Results for “Convolution” — Page 15

NASA NTRS2010

Performance Bounds on Two Concatenated, Interleaved Codes

A method has been developed of computing bounds on the performance of a code comprised of two linear binary codes generated by two encoders serially concatenated through an interleaver. Originally intended for use in evaluating the performances of some codes proposed for deep-space communication links, the method can also be used in evaluating the performances of short-block-length codes in other applications. The method applies, more specifically, to a communication system in which following processes take place: At the transmitter, the original binary information that one seeks to transmit is first processed by an encoder into an outer code (Co) characterized by, among other things, a pair of numbers (n,k), where n (n > k)is the total number of code bits associated with k information bits and n k bits are used for correcting or at least detecting errors. Next, the outer code is processed through either a block or a convolutional interleaver. In the block interleaver, the words of the outer code are processed in blocks of I words. In the convolutional interleaver, the interleaving operation is performed bit-wise in N rows with delays that are multiples of B bits. The output of the interleaver is processed through a second encoder to obtain an inner code (Ci) characterized by (ni,ki). The output of the inner code is transmitted over an additive-white-Gaussian- noise channel characterized by a symbol signal-to-noise ratio (SNR) Es/No and a bit SNR Eb/No. At the receiver, an inner decoder generates estimates of bits. Depending on whether a block or a convolutional interleaver is used at the transmitter, the sequence of estimated bits is processed through a block or a convolutional de-interleaver, respectively, to obtain estimates of code words. Then the estimates of the code words are processed through an outer decoder, which generates estimates of the original information along with flags indicating which estimates are presumed to be correct and which are found to be erroneous. From the perspective of the present method, the topic of major interest is the performance of the communication system as quantified in the word-error rate and the undetected-error rate as functions of the SNRs and the total latency of the interleaver and inner code. The method is embodied in equations that describe bounds on these functions. Throughout the derivation of the equations that embody the method, it is assumed that the decoder for the outer code corrects any error pattern of t or fewer errors, detects any error pattern of s or fewer errors, may detect some error patterns of more than s errors, and does not correct any patterns of more than t errors. Because a mathematically complete description of the equations that embody the method and of the derivation of the equations would greatly exceed the space available for this article, it must suffice to summarize by reporting that the derivation includes consideration of several complex issues, including relationships between latency and memory requirements for block and convolutional codes, burst error statistics, enumeration of error-event intersections, and effects of different interleaving depths. In a demonstration, the method was used to calculate bounds on the performances of several communication systems, each based on serial concatenation of a (63,56) expurgated Hamming code with a convolutional inner code through a convolutional interleaver. The bounds calculated by use of the method were compared with results of numerical simulations of performances of the systems to show the regions where the bounds are tight (see figure).

Moision, Bruce↗

NASA NTRS2022

A Novel Machine Learning-Based Gap-Filling of Fine-Resolution Remotely Sensed Snow Cover Fraction Data By Combining Downscaling and Regression

Satellite-based remotely sensed observations of snow cover fraction (SCF) can have data gaps in spatially distributed coverage from sensor and orbital limitations. We mitigate these limitations in the example fine-resolution Moderate Resolution Imaging Spectroradiometer (MODIS) data by gap-filling using auxiliary 1-km datasets that either aid in downscaling from coarser-resolution (5 km) MODIS SCF wherever not fully covered by clouds, or else by themselves via regression wherever fully cloud covered. This study’s prototype predicts a 1-km version of the 500-m MOD10A1 SCF target. Due to noncollocatedness of spatial gaps even across input and auxiliary datasets, we consider a recent gap-agnostic advancement of partial convolution in computer vision for both training and predictive gap-filling. Partial convolution accommodates spatially consistent gaps across the input images, effectively implementing a two-dimensional masking. To overcome reduced usable data from noncollocated spatial gaps across inputs, we innovate a fully generalized three-dimensional masking in this partial convolution. This enables a valid output value at a pixel even if only a single valid input variable and its value exist in the neighborhood covered by the convolutional filter zone centered around that pixel. Thus, our gap-agnostic technique can use significantly more examples for training (∼67%) and prediction (∼100%), instead of only less than 10% for the previous partial convolution. We train an example simple three-layer legacy super-resolution convolutional neural network (SRCNN) to obtain downscaling and regression component performances that are better than baseline values of either climatology or MOD10C1 SCF as relevant. Our generalized partial convolution can enable multiple Earth science applications like downscaling, regression, classification, and segmentation that were hindered by data gaps.

