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All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Error-Rate Bounds for Coded PPM on a Poisson Channel

Equations for computing tight bounds on error rates for coded pulse-position modulation (PPM) on a Poisson channel at high signal-to-noise ratio have been derived. These equations and elements of the underlying theory are expected to be especially useful in designing codes for PPM optical communication systems. The equations and the underlying theory apply, more specifically, to a case in which a) At the transmitter, a linear outer code is concatenated with an inner code that includes an accumulator and a bit-to-PPM-symbol mapping (see figure) [this concatenation is known in the art as "accumulate-PPM" (abbreviated "APPM")]; b) The transmitted signal propagates on a memoryless binary-input Poisson channel; and c) At the receiver, near-maximum-likelihood (ML) decoding is effected through an iterative process. Such a coding/modulation/decoding scheme is a variation on the concept of turbo codes, which have complex structures, such that an exact analytical expression for the performance of a particular code is intractable. However, techniques for accurately estimating the performances of turbo codes have been developed. The performance of a typical turbo code includes (1) a "waterfall" region consisting of a steep decrease of error rate with increasing signal-to-noise ratio (SNR) at low to moderate SNR, and (2) an "error floor" region with a less steep decrease of error rate with increasing SNR at moderate to high SNR. The techniques used heretofore for estimating performance in the waterfall region have differed from those used for estimating performance in the error-floor region. For coded PPM, prior to the present derivations, equations for accurate prediction of the performance of coded PPM at high SNR did not exist, so that it was necessary to resort to time-consuming simulations in order to make such predictions. The present derivation makes it unnecessary to perform such time-consuming simulations.

Moision, Bruce↗
NASA NTRS2009

Joint Carrier-Phase Synchronization and LDPC Decoding

A method has been proposed to increase the degree of synchronization of a radio receiver with the phase of a suppressed carrier signal modulated with a binary- phase-shift-keying (BPSK) or quaternary- phase-shift-keying (QPSK) signal representing a low-density parity-check (LDPC) code. This method is an extended version of the method described in Using LDPC Code Constraints to Aid Recovery of Symbol Timing (NPO-43112), NASA Tech Briefs, Vol. 32, No. 10 (October 2008), page 54. Both methods and the receiver architectures in which they would be implemented belong to a class of timing- recovery methods and corresponding receiver architectures characterized as pilotless in that they do not require transmission and reception of pilot signals. The proposed method calls for the use of what is known in the art as soft decision feedback to remove the modulation from a replica of the incoming signal prior to feeding this replica to a phase-locked loop (PLL) or other carrier-tracking stage in the receiver. Soft decision feedback refers to suitably processed versions of intermediate results of iterative computations involved in the LDPC decoding process. Unlike a related prior method in which hard decision feedback (the final sequence of decoded symbols) is used to remove the modulation, the proposed method does not require estimation of the decoder error probability. In a basic digital implementation of the proposed method, the incoming signal (having carrier phase theta theta (sub c) plus noise would first be converted to inphase (I) and quadrature (Q) baseband signals by mixing it with I and Q signals at the carrier frequency [wc/(2 pi)] generated by a local oscillator. The resulting demodulated signals would be processed through one-symbol-period integrate and- dump filters, the outputs of which would be sampled and held, then multiplied by a soft-decision version of the baseband modulated signal. The resulting I and Q products consist of terms proportional to the cosine and sine of the carrier phase cc as well as correlated noise components. These products would be fed as inputs to a digital PLL that would include a number-controlled oscillator (NCO), which provides an estimate of the carrier phase, theta(sub c).

Simon, Marvin↗
NASA NTRS1996

Error Control Techniques for Satellite and Space Communications

In this report, we present the results of our recent work on turbo coding in two formats. Appendix A includes the overheads of a talk that has been given at four different locations over the last eight months. This presentation has received much favorable comment from the research community and has resulted in the full-length paper included as Appendix B, 'A Distance Spectrum Interpretation of Turbo Codes'. Turbo codes use a parallel concatenation of rate 1/2 convolutional encoders combined with iterative maximum a posteriori probability (MAP) decoding to achieve a bit error rate (BER) of 10(exp -5) at a signal-to-noise ratio (SNR) of only 0.7 dB. The channel capacity for a rate 1/2 code with binary phase shift-keyed modulation on the AWGN (additive white Gaussian noise) channel is 0 dB, and thus the Turbo coding scheme comes within 0.7 DB of capacity at a BER of 10(exp -5).

