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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Coset Codes Viewed as Terminated Convolutional Codes

In this paper, coset codes are considered as terminated convolutional codes. Based on this approach, three new general results are presented. First, it is shown that the iterative squaring construction can equivalently be defined from a convolutional code whose trellis terminates. This convolutional code determines a simple encoder for the coset code considered, and the state and branch labelings of the associated trellis diagram become straightforward. Also, from the generator matrix of the code in its convolutional code form, much information about the trade-off between the state connectivity and complexity at each section, and the parallel structure of the trellis, is directly available. Based on this generator matrix, it is shown that the parallel branches in the trellis diagram of the convolutional code represent the same coset code C(sub 1), of smaller dimension and shorter length. Utilizing this fact, a two-stage optimum trellis decoding method is devised. The first stage decodes C(sub 1), while the second stage decodes the associated convolutional code, using the branch metrics delivered by stage 1. Finally, a bidirectional decoding of each received block starting at both ends is presented. If about the same number of computations is required, this approach remains very attractive from a practical point of view as it roughly doubles the decoding speed. This fact is particularly interesting whenever the second half of the trellis is the mirror image of the first half, since the same decoder can be implemented for both parts.

Fossorier, Marc P. C.↗
NASA NTRS1999

Punctured Parallel and Serial Concatenated Convolutional Codes for BPSK/QPSK Channels

As available bandwidth for communication applications becomes scarce, bandwidth-efficient modulation and coding schemes become ever important. Since their discovery in 1993, turbo codes (parallel concatenated convolutional codes) have been the center of the attention in the coding community because of their bit error rate performance near the Shannon limit. Serial concatenated convolutional codes have also been shown to be as powerful as turbo codes. In this dissertation, we introduce algorithms for designing bandwidth-efficient rate r = k/(k + 1),k = 2, 3,..., 16, parallel and rate 3/4, 7/8, and 15/16 serial concatenated convolutional codes via puncturing for BPSK/QPSK (Binary Phase Shift Keying/Quadrature Phase Shift Keying) channels. Both parallel and serial concatenated convolutional codes have initially, steep bit error rate versus signal-to-noise ratio slope (called the -"cliff region"). However, this steep slope changes to a moderate slope with increasing signal-to-noise ratio, where the slope is characterized by the weight spectrum of the code. The region after the cliff region is called the "error rate floor" which dominates the behavior of these codes in moderate to high signal-to-noise ratios. Our goal is to design high rate parallel and serial concatenated convolutional codes while minimizing the error rate floor effect. The design algorithm includes an interleaver enhancement procedure and finds the polynomial sets (only for parallel concatenated convolutional codes) and the puncturing schemes that achieve the lowest bit error rate performance around the floor for the code rates of interest.

Acikel, Omer Fatih↗
NASA NTRSDate not supplied

Parallelized Convolutional Interleaver Implementation for Efficient DDR Memory Access

Convolutional interleavers are used in many different communications systems to correct for burst errors due to atmospheric fades and scintillation. The interleaver size is related to the channel coherence time and the data rate. Small convolutional interleavers can be implemented in a field programmable gate array (FPGA) block random access memory (BRAM). However, large interleavers exceeding the size of the BRAM on the FPGA are necessary for channels with longer fades and higher data rates. Therefore, an implementation utilizing double data rate (DDR) memory external to the FPGA is necessary. Wide DDR memory data buses can make the use of DDR memory for convolutional interleavers inefficient when individual symbols are written to and read from the memory. DDR memory operational speeds can also limit the data rate of the interleaver. The Consultative Committee for Space Data Systems (CCSDS) Optical Communications High Photon Efficiency (HPE) standard utilizes a convolutional channel symbol interleaver. A previous implementation of the HPE standard utilized BRAM for the convolutional interleaver, but mission requirements for the upcoming Optical Artemis-2 Orion (O2O) communications demonstration dictate the use of an interleaver exceeding the size of the BRAM. An algorithm and method for implementing the convolutional interleaver in the FPGA with DDR memory is described in this paper.

