Decoding of Nonbinary Linear Codes Over Prime Fields

In this work, we consider adaptive linear programming (ALP) decoding of linear codes over prime fields, i.e., the finite fields $\mathbb F_{p}$ of size $p$ where $p$ is a prime, when used over a $p$ -ary input memoryless channel. In particular, we provide a general construction of valid inequalities (using no auxiliary variables) for the codeword polytope (or the convex hull) of the so-called constant-weight embedding of a single parity-check (SPC) code over any prime field. The construction is based on sets of vectors, called building block classes , that are assembled to form the left-hand side of an inequality according to several rules. In the case of almost doubly-symmetric valid classes we prove that the resulting inequalities are all facet-defining , while we conjecture this to be true if and only if the class is valid and symmetric . Valid symmetric classes impose certain symmetry conditions on the elements of the vectors from the class, while valid doubly-symmetric classes impose further technical symmetry conditions. For $p=3$ , there is only a single valid symmetric class and we prove that the resulting inequalities together with the so-called simplex constraints give a complete and irredundant description of the codeword polytope of the embedded SPC code. For $p > 5$ , we show that there are additional facets beyond those from the proposed construction. As an example, for $p=7$ , we provide additional inequalities that all define facets of the embedded codeword polytope. The resulting overall set of linear (in)equalities is conjectured to be irredundant and complete. Such sets of linear (in)equalities have not appeared in the literature before, have a strong theoretical interest, and we use them to develop an efficient (relaxed) ALP decoder for general (non-SPC) linear codes over prime fields. The key ingredient is an efficient separation algorithm based on the principle of dynamic programming. Furthermore, we construct a decoder for linear codes over arbitrary fields $\mathbb F_{q}$ with $q =p^{m}$ and $m>1$ by a factor graph representation that reduces to several instances of the case $m=1$ , which results, in general, in a relaxation of the original decoding polytope. Finally, we present an efficient cut-generating algorithm to search for redundant parity-checks to further improve the performance towards maximum-likelihood decoding for short-to-medium block lengths. Numerical experiments confirm that our new decoder is very efficient compared to a static LP decoder for various field sizes, check-node degrees, and block lengths.

Functional diversity among sensory neurons from efficient coding principles.

In many sensory systems the neural signal is coded by the coordinated response of heterogeneous populations of neurons. What computational benefit does this diversity confer on information processing? We derive an efficient coding framework assuming that neurons have evolved to communicate signals optimally given natural stimulus statistics and metabolic constraints. Incorporating nonlinearities and realistic noise, we study optimal population coding of the same sensory variable using two measures: maximizing the mutual information between stimuli and responses, and minimizing the error incurred by the optimal linear decoder of responses. Our theory is applied to a commonly observed splitting of sensory neurons into ON and OFF that signal stimulus increases or decreases, and to populations of monotonically increasing responses of the same type, ON. Depending on the optimality measure, we make different predictions about how to optimally split a population into ON and OFF, and how to allocate the firing thresholds of individual neurons given realistic stimulus distributions and noise, which accord with certain biases observed experimentally.

Towards Intelligent Intracortical BMI (i 2BMI): Low-Power Neuromorphic Decoders That Outperform Kalman Filters.

Fully-implantable wireless intracortical Brain Machine Interfaces (iBMI) is one of the most promising next frontiers in the nascent field of neurotechnology. However, scaling the number of channels in such systems by another 10× is difficult due to power and bandwidth requirements of the wireless transmitter. One promising solution for that is to include more processing, up to the decoder, in the implant so that transmission data-rate is reduced drastically. Earlier work on neuromorphic decoder chips only showed classification of discrete states. We present results for continuous state decoding using a low-power neuromorphic decoder chip termed Spike-input Extreme Learning Machine (SELMA) that implements a nonlinear decoder without memory and its memory-based version with time-delayed bins, SELMA-bins. We have compared SELMA, SELMA-bins against state-of-the-art Steady-State Kalman Filter (SSKF), a linear decoder with memory, across two different datasets involving a total of 4 non-human primates (NHPs). Results show at least a 10% (20%) or more increase in the fraction of variance accounted for (FVAF) by SELMA (SELMA-bins) over SSKF across the datasets. Estimated energy consumption comparison shows SELMA (SELMA-bins) consuming ≈ 9 nJ/update (23 nJ/update) against SSKF's ≈ 7.4 nJ/update for an iBMI with a 10 degree of freedom control. Thus, SELMA yields better performance against SSKF while consuming energy in the same range as SSKF whereas SELMA-bins performs the best with moderately increased energy consumption, albeit far less than energy required for raw data transmission. This paves the way for reducing transmission data rates in future scaled iBMI systems.