Costello, Daniel J., Jr.↗
NASA NTRS2004

A Scalable Architecture of a Structured LDPC Decoder

We present a scalable decoding architecture for a certain class of structured LDPC codes. The codes are designed using a small (n,r) protograph that is replicated Z times to produce a decoding graph for a (Z x n, Z x r) code. Using this architecture, we have implemented a decoder for a (4096,2048) LDPC code on a Xilinx Virtex-II 2000 FPGA, and achieved decoding speeds of 31 Mbps with 10 fixed iterations. The implemented message-passing algorithm uses an optimized 3-bit non-uniform quantizer that operates with 0.2dB implementation loss relative to a floating point decoder.

optical communications↗
NASA NTRS1973

Minimum switching network for generating the weight of a binary vector

Vector is divided into three variable sections, and each section is processed by unary-to-binary decoder or adder. Resulting network performs on iterative collection process; all outputs of same kind are collected in same manner. In combination with simple comparator gates, weighting network can also be used as majority network.

Anderson, T. O.↗
NASA NTRS2005

Encoders for block-circulant LDPC codes

In this paper, we present two encoding methods for block-circulant LDPC codes. The first is an iterative encoding method based on the erasure decoding algorithm, and the computations required are well organized due to the block-circulant structure of the parity check matrix. The second method uses block-circulant generator matrices, and the encoders are very similar to those for recursive convolutional codes. Some encoders of the second type have been implemented in a small Field Programmable Gate Array (FPGA) and operate at 100 Msymbols/second.

encoders↗
NASA NTRS1994

Blocking reduction of Landsat Thematic Mapper JPEG browse images using optimal PSNR estimated spectra adaptive postfiltering

Two representative sample images of Band 4 of the Landsat Thematic Mapper are compressed with the JPEG algorithm at 8:1, 16:1 and 24:1 Compression Ratios for experimental browsing purposes. We then apply the Optimal PSNR Estimated Spectra Adaptive Postfiltering (ESAP) algorithm to reduce the DCT blocking distortion. ESAP reduces the blocking distortion while preserving most of the image's edge information by adaptively postfiltering the decoded image using the block's spectral information already obtainable from each block's DCT coefficients. The algorithm iteratively applied a one dimensional log-sigmoid weighting function to the separable interpolated local block estimated spectra of the decoded image until it converges to the optimal PSNR with respect to the original using a 2-D steepest ascent search. Convergence is obtained in a few iterations for integer parameters. The optimal logsig parameters are transmitted to the decoder as a negligible byte of overhead data. A unique maxima is guaranteed due to the 2-D asymptotic exponential overshoot shape of the surface generated by the algorithm. ESAP is based on a DFT analysis of the DCT basis functions. It is implemented with pixel-by-pixel spatially adaptive separable FIR postfilters. PSNR objective improvements between 0.4 to 0.8 dB are shown together with their corresponding optimal PSNR adaptive postfiltered images.