optical communications↗
DOE OSTI2023

Generalized Quantum Convolution for Multidimensional Data

The convolution operation plays a vital role in a wide range of critical algorithms across various domains, such as digital image processing, convolutional neural networks, and quantum machine learning. In existing implementations, particularly in quantum neural networks, convolution operations are usually approximated by the application of filters with data strides that are equal to the filter window sizes. One challenge with these implementations is preserving the spatial and temporal localities of the input features, specifically for data with higher dimensions. In addition, the deep circuits required to perform quantum convolution with a unity stride, especially for multidimensional data, increase the risk of violating decoherence constraints. In this work, we propose depth-optimized circuits for performing generalized multidimensional quantum convolution operations with unity stride targeting applications that process data with high dimensions, such as hyperspectral imagery and remote sensing. We experimentally evaluate and demonstrate the applicability of the proposed techniques by using real-world, high-resolution, multidimensional image data on a state-of-the-art quantum simulator from IBM Quantum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Window convolution of the galaxy clustering bispectrum

In galaxy survey analysis, the observed clustering statistics do not directly match theoretical predictions but rather have been processed by a window function that arises from the survey geometry including the sky footprint, redshift-dependent background number density and systematic weights. While window convolution of the power spectrum is well studied, for the bispectrum with a larger number of degrees of freedom, it poses a significant numerical and computational challenge. In this work, we consider the effect of the survey window in the tripolar spherical harmonic decomposition of the bispectrum and lay down a formal procedure for their convolution via a series expansion of configuration-space three-point correlation functions, which was first proposed by Sugiyama et al. (2019). We then provide a linear algebra formulation of the full window convolution, where an unwindowed bispectrum model vector can be directly premultiplied by a window matrix specific to each survey geometry. To validate the pipeline, we focus on the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) luminous red galaxy (LRG) sample in the South Galactic Cap (SGC) in the redshift bin 0.4 ≤ z ≤ 0.6. We first perform convergence checks on the measurement of the window function from discrete random catalogues, and then investigate the convergence of the window convolution series expansion truncated at a finite of number of terms as well as the performance of the window matrix. This work highlights the differences in window convolution between the power spectrum and bispectrum, and provides a streamlined pipeline for the latter for current surveys such as DESI and the Euclid mission.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1993

Search for optimal distance spectrum convolutional codes

In order to communicate reliably and to reduce the required transmitter power, NASA uses coded communication systems on most of their deep space satellites and probes (e.g. Pioneer, Voyager, Galileo, and the TDRSS network). These communication systems use binary convolutional codes. Better codes make the system more reliable and require less transmitter power. However, there are no good construction techniques for convolutional codes. Thus, to find good convolutional codes requires an exhaustive search over the ensemble of all possible codes. In this paper, an efficient convolutional code search algorithm was implemented on an IBM RS6000 Model 580. The combination of algorithm efficiency and computational power enabled us to find, for the first time, the optimal rate 1/2, memory 14, convolutional code.

Connor, Matthew C.↗
NASA NTRS1994

Achieving unequal error protection with convolutional codes

This paper examines the unequal error protection capabilities of convolutional codes. Both time-invariant and periodically time-varying convolutional encoders are examined. The effective free distance vector is defined and is shown to be useful in determining the unequal error protection (UEP) capabilities of convolutional codes. A modified transfer function is used to determine an upper bound on the bit error probabilities for individual input bit positions in a convolutional encoder. The bound is heavily dependent on the individual effective free distance of the input bit position. A bound relating two individual effective free distances is presented. The bound is a useful tool in determining the maximum possible disparity in individual effective free distances of encoders of specified rate and memory distribution. The unequal error protection capabilities of convolutional encoders of several rates and memory distributions are determined and discussed.

