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NASA NTRS1979

Time history solution program, L225 (TEV126). Volume 2: Supplemental system design and maintenance document

The time history solution program L225 (TEV126) is described. The program calculates the time responses of a linear system by convoluting the impulsive response functions with the time dependent excitation. The convolution is performed as a multiplication in the frequency domain. Fast Fourier transform techniques are used to transform the product back into the time domain to obtain response time histories. The design and structure of the program is presented.

Tornallyay, A.↗

NASA NTRS1977

50 Mbps hardware development for Shuttle Ku-band communications

The performance of a 5-Mbps coded system developed for Shuttle Ku-band communications is described. The system consists of a rate 1/2, constraint length 7 convolutional encoder-decoder and soft decision symbol synchronizer; the system has been band-limited at the transmitted symbol rate. Five convolutional decoders are operated in parallel to permit operation at the required data rate. It is found that the multiplexed encoder-decoder system does not exhibit any observable coding gain degradation when the channel is limited to the symbol rate at baseband.

Vang, H. A.↗

NASA NTRS1978

Effects of data asymmetry on Shuttle Ku-band communications link performance

This paper systematically analyzes the signal-to-noise ratio degradations which can potentially occur due to data asymmetry in digital transmission systems. Suitable asymmetry models are developed and error probability performance for various types of data detectors (integrate-and-dump filter, filter-sample detector, and gated-integrate-and-dump filter) is derived. Although this work was done to resolve problems being encountered in the Shuttle Ku-band return link design, specifically for the 50 Mbit/s convolutionally encoded channel (NRZ format), generalizations are made which provide results for other cases of interest (other Ku-band return link channels, or other systems entirely). This paper therefore considers Manchester data formats (in addition to NRZ) and uncoded transmission (in addition to convolutionally coded transmission). The effects of bandlimiting are also considered.

Simon, M. K.↗

NASA NTRS1978

Deconvolution estimation theory applied to Nimbus 6 ERB data

It is pointed out that the ERB (Earth Radiation Budget) Experiment aboard the Nimbus 6 spacecraft has provided nearly 3 years of data thus far from its wide field of view (WFOV) radiometers. Each data point is an integral of the irradiance from all points within the field of view of the WFOV sensor, which is an approximately 60 deg diameter circular region on the earth. House (1972) proposed that the data, being a convolution of the flux field at the top of the atmosphere, could be convoluted so as to enhance the resolution. The problem was solved by Smith and Green (1975-76) for the case of earth emitted radiation. A parameter estimation approach to the deconvolution problem was formulated. A description is presented of the deconvolution estimation concept and the results obtained by its application to the Nimbus 6 ERB WFOV data for earth emitted radiation for August 1975.

Green, R. N.↗

NASA NTRS1979

Correction of instrumental distortion by analytical deconvolution of data

A general analytical theorem developed by van de Hulst (1946) for inverting the convolution integral is reviewed and illustrated both with synthetic data and with experimental data from time-of-flight measurements. If the undesired influence of an instrument used in an experimental measurement can be represented by the convolution integral, the original undistorted or true distribution may sometimes be recovered in postprocessing the data by means of deconvolution. Analytical deconvolution is achieved by using the coefficients from a power series representation of the distorted output distribution and a set of 'solving polynomials' which may be readily derived from the response function of the instrument.

Morton, D. C.↗

NASA NTRS1980

Capacity, cutoff rate, and coding for a direct-detection optical channel

It is shown that Pierce's pulse position modulation scheme with 2 to the L pulse positions used on a self-noise-limited direct detection optical communication channel results in a 2 to the L-ary erasure channel that is equivalent to the parallel combination of L completely correlated binary erasure channels. The capacity of the full channel is the sum of the capacities of the component channels, but the cutoff rate of the full channel is shown to be much smaller than the sum of the cutoff rates. An interpretation of the cutoff rate is given that suggests a complexity advantage in coding separately on the component channels. It is shown that if short-constraint-length convolutional codes with Viterbi decoders are used on the component channels, then the performance and complexity compare favorably with the Reed-Solomon coding system proposed by McEliece for the full channel. The reasons for this unexpectedly fine performance by the convolutional code system are explored in detail, as are various facets of the channel structure.

Massey, J. L.↗

NASA NTRS1981

Performance of concatenated codes for deep space missions

Computer simulation results are presented on the performance of convolutional codes of constraint lengths 7 and 10 concatenated with the (255, 223) Reed-Solomon code (a proposed NASA standard). These results indicate that as much as 0.8 dB can be gained by concatenating this Reed-Solomon code with a (10, 1/3) convolutional code, instead of the (7, 1/2) code currently used by the DSN.

Butman, S. A.↗

NASA NTRS1981

An experimental study of the concatenated Reed-Solomon/Viterbi channel coding system performance and its impact on space communications

The need for efficient space communication at very low bit error probabilities to the specification and implementation of a concatenated coding system using an interleaved Reed-Solomon code as the outer code and a Viterbi-decoded convolutional code as the inner code. Experimental results of this channel coding system are presented under an emulated S-band uplink and X-band downlink two-way space communication channel, where both uplink and downlink have strong carrier power. This work was performed under the NASA End-to-End Data Systems program at JPL. Test results verify that at a bit error probability of 10 to the -6 power or less, this concatenated coding system does provide a coding gain of 2.5 dB or more over the Viterbi-decoded convolutional-only coding system. These tests also show that a desirable interleaving depth for the Reed-Solomon outer code is 8 or more. The impact of this "virtually" error-free space communication link on the transmission of images is discussed and examples of simulation results are