Linares, Irving↗
NASA NTRS2005

Coupled Receiver/Decoders for Low-Rate Turbo Codes

been proposed for receiving weak single- channel phase-modulated radio signals bearing low-rate-turbo-coded binary data. Originally intended for use in receiving telemetry signals from distant spacecraft, the proposed receiver/ decoders may also provide enhanced reception in mobile radiotelephone systems. A radio signal of the type to which the proposal applies comprises a residual carrier signal and a phase-modulated data signal. The residual carrier signal is needed as a phase reference for demodulation as a prerequisite to decoding. Low-rate turbo codes afford high coding gains and thereby enable the extraction of data from arriving radio signals that might otherwise be too weak. In the case of a conventional receiver, if the signal-to-noise ratio (specifically, the symbol energy to one-sided noise power spectral density) of the arriving signal is below approximately 0 dB, then there may not be enough energy per symbol to enable the receiver to recover properly the carrier phase. One could solve the problem at the transmitter by diverting some power from the data signal to the residual carrier. A better solution . a coupled receiver/decoder according to the proposal . could reduce the needed amount of residual carrier power. In all that follows, it is to be understood that all processing would be digital and the incoming signals to be processed would be, more precisely, outputs of analog-to-digital converters that preprocess the residual carrier and data signals at a rate of multiple samples per symbol. The upper part of the figure depicts a conventional receiving system, in which the receiver and decoder are uncoupled, and which is also called a non-data-aided system because output data from the decoder are not used in the receiver to aid in recovering the carrier phase. The receiver tracks the carrier phase from the residual carrier signal and uses the carrier phase to wipe phase noise off the data signal. The receiver typically includes a phase-locked loop (PLL) or Costas loop that requires no delay or perhaps a single sample delay. The lower part of the figure depicts a basic coupled receiver/decoder . a data-aided system that would implement an iterative receiving/decoding process. The receiver would include a PLL or a Wiener filter that, to the extent possible, would track the residual carrier signal, wipe phase noise off the data signal, then send the result to the turbo decoder. Recovery of timing could be effected by, for example, a digital transition tracking loop (DTTL) or other, similar loop. The first iteration of turbo decoding would yield soft data symbols, which would be sent back to the receiver for use in softly wiping off the data signal in an effort to recover the residual carrier signal. The wiped signal would contain a relatively large carrier-phase component that could be tracked by use of a second Wiener filter.

Hamkins, Jon↗
NASA NTRS1997

Error Control Coding Techniques for Space and Satellite Communications

Bootstrap Hybrid Decoding (BHD) (Jelinek and Cocke, 1971) is a coding/decoding scheme that adds extra redundancy to a set of convolutionally encoded codewords and uses this redundancy to provide reliability information to a sequential decoder. Theoretical results indicate that bit error probability performance (BER) of BHD is close to that of Turbo-codes, without some of their drawbacks. In this report we study the use of the Multiple Stack Algorithm (MSA) (Chevillat and Costello, Jr., 1977) as the underlying sequential decoding algorithm in BHD, which makes possible an iterative version of BHD.

Costello, Daniel J., Jr.↗
NASA NTRS2006

An Iterative Information-Reduced Quadriphase-Shift-Keyed Carrier Synchronization Scheme Using Decision Feedback for Low Signal-to-Noise Ratio Applications

In a previous publication [1], an iterative closed-loop carrier synchronization scheme for binary phase-shift keyed (BPSK) modulation was proposed that was based on feeding back data decisions to the input of the loop, the purpose being to remove the modulation prior to carrier synchronization as opposed to the more conventional decision-feedback schemes that incorporate such feedback inside the loop. The idea there was that, with sufficient independence between the received data and the decisions on it that are fed back (as would occur in an error-correction coding environment with sufficient decoding delay), a pure tone in the presence of noise would ultimately be produced (after sufficient iteration and low enough error probability) and thus could be tracked without any squaring loss. This article demonstrates that, with some modification, the same idea of iterative information reduction through decision feedback can be applied to quadrature phase-shift keyed (QPSK) modulation, something that was mentioned in the previous publication but never pursued.

Simon, M.↗
NASA NTRS2013

Self-configurable radio receiver system and method for use with signals without prior knowledge of signal defining characteristics

A method, radio receiver, and system to autonomously receive and decode a plurality of signals having a variety of signal types without a priori knowledge of the defining characteristics of the signals is disclosed. The radio receiver is capable of receiving a signal of an unknown signal type and, by estimating one or more defining characteristics of the signal, determine the type of signal. The estimated defining characteristic(s) is/are utilized to enable the receiver to determine other defining characteristics. This in turn, enables the receiver, through multiple iterations, to make a maximum-likelihood (ML) estimate for each of the defining characteristics. After the type of signal is determined by its defining characteristics, the receiver selects an appropriate decoder from a plurality of decoders to decode the signal.