Soni Yatheendradas↗

NASA NTRS1995

Further Developments in the Communication Link and Error Analysis (CLEAN) Simulator

During the period 1 July 1993 - 30 June 1994, significant developments to the Communication Link and Error ANalysis (CLEAN) simulator were completed. Many of these were reported in the Semi-Annual report dated December 1993 which has been included in this report in Appendix A. Since December 1993, a number of additional modules have been added involving Unit-Memory Convolutional codes (UMC). These are: (1) Unit-Memory Convolutional Encoder module (UMCEncd); (2) Hard decision Unit-Memory Convolutional Decoder using the Viterbi decoding algorithm (VitUMC); and (3) a number of utility modules designed to investigate the performance of LTMC's such as LTMC column distance function (UMCdc), UMC free distance function (UMCdfree), UMC row distance function (UMCdr), and UMC Transformation (UMCTrans). The study of UMC's was driven, in part, by the desire to investigate high-rate convolutional codes which are better suited as inner codes for a concatenated coding scheme. A number of high-rate LTMC's were found which are good candidates for inner codes. Besides the further developments of the simulation, a study was performed to construct a table of the best known Unit-Memory Convolutional codes. Finally, a preliminary study of the usefulness of the Periodic Convolutional Interleaver (PCI) was completed and documented in a Technical note dated March 17, 1994. This technical note has also been included in this final report.

Ebel, William J.↗

NASA NTRS1993

Digital Low-Pass Filter Without Phase Shift

Relatively simple low-pass-filtering algorithm suppresses high-frequency noise in digitally sampled signal. Algorithm derived from convolution of signal with causal exponential. Filter implemented by algorithm does not introduce phase shift. Algorithm applies forward convolution in time followed by backward convolution in time, and phase shift in second convolution cancels phase shift in first convolution.

Simon, Wayne E.↗

NASA NTRS1994

On the application of under-decimated filter banks

Maximally decimated filter banks have been extensively studied in the past. A filter bank is said to be under-decimated if the number of channels is more than the decimation ratio in the subbands. A maximally decimated filter bank is well known for its application in subband coding. Another application of maximally decimated filter banks is in block filtering. Convolution through block filtering has the advantages that parallelism is increased and data are processed at a lower rate. However, the computational complexity is comparable to that of direct convolution. More recently, another type of filter bank convolver has been developed. In this scheme, the convolution is performed in the subbands. Quantization and bit allocation of subband signals are based on signal variance, as in subband coding. Consequently, for a fixed rate, the result of convolution is more accurate than is direct convolution. This type of filter bank convolver also enjoys the advantages of block filtering, parallelism, and a lower working rate. Nevertheless, like block filtering, there is no computational saving. In this article, under-decimated systems are introduced to solve the problem. The new system is decimated only by half the number of channels. Two types of filter banks can be used in the under-decimated system: the discrete Fourier transform (DFT) filter banks and the cosine modulated filter banks. They are well known for their low complexity. In both cases, the system is approximately alias free, and the overall response is equivalent to a tunable multilevel filter. Properties of the DFT filter banks and the cosine modulated filter banks can be exploited to simultaneously achieve parallelism, computational saving, and a lower working rate. Furthermore, for both systems, the implementation cost of the analysis or synthesis bank is comparable to that of one prototype filter plus some low-complexity modulation matrices. The individual analysis and synthesis filters have complex coefficients in the DFT filter banks but have real coefficients in the cosine modulated filter banks.