Mills, D. G.↗
NASA NTRS1999

Effects of Convoluted Divergent Flap Contouring on the Performance of a Fixed-Geometry Nonaxisymmetric Exhaust Nozzle

An investigation was conducted in the model preparation area of the Langley 16-Foot Transonic Tunnel to determine the effects of convoluted divergent-flap contouring on the internal performance of a fixed-geometry, nonaxisymmetric, convergent-divergent exhaust nozzle. Testing was conducted at static conditions using a sub-scale nozzle model with one baseline and four convoluted configurations. All tests were conducted with no external flow at nozzle pressure ratios from 1.25 to approximately 9.50. Results indicate that baseline nozzle performance was dominated by unstable, shock-induced, boundary-layer separation at overexpanded conditions. Convoluted configurations were found to significantly reduce, and in some cases totally alleviate separation at overexpanded conditions. This result was attributed to the ability of convoluted contouring to energize and improve the condition of the nozzle boundary layer. Separation alleviation offers potential for installed nozzle aeropropulsive (thrust-minus-drag) performance benefits by reducing drag at forward flight speeds, even though this may reduce nozzle thrust ratio as much as 6.4% at off-design conditions. At on-design conditions, nozzle thrust ratio for the convoluted configurations ranged from 1% to 2.9% below the baseline configuration; this was a result of increased skin friction and oblique shock losses inside the nozzle.

Asbury, Scott C.↗
DOE OSTI2023

Automated, high-accuracy classification of textured microstructures using a convolutional neural network

Crystallographic texture is an important descriptor of material properties but requires time-intensive electron backscatter diffraction (EBSD) for identifying grain orientations. While some metrics such as grain size or grain aspect ratio can distinguish textured microstructures from untextured microstructures after significant grain growth, such morphological differences are not always visually observable. This paper explores the use of deep learning to classify experimentally measured textured microstructures without knowledge of crystallographic orientation. A deep convolutional neural network is used to extract high-order morphological features from binary images to distinguish textured microstructures from untextured microstructures. The convolutional neural network results are compared with a statistical Kolmogorov–Smirnov tests with traditional morphological metrics for describing microstructures. Results show that the convolutional neural network achieves a significantly improved classification accuracy, particularly at early stages of grain growth, highlighting the capability of deep learning to identify the subtle morphological patterns resulting from texture. The results demonstrate the potential of a convolutional neural network as a tool for reliable and automated microstructure classification with minimal preprocessing.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Versatile feature learning with graph convolutions and graph structures

Graphs represent real world relationships, and graph embedding projects nodes in a graph to a latent space that can help simplify downstream tasks. Recent development of graph convolutions in deep learning significantly improves the performance of many learning tasks on graphs. Unfortunately, prior embedding methods either do not embed graphs with node features, or fail to produce high-quality embeddings for downstream learning tasks that result in large performance gap in comparison to direct learning on graphs.We present a versatile and effective embedding method, Conv2Vec, for embedding graphs with or without node features. It is based on graph convolutions with objective functions motivated by concepts and structures from classical graph algorithms. Conv2Vec produce high-quality embedding for both plain graphs and graphs with node features for downstream tasks.We evaluate the embeddings generated by Conv2Vec with a transductive node classification task. With the generated embeddings and very simple machine learning approaches, we are able to achieve accuracies similar to those achieved by direct learning with graph convolutions. Interestingly, if we strip the node features from the graph and thus learning an embedding has to rely entirely on the graph topology, node classification with our embedding significantly outperforms direct learning with various graph convolutions. This suggests that structures from classical graph algorithms may play an important role in learning on graphs.