A Sparse Probabilistic Code Underlies the Limits of Behavioral Discrimination.

The cortical code that underlies perception must enable subjects to perceive the world at time scales relevant for behavior. We find that mice can integrate visual stimuli very quickly (<100 ms) to reach plateau performance in an orientation discrimination task. To define features of cortical activity that underlie performance at these time scales, we measured single-unit responses in the mouse visual cortex at time scales relevant to this task. In contrast to high-contrast stimuli of longer duration, which elicit reliable activity in individual neurons, stimuli at the threshold of perception elicit extremely sparse and unreliable responses in the primary visual cortex such that the activity of individual neurons does not reliably report orientation. Integrating information across neurons, however, quickly improves performance. Using a linear decoding model, we estimate that integrating information over 50–100 neurons is sufficient to account for behavioral performance. Thus, at the limits of visual perception, the visual system integrates information encoded in the probabilistic firing of unreliable single units to generate reliable behavior.

Design of Linear Block Code Encoder and Decoder Using Electro-optical and All-optical Units

Abstract In this paper novel designs for linear block code encoder and decoder using optical techniques have been proposed. The structures are designed and simulated using lithium niobate based Mach–Zehnder Interferometer (LN-MZI) and nonlinear material MEH-PPV [poly (2-methoxy-5-(28-ethylhexyloxy)-PPV)] (plasmonic) based MZI (P-MZI). The proposed LN-MZI designs offer attractive parameters such as high extinction ratio (&gt;35 dB) and low insertion loss (&lt;0.095 dB), while the proposed P-MZI designs possess a compact structure (3,020–12,375 µm2). An analytical comparison between the two design methodologies and other earlier proposed designs is presented. Each design is presented with a verified mathematical structure. Other performance parameters like contrast ratio and amplitude modulation have also been computed for the presented designs.

Minimum-Polytope-Based Linear Programming Decoder for LDPC Codes via ADMM Approach

In this letter, we develop an efficient linear programming (LP) decoding algorithm for low-density parity-check (LDPC) codes. We first relax the maximum likelihood (ML) decoding problem to a LP problem by using check-node decomposition. Then, to solve the resulting LP problem, we propose an efficient iterative algorithm based on the alternating direction method of multipliers (ADMM) technique. In addition, the feasibility analysis of the proposed algorithm is presented. Furthermore, through exploiting the sparsity and orthogonality structures of the LP problem, the computational complexity of the proposed decoding algorithm increases linearly with the length of the LDPC code. Simulation results demonstrate that our proposed algorithm achieves better performance than other competing algorithms in terms of decoding time.

Multi-Dimensional Space-Time Block Coding Aided Downlink MIMO-SCMA

Multiple-input multiple-output (MIMO) and sparse code multiple access (SCMA) are two key techniques supporting high spectral efficiency and massive connectivity. In this paper, we consider the downlink MIMO communication scenario where SCMA is used for multiuser access. We aim to improve the performance of the traditional single-input single-output SCMA (SISO-SCMA) by exploiting the transmit diversity of multiple antennas at the transmitter. Specifically, we propose a multi-dimensional space-time block code (MSTBC) aided downlink MIMO-SCMA and derive the design criteria of MSTBC that can achieve full diversity while keep the symbol rate same as the traditional SISO-SCMA system. In particular, the MSTBC-2 for two transmit antennas and the MSTBC-4 for four transmit antennas are designed by extending the Alamouti code and quasi-orthogonal STBC into multi-dimension. Due to the orthogonality/quasi-orthogonality of the two MSTBCs, a linear decoder is available at the receiver, which keeps the complexity of the proposed MSTBC aided MIMO-SCMA almost the same as the conventional SISO-SCMA. Furthermore, the performance of the proposed schemes is evaluated based on both Monte Carlo simulations and analytical results. Simulation results show that the proposed MSTBC aided MIMO-SCMA can significantly outperform the conventional SISO-SCMA, STBC-MIMO-OFDM, and multiplexing MIMO-SCMA schemes.