Lin, Y.-P.↗

NASA NTRS1976

Shear flexibility for structures

This device comprises a flexible sheet member having cross convolutions oriented 45.degree. to the shear vector with spherical reliefs at the convolution junctions. The spherical reliefs are essential to the shear flexibility by interrupting the principal stress lines that act along the ridges of the convolutions. The spherical reliefs provide convolutions in both directions in the plane of the cross-convolution ridges.

Stangeland, Maynard L.↗

NASA NTRS1977

Shear flexibility for structures

This device comprises a flexible sheet member having cross convolutions oriented 45.degree. to the shear vector with spherical reliefs at the convolution junctions. The spherical reliefs are essential to the shear flexibility by interrupting the principal stress lines that act along the ridges of the convolutions. The spherical reliefs provide convolutions in both directions in the plane of the cross-convolution ridges.

Stangeland, Maynard L.↗

NASA NTRS2014

Protograph-Based Raptor-Like Codes

Theoretical analysis has long indicated that feedback improves the error exponent but not the capacity of pointto- point memoryless channels. The analytic and empirical results indicate that at short blocklength regime, practical rate-compatible punctured convolutional (RCPC) codes achieve low latency with the use of noiseless feedback. In 3GPP, standard rate-compatible turbo codes (RCPT) did not outperform the convolutional codes in the short blocklength regime. The reason is the convolutional codes for low number of states can be decoded optimally using Viterbi decoder. Despite excellent performance of convolutional codes at very short blocklengths, the strength of convolutional codes does not scale with the blocklength for a fixed number of states in its trellis.

Divsalar, Dariush↗

NASA NTRS1977

Resampling study

The author has identified the following significant results. The nearest neighbor and cubic convolution resampling algorithms were applied to a variety of images extracted from LANDSAT MSS data. A comparison of the results demonstrated that (1) cubic convolution can cause spreading of small features and can introduce noticeable overshoot (ringing) into the data; (2) cubic convolution attenuates the high spatial frequencies compared to the original and nearest neighbor resampled data; and (3) cubic convolution generally produces photographic products of superior visual quality. The effects of the resampling algorithms on multispectral classification were not conclusively determined due to the small number of images tested.

Ferneyhough, D. G.↗

NASA NTRS1987

Fast-Polynomial-Transform Program

Computer program uses fast-polynomial-transformation (FPT) algorithm applicable to two-dimensional mathematical convolutions. Two-dimensional cyclic convolutions converted to one-dimensional convolutions in polynomial rings. Program decomposes cyclic polynomials into polynomial convolutions of same length. Only FPT's and fast Fourier transforms of same length required. Modular approach saves computional resources. Program written in C.

Truong, T. K.↗

NASA NTRS1992

Error control techniques for satellite and space communications

Worked performed during the reporting period is summarized. Construction of robustly good trellis codes for use with sequential decoding was developed. The robustly good trellis codes provide a much better trade off between free distance and distance profile. The unequal error protection capabilities of convolutional codes was studied. The problem of finding good large constraint length, low rate convolutional codes for deep space applications is investigated. A formula for computing the free distance of 1/n convolutional codes was discovered. Double memory (DM) codes, codes with two memory units per unit bit position, were studied; a search for optimal DM codes is being conducted. An algorithm for constructing convolutional codes from a given quasi-cyclic code was developed. Papers based on the above work are included in the appendix.