Cong, Guojing↗
DOE OSTI2024

Impedance-Aware Graph Convolutional Networks for Voltage Estimation in Active Distribution Networks

Voltage estimation plays a key role in ensuring the effective control and reliability of distribution networks. However, traditional machine learning methods often fail to capture the details of the distribution network’s topology. To overcome this challenge, graph convolutional networks (GCN) have emerged as an alternative. Graph convolutional networks inherently capture the topology of the grid, utilizing correlations to achieve precise voltage estimation. Other machine learning models and conventional GCNs fail to account for the distribution line characteristics found in the real world, limiting their effectiveness. This paper proposes an advanced variant of GCN called the Impedance-Aware Graph Convolutional Network (IA-GCN). The IA-GCN layer incorporates the magnitude of the impedance into the graph convolution mechanism, allowing it to capture topological nuances and provide valuable insights into node interrelationships by considering impedance as an intrinsic dimension. The performance of the IA-GCN layer is then compared with that of GCN and GraphSAGE layers through a surrogate model for voltage estimation. The performance analysis demonstrates that IA-GCN outperforms GCN by reducing the MAE by 87.55% and improving the R-squared value by 98%.

Ravi, Abhijith↗
NASA NTRS1977

Comparison of convolutional and block code performance on the Rician channel

The paper is concerned with the relative performance of short constraint length convolutional codes vis-a-vis block codes when used in conjunction with either BPSK or DPSK modulation on the classical Rician fading channel. A variety of soft-decision decoding algorithms is considered for block codes while the Viterbi algorithm is used exclusively for decoding convolutional codes. Results indicate a substantial performance/complexity advantage in favor of short constraint length convolutional codes and Viterbi decoding which increases with fading severity. The work reported here extends the well-known performance advantage of convolutional codes on the AWGN channel to representative fading channels.

Mui, S. Y.↗
NASA NTRS1983

A parallel-pipeline architecture of the fast polynomial transform for computing a two-dimensional cyclic convolution

It is pointed out that the two-dimensional cyclic convolution is a useful tool for many two-dimensional digital signal processing applications. Two important applications are related to spaceborne high-resolution synthetic aperture radar (SAR) processing and image processing. Nussbaumer and Quandalle (1978) showed that a radix-2 polynomial transform analogous to the conventional radix-2 FFT algorithm can be used to compute a two-dimensional cyclic convolution. On the basis of results reported by Arambepola and Rayner (1979), a radix-2 polynomial transform can be defined to compute a multidimensional cyclic convolution. Truong et al. (1981) used the considered ideas together with the Chinese Theorem to further reduce the complexity of the radix-2 fast polynomial transform (FPT). Reed et al. (1981) demonstrated that such a new FPT algorithm is significantly faster than the FFT algorithm for computing a two-dimensional convolution. In the present investigation, a parallel-pipeline architecture is considered for implementing the FPT developed by Truong et al.

Truong, T. K.↗
NASA NTRS1983

Parallel architectures for computing cyclic convolutions

In the paper two parallel architectural structures are developed to compute one-dimensional cyclic convolutions. The first structure is based on the Chinese remainder theorem and Kung's pipelined array. The second structure is a direct mapping from the mathematical definition of a cyclic convolution to a computational architecture. To compute a d-point cyclic convolution the first structure needs d/2 inner product cells, while the second structure and Kung's linear array require d cells. However, to compute a cyclic convolution, the second structure requires less time than both the first structure and Kung's linear array. Another application of the second structure is to multiply a Toeplitz matrix by a vector. A table is listed to compare these two structures and Kung's linear array. Both structures are simple and regular and are therefore suitable for VLSI implementation.

Yeh, C.-S.↗
NASA NTRS1985

Convoluted nozzle design for the RL10 derivative 2B engine

The convoluted nozzle is a conventional refractory metal nozzle extension that is formed with a portion of the nozzle convoluted to show the extendible nozzle within the length of the rocket engine. The convoluted nozzle (CN) was deployed by a system of four gas driven actuators. For spacecraft applications the optimum CN may be self-deployed by internal pressure retained, during deployment, by a jettisonable exit closure. The convoluted nozzle is included in a study of extendible nozzles for the RL10 Engine Derivative 2B for use in an early orbit transfer vehicle (OTV). Four extendible nozzle configurations for the RL10-2B engine were evaluated. Three configurations of the two position nozzle were studied including a hydrogen dump cooled metal nozzle and radiation cooled nozzles of refractory metal and carbon/carbon composite construction respectively.