Hamkins, Jon↗
DOE OSTI2020

Executing a composite VLIW instruction having a scalar atom that indicates an iteration of execution

A processor core includes a storage device which stores a composite very large instruction word (VLIW) instruction, an instruction unit which obtains the composite VLIW instruction from the storage device and decodes the composite VLIW instruction to determine an operation to perform, and a composite VLIW instruction execution unit which executes the decoded composite VLIW instruction to perform the operation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Dynamic energy system modeling using hybrid physics-based and machine learning encoder–decoder models

Three model configurations are presented for multi-step time series predictions of the heat absorbed by the water and steam in a thermal power plant. The models predict over horizons of 2, 4, and 6 steps into the future, where each step is a 5-minute increment. The evaluated models are a pure machine learning model, a novel hybrid machine learning and physics-based model, and the hybrid model with an incomplete dataset. The hybrid model deconstructs the machine learning into individual boiler heat absorption units: economizer, water wall, superheater, and reheater. Each configuration uses a gated recurrent unit (GRU) or a GRU-based encoder–decoder as the deep learning architecture. Mean squared error is used to evaluate the models compared to target values. The encoder–decoder architecture is over 11% more accurate than the GRU only models. The hybrid model with the incomplete dataset highlights the importance of the manipulated variables to the system. The hybrid model, compared to the pure machine learning model, is over 10% more accurate on average over 20 iterations of each model. Automatic differentiation is applied to the hybrid model to perform a local sensitivity analysis to identify the most impactful of the 72 manipulated variables on the heat absorbed in the boiler. The models and sensitivity analyses are used in a discussion about optimizing the thermal power plant.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1970

Rapid method for interconversion of binary and decimal numbers

Decoding tree consisting of 40-bit semiconductor read-only memories interconverts binary and decimal numbers 50 to 100 times faster than current methods. Decimal-to-binary conversion algorithm is based on a divided-by-2 iterative equation, binary-to-decimal conversion algorithm utilizes multiplied-by-2 iterative equation.

Lim, R. S.↗
NASA NTRS2009

Hardware Implementation of Serially Concatenated PPM Decoder

A prototype decoder for a serially concatenated pulse position modulation (SCPPM) code has been implemented in a field-programmable gate array (FPGA). At the time of this reporting, this is the first known hardware SCPPM decoder. The SCPPM coding scheme, conceived for free-space optical communications with both deep-space and terrestrial applications in mind, is an improvement of several dB over the conventional Reed-Solomon PPM scheme. The design of the FPGA SCPPM decoder is based on a turbo decoding algorithm that requires relatively low computational complexity while delivering error-rate performance within approximately 1 dB of channel capacity. The SCPPM encoder consists of an outer convolutional encoder, an interleaver, an accumulator, and an inner modulation encoder (more precisely, a mapping of bits to PPM symbols). Each code is describable by a trellis (a finite directed graph). The SCPPM decoder consists of an inner soft-in-soft-out (SISO) module, a de-interleaver, an outer SISO module, and an interleaver connected in a loop (see figure). Each SISO module applies the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm to compute a-posteriori bit log-likelihood ratios (LLRs) from apriori LLRs by traversing the code trellis in forward and backward directions. The SISO modules iteratively refine the LLRs by passing the estimates between one another much like the working of a turbine engine. Extrinsic information (the difference between the a-posteriori and a-priori LLRs) is exchanged rather than the a-posteriori LLRs to minimize undesired feedback. All computations are performed in the logarithmic domain, wherein multiplications are translated into additions, thereby reducing complexity and sensitivity to fixed-point implementation roundoff errors. To lower the required memory for storing channel likelihood data and the amounts of data transfer between the decoder and the receiver, one can discard the majority of channel likelihoods, using only the remainder in operation of the decoder. This is accomplished in the receiver by transmitting only a subset consisting of the likelihoods that correspond to time slots containing the largest numbers of observed photons during each PPM symbol period. The assumed number of observed photons in the remaining time slots is set to the mean of a noise slot. In low background noise, the selection of a small subset in this manner results in only negligible loss. Other features of the decoder design to reduce complexity and increase speed include (1) quantization of metrics in an efficient procedure chosen to incur no more than a small performance loss and (2) the use of the max-star function that allows sum of exponentials to be computed by simple operations that involve only an addition, a subtraction, and a table lookup. Another prominent feature of the design is a provision for access to interleaver and de-interleaver memory in a single clock cycle, eliminating the multiple clock-cycle latency characteristic of prior interleaver and de-interleaver designs.