Costello, Daniel J., Jr.↗

NASA NTRS1998

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes

Decoding algorithms based on the trellis representation of a code (block or convolutional) drastically reduce decoding complexity. The best known and most commonly used trellis-based decoding algorithm is the Viterbi algorithm. It is a maximum likelihood decoding algorithm. Convolutional codes with the Viterbi decoding have been widely used for error control in digital communications over the last two decades. This chapter is concerned with the application of the Viterbi decoding algorithm to linear block codes. First, the Viterbi algorithm is presented. Then, optimum sectionalization of a trellis to minimize the computational complexity of a Viterbi decoder is discussed and an algorithm is presented. Some design issues for IC (integrated circuit) implementation of a Viterbi decoder are considered and discussed. Finally, a new decoding algorithm based on the principle of compare-select-add is presented. This new algorithm can be applied to both block and convolutional codes and is more efficient than the conventional Viterbi algorithm based on the add-compare-select principle. This algorithm is particularly efficient for rate 1/n antipodal convolutional codes and their high-rate punctured codes. It reduces computational complexity by one-third compared with the Viterbi algorithm.

Lin, Shu↗

NASA NTRSDate not supplied

Performance of A Real-Time Photon Counting Optical Receiver in the Presence of Emulated Channel Fading

Free-space optical communication links with terrestrial ground stations experience fading due to atmospheric scintillation and beam pointing. Fiber-coupled receiver systems experience additional fading at the interface between the fiber and free-space optics of the telescope. The National Aeronautics and Space Administration (NASA) Glenn Research Center (GRC) has characterized a real-time photon-counting optical ground receiver system with an atmospheric fade emulation system. The receiver system is comprised of a fiber interconnect, an array of superconducting nanowire single photon detectors (SNSPDs), and a field programmable gate array (FPGA) based receive modem. Two fiber interconnect/detector architectures have been studied. One architecture uses a 70-mode photonic lantern coupled to seven single pixel SNSPDs. The other architecture uses a 10-mode few-mode fiber (FMF) coupled to a 15-pixel SNSPD array. The receiver system complies with the Consultative Committee for Space Data Systems (CCSDS) Optical Communications High Photon Efficiency Coding and Synchronization Standard, which uses serially concatenated convolutionally coded pulse-position modulation (SCPPM). The CCSDS standard is designed for use in low photon flux missions, including the Orion Artemis-II Optical (O2O) communications demonstration. The standard utilizes a convolutional symbol interleaver which can be resized to mitigate different fades. The fade emulation system employed in this work emulates scintillation-induced, pointing-induced, and coupling-induced fading. This paper gives an overview of the real-time optical receiver system and the fade emulation system. It presents tests results which show the impact of fading on the performance on the receiver. The test results show that in the presence of channel fading, the 70-mode photonic lantern outperforms the 10-mode FMF under higher (D/r_0=9) turbulence conditions due to high fiber-coupling-induced fading and fiber coupling loss on the 10-mode FMF. When operating in lower turbulence (D/r_0=4), the 10-mode FMF outperforms the 70-mode photonic lantern. The paper also shows a larger convolutional interleaver improves the system performance as long as the receiver does not lose acquisition.

optical communications↗

NASA NTRSDate not supplied

Performance of a real-time photon counting optical receiver in the presence of emulated channel fading

Free-space optical communication links with terrestrial ground stations experience fading due to atmospheric scintillation and beam pointing. Fiber-coupled receiver systems experience additional fading at the interface between the fiber and free-space optics of the telescope. The National Aeronautics and Space Administration (NASA) Glenn Research Center (GRC) has characterized a real-time photon-counting optical ground receiver system with an atmospheric fade emulation system. The receiver system is comprised of a fiber interconnect, an array of superconducting nanowire single photon detectors (SNSPDs), and a field programmable gate array (FPGA) based receive modem. Two fiber interconnect/detector architectures have been studied. One architecture uses a 70-mode photonic lantern coupled to seven single pixel SNSPDs. The other architecture uses a 10-mode few-mode fiber (FMF) coupled to a 15-pixel SNSPD array. The receiver system complies with the Consultative Committee for Space Data Systems (CCSDS) Optical Communications High Photon Efficiency Coding and Synchronization Standard, which uses serially concatenated convolutionally coded pulse-position modulation (SCPPM). The CCSDS standard is designed for use in low photon flux missions, including the Orion Artemis-II Optical (O2O) communications demonstration. The standard utilizes a convolutional symbol interleaver which can be resized to mitigate different fades. The fade emulation system employed in this work emulates scintillation-induced, pointing-induced, and coupling-induced fading. This paper gives an overview of the real-time optical receiver system and the fade emulation system. It presents tests results which show the impact of fading on the performance on the receiver. The test results show that in the presence of channel fading, the 70-mode photonic lantern outperforms the 10-mode FMF under higher (D/r_0=9) turbulence conditions due to high fiber-coupling-induced fading and fiber coupling loss on the 10-mode FMF. When operating in lower turbulence (D/r_0=4), the 10-mode FMF outperforms the 70-mode photonic lantern. The paper also shows a larger convolutional interleaver improves the system performance as long as the receiver does not lose acquisition.