Coded Computation Over Heterogeneous Clusters

In large-scale distributed computing clusters, such as Amazon EC2, there are several types of “system noise” that can result in major degradation of performance: system failures, bottlenecks due to limited communication bandwidth, latency due to straggler nodes, and so on. There have been recent results that demonstrate the impact of coding for efficient utilization of computation and storage redundancy to alleviate the effect of stragglers and communication bottlenecks in homogeneous clusters. In this paper, we focus on general heterogeneous distributed computing clusters consist of a variety of computing machines with different capabilities. We propose a coding framework for speeding up distributed computing in heterogeneous clusters by trading redundancy for reducing the latency of computation. In particular, we propose heterogeneous coded matrix multiplication (HCMM) algorithm for performing distributed matrix multiplication over heterogeneous clusters that are provably asymptotically optimal for a broad class of processing time distributions. Moreover, we show that HCMM is unboundedly faster than any uncoded scheme that partitions the total workload among the workers. To demonstrate how the proposed HCMM scheme can be applied in practice, we provide results from numerical studies and Amazon EC2 experiments comparing HCMM with three benchmark load allocation schemes—uniform uncoded, load-balanced uncoded, and uniform coded. In particular, in our numerical studies, HCMM achieves speedups of up to 73%, 56%, and 42%, respectively, over the three benchmark schemes mentioned earlier. Furthermore, we carry out experiments over Amazon EC2 clusters and demonstrate how HCMM can be combined with rateless codes with nearly linear decoding complexity. In particular, we show that HCMM combined with the Luby transform codes can significantly reduce the overall execution time. HCMM is found to be up to 61%, 46%, and 36% faster than the aforementioned three benchmark schemes, respectively. Additionally, we provide a generalization to the problem of optimal load allocation in heterogeneous settings, where we take into account the monetary costs associated with distributed computing clusters. We argue that HCMM is asymptotically optimal for budget-constrained scenarios as well. In particular, we characterize the minimum possible expected cost associated with a computation task over a given cluster of machines. Furthermore, we develop a heuristic algorithm for (HCMM) load allocation for the distributed implementation of budget-limited computation tasks.

Principled BCI Decoder Design and Parameter Selection Using a Feedback Control Model

Decoders optimized offline to reconstruct intended movements from neural recordings sometimes fail to achieve optimal performance online when they are used in closed-loop as part of an intracortical brain-computer interface (iBCI). This is because typical decoder calibration routines do not model the emergent interactions between the decoder, the user, and the task parameters (e.g. target size). Here, we investigated the feasibility of simulating online performance to better guide decoder parameter selection and design. Three participants in the BrainGate2 pilot clinical trial controlled a computer cursor using a linear velocity decoder under different gain (speed scaling) and temporal smoothing parameters and acquired targets with different radii and distances. We show that a user-specific iBCI feedback control model can predict how performance changes under these different decoder and task parameters in held-out data. We also used the model to optimize a nonlinear speed scaling function for the decoder. When used online with two participants, it increased the dynamic range of decoded speeds and decreased the time taken to acquire targets (compared to an optimized standard decoder). These results suggest that it is feasible to simulate iBCI performance accurately enough to be useful for quantitative decoder optimization and design.

Design teacher and supervised dual stacked auto-encoders for quality-relevant fault detection in industrial process

Current fault detection methods based on deep neural networks only consider process information and ignore quality indicators. In order to obtain features representing both process variables and quality indicators efficiently, this paper designs teacher and supervise dual stacked auto-encoder (TSSAE) for quality-relevant fault detection in industrial process which separates the feature extraction and model construction. To separate the feature extraction and model construction, a mixing stacked auto-encoder which consists of a nonlinear encoder and a linear decoder is designed to extract features of process variables and quality indicators. Another encoder is supervised by the extracted features and further predict the process variables and quality indicators only from process variables. Then quality-relevant, quality-irrelevant and residual subspaces are constructed in a linear way and fault detection is implemented in these subspaces based on Euclidean distance and kernel density estimation. Finally, the effectiveness of TSSAE is evaluated by a numerical example and the Tennessee-Eastman process.

Optimal quantum subsystem codes in two dimensions

Given any two classical codes with parameters $[n_1,k,d_1]$ and $[n_2,k,d_2]$, we show how to construct a quantum subsystem code in 2-dimensions with parameters $[[N,K,D]]$ satisfying $N\le 2n_1n_2$, $K=k$, and $D=\min(d_1,d_2)$. These quantum codes are in the class of generalized Bacon-Shor codes introduced by Bravyi. We note that constructions of good classical codes can be used to construct quantum codes that saturate Bravyi's bound $KD=O(N)$ on the code parameters of 2-dimensional subsystem codes. One of these good constructions uses classical expander codes. This construction has the additional advantage of a linear time quantum decoder based on the classical Sipser-Spielman flip decoder. Finally, while the subsystem codes we create do not have asymptotic thresholds, we show how they can be gauge-fixed to certain hypergraph product codes that do.

Conv-TasNet: Surpassing Ideal Time-Frequency Magnitude Masking for Speech Separation.

Single-channel, speaker-independent speech separation methods have recently seen great progress. However, the accuracy, latency, and computational cost of such methods remain insufficient. The majority of the previous methods have formulated the separation problem through the time-frequency representation of the mixed signal, which has several drawbacks, including the decoupling of the phase and magnitude of the signal, the suboptimality of time-frequency representation for speech separation, and the long latency of the entire system. To address these shortcomings, we propose a fully-convolutional time-domain audio separation network (Conv-TasNet), a deep learning framework for end-to-end time-domain speech separation. Conv-TasNet uses a linear encoder to generate a representation of the speech waveform optimized for separating individual speakers. Speaker separation is achieved by applying a set of weighting functions (masks) to the encoder output. The modified encoder representations are then inverted back to the waveforms using a linear decoder. The masks are found using a temporal convolutional network (TCN) consisting of stacked 1-D dilated convolutional blocks, which allows the network to model the long-term dependencies of the speech signal while maintaining a small model size. The proposed Conv-TasNet system significantly outperforms previous time-frequency masking methods in separating two- and three-speaker mixtures. Additionally, Conv-TasNet surpasses several ideal time-frequency magnitude masks in two-speaker speech separation as evaluated by both objective distortion measures and subjective quality assessment by human listeners. Finally, Conv-TasNet has a significantly smaller model size and a much shorter minimum latency, making it a suitable solution for both offline and real-time speech separation applications. This study therefore represents a major step toward the realization of speech separation systems for real-world speech processing technologies.

The Advantage of Low-Delta Electroencephalogram Phase Feature for Reconstructing the Center-Out Reaching Hand Movements

It is an emerging frontier of research on the use of neural signals for prosthesis control, in order to restore lost function to amputees and patients after spinal cord injury. Compared to the invasive neural signal based brain-machine interface (BMI), a non-invasive alternative, i.e., the electroencephalogram (EEG)-based BMI would be more widely accepted by the patients above. Ideally, a real-time continuous neuroprosthestic control is required for practical applications. However, conventional EEG-based BMIs mainly deal with the discrete brain activity classification. Until recently, the literature has reported several attempts for achieving the real-time continuous control by reconstructing the continuous movement parameters (e.g., speed, position, etc.) from the EEG recordings, and the low-frequency band EEG is consistently reported to encode the continuous motor control information. Previous studies with executed movement tasks have extensively relied on the amplitude representation of such slow oscillations of EEG signals for building models to decode kinematic parameters. Inspired by the recent successes of instantaneous phase of low-frequency invasive brain signals in the motor control and sensory processing domains, this study examines the extension of such a slow-oscillation phase representation to the reconstructing two-dimensional hand movements, with the non-invasive EEG signals for the first time. The data for analysis are collected on five healthy subjects performing 2D hand center-out reaching along four directions in two sessions. On representative channels over the cortices encoding the execution information of reaching movements, we show that the low-delta EEG phase representation is characterized by higher signal-to-noise ratio and stronger modulation by the movement tasks, compared to the low-delta EEG amplitude representation. Furthermore, we have tested the low-delta EEG phase representation with two commonly used linear decoding models. The results demonstrate that the low-delta EEG phase based decoders lead to superior performance for 2D executed movement reconstruction to its amplitude based counterparts, as well as the other-frequency band amplitude and power based features. Thus, our study contributes to improve the movement reconstruction from EEG by introducing a new feature set based on the low-delta EEG phase patterns, and demonstrates its potential for continuous fine motion control of neuroprostheses.