Moision, Bruce↗
DOE OSTI2018

Joint Sparsity Pattern Recovery With 1-b Compressive Sensing in Distributed Sensor Networks

In this paper, we study the problem of joint sparse support recovery with 1-b quantized compressive measurements in a distributed sensor network. Multiple nodes in the network are assumed to observe sparse signals having the same but unknown sparse support. Each node quantizes its measurement vector element-wise to 1 b. First, we consider that all the quantized measurements are available at a central fusion center. We derive performance bounds for sparsity pattern recovery using 1-bit quantized measurements from multiple sensors when the maximum likelihood decoder is employed. We further develop two computationally tractable algorithms for joint sparse support recovery in the centralized setting. One algorithm minimizes a cost function defined as the sum of the likelihood function and the l-∝ quasi-norm, while the other algorithm extends the binary iterative hard thresholding algorithm to the multiple measurement vector case. Second, we consider a decentralized setting where each node transmits 1-b measurements to its one-hop neighbors. The basic idea behind the algorithms developed in the decentralized setting is to embed collaboration among nodes and fusion strategies. We show that even with noisy 1-b compressed measurements, joint support recovery can be carried out accurately in both centralized and decentralized settings. Additionally, we further show that the performance of the proposed 1-bit compressive sensing-based algorithms is very close to that of their real-valued counterparts except when the signal-to-noise ratio is very small.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1978

A decoding procedure for the Reed-Solomon codes

A decoding procedure is described for the (n,k) t-error-correcting Reed-Solomon (RS) code, and an implementation of the (31,15) RS code for the I4-TENEX central system. This code can be used for error correction in large archival memory systems. The principal features of the decoder are a Galois field arithmetic unit implemented by microprogramming a microprocessor, and syndrome calculation by using the g(x) encoding shift register. Complete decoding of the (31,15) code is expected to take less than 500 microsecs. The syndrome calculation is performed by hardware using the encoding shift register and a modified Chien search. The error location polynomial is computed by using Lin's table, which is an interpretation of Berlekamp's iterative algorithm. The error location numbers are calculated by using the Chien search. Finally, the error values are computed by using Forney's method.

Lim, R. S.↗
DOE OSTI2026

Autonomous fabrication of tailored defect structures in 2D materials using machine learning-enabled scanning transmission electron microscopy

Materials with tailored quantum properties can be engineered from atomic-scale assembly techniques, but existing methods often lack the agility and accuracy to precisely and intelligently control the manufacturing process. Here, we demonstrate a fully autonomous approach for fabricating atomic-level defects using electron beams in scanning transmission electron microscopy (STEM) that combines advanced machine learning and automated beam control. As a proof of concept, we achieved controlled fabrication of MoS-nanowire (MoS-NW) edge structures by iterative and targeted exposure of MoS 2 monolayer to a focused electron beam to selectively eject sulfur atoms, utilizing high-angle annular dark-field (HAADF) imaging for feedback-controlled monitoring of structural evolution of defects. A machine learning framework combining a random forest model and a convolutional neural network (CNN) was developed to decode the HAADF image and accurately identify atomic positions and species. This atomic-level information was then integrated into an autonomous decision-making platform, which applied predefined fabrication strategies to instruct beam control about atomic sites to be ejected. The selected sites were subsequently exposed to a localized electron beam using an FPGA-controlled scan routine with precise control over beam positioning and duration. While the MoS-NW edge structures produced exhibit promising mechanical and electronic properties, the proposed methods to build the autonomous fabrication framework is material-agnostic and can be extended to other 2D materials for the creation of diverse defect structures and heterostructures beyond Mo S2 .

Engineering↗