optical communications↗

NASA NTRS1972

Manufacture and quality control of interconnecting wire hardnesses, Volume 1

A standard is presented for manufacture, installation, and quality control of eight types of interconnecting wire harnesses. The processes, process controls, and inspection and test requirements reflected are based on acknowledgment of harness design requirements, acknowledgment of harness installation requirements, identification of the various parts, materials, etc., utilized in harness manufacture, and formulation of a typical manufacturing flow diagram for identification of each manufacturing and quality control process, operation, inspection, and test. The document covers interconnecting wire harnesses defined in the design standard, including type 1, enclosed in fluorocarbon elastomer convolute, tubing; type 2, enclosed in TFE convolute tubing lines with fiberglass braid; type 3, enclosed in TFE convolute tubing; and type 5, combination of types 3 and 4. Knowledge gained through experience on the Saturn 5 program coupled with recent advances in techniques, materials, and processes was incorporated.

Source record↗

NASA NTRS1973

Lp-stability (1 less than or equal to p less than or equal to infinity) of multivariable nonlinear time-varying feedback systems that are open-loop unstable

A class of multivariable, nonlinear time-varying feedback systems with an unstable convolution subsystem as feedforward and a time-varying nonlinear gain as feedback was considered. The impulse response of the convolution subsystem is the sum of a finite number of increasing exponentials multiplied by nonnegative powers of the time t, a term that is absolutely integrable and an infinite series of delayed impulses. The main result is a theorem. It essentially states that if the unstable convolution subsystem can be stabilized by a constant feedback gain F and if incremental gain of the difference between the nonlinear gain function and F is sufficiently small, then the nonlinear system is L(p)-stable for any p between one and infinity. Furthermore, the solutions of the nonlinear system depend continuously on the inputs in any L(p)-norm. The fixed point theorem is crucial in deriving the above theorem.

Callier, F. M.↗

NASA NTRS1974

An investigation of the facsimile camera response to object motion

A general analytical model of the facsimile camera response to object motion is derived as an initial step toward characterizing the resulting image degradation. This model expresses the spatial convolution of a time-varying object radiance distribution and camera point-spread function for each picture element in the image. Time variations and these two functions during each convolution account for blurring of small image detail, and variations between, as well as during, successive convolutions account for geometric image distortions. If the object moves beyond the angular extent of several picture elements while it is being imaged, then geometric distortion tends to dominate blurring as the primary cause of image degradation. The extent of distortion depends not only on object size and velocity but also on the direction of object motion, and is therefore difficult to classify in a general sense.

Huck, F. O.↗

NASA NTRS1976

Coordinated design of coding and modulation systems

The joint optimization of the coding and modulation systems employed in telemetry systems was investigated. Emphasis was placed on formulating inner and outer coding standards used by the Goddard Spaceflight Center. Convolutional codes were found that are nearly optimum for use with Viterbi decoding in the inner coding of concatenated coding systems. A convolutional code, the unit-memory code, was discovered and is ideal for inner system usage because of its byte-oriented structure. Simulations of sequential decoding on the deep-space channel were carried out to compare directly various convolutional codes that are proposed for use in deep-space systems.

Massey, J. L.↗