Source record↗
NASA NTRS1989

Some easily analyzable convolutional codes

Convolutional codes have played and will play a key role in the downlink telemetry systems on many NASA deep-space probes, including Voyager, Magellan, and Galileo. One of the chief difficulties associated with the use of convolutional codes, however, is the notorious difficulty of analyzing them. Given a convolutional code as specified, say, by its generator polynomials, it is no easy matter to say how well that code will perform on a given noisy channel. The usual first step in such an analysis is to computer the code's free distance; this can be done with an algorithm whose complexity is exponential in the code's constraint length. The second step is often to calculate the transfer function in one, two, or three variables, or at least a few terms in its power series expansion. This step is quite hard, and for many codes of relatively short constraint lengths, it can be intractable. However, a large class of convolutional codes were discovered for which the free distance can be computed by inspection, and for which there is a closed-form expression for the three-variable transfer function. Although for large constraint lengths, these codes have relatively low rates, they are nevertheless interesting and potentially useful. Furthermore, the ideas developed here to analyze these specialized codes may well extend to a much larger class.

Mceliece, R.↗
NASA NTRS1993

A simulation study of the performance of the NASA (2,1,6) convolutional code on RFI/burst channels

In an earlier report, the LINKABIT Corporation studied the performance of the (2,1,6) convolutional code on the radio frequency interference (RFI)/burst channel using analytical methods. Using an R(sub 0) analysis, the report concluded that channel interleaving was essential to achieving reliable performance. In this report, Monte Carlo simulation techniques are used to study the performance of the convolutional code on the RFI/burst channel in more depth. The basic system model under consideration is shown. The convolutional code is the NASA standard code with generators g(exp 1) = 1+D(exp 2)+D(exp 3)+D(exp 5)+D(exp 6) and g(exp 2) = 1+D+D(exp 2)+D(exp 3)+D(exp 6) and d(sub free) = 10. The channel interleaver is of the convolutional or periodic type. The binary output of the channel interleaver is transmitted across the channel using binary phase shift keying (BPSK) modulation. The transmitted symbols are corrupted by an RFI/burst channel consisting of a combination of additive white Gaussian noise (AWGN) and RFI pulses. At the receiver, a soft-decision Viterbi decoder with no quantization and variable truncation length is used to decode the deinterleaved sequence.

Perez, Lance C.↗
NASA NTRS2006

Application of the Convolution Formalism to the Ocean Tide Potential: Results from the Gravity and Recovery and Climate Experiment (GRACE)

A computationally efficient approach to reducing omission errors in ocean tide potential models is derived and evaluated using data from the Gravity Recovery and Climate Experiment (GRACE) mission. Ocean tide height models are usually explicitly available at a few frequencies, and a smooth unit response is assumed to infer the response across the tidal spectrum. The convolution formalism of Munk and Cartwright (1966) models this response function with a Fourier series. This allows the total ocean tide height, and therefore the total ocean tide potential, to be modeled as a weighted sum of past, present, and future values of the tide-generating potential. Previous applications of the convolution formalism have usually been limited to tide height models, but we extend it to ocean tide potential models. We use luni-solar ephemerides to derive the required tide-generating potential so that the complete spectrum of the ocean tide potential is efficiently represented. In contrast, the traditionally adopted harmonic model of the ocean tide potential requires the explicit sum of the contributions from individual tidal frequencies. It is therefore subject to omission errors from neglected frequencies and is computationally more intensive. Intersatellite range rate data from the GRACE mission are used to compare convolution and harmonic models of the ocean tide potential. The monthly range rate residual variance is smaller by 4-5%, and the daily residual variance is smaller by as much as 15% when using the convolution model than when using a harmonic model that is defined by twice the number of parameters.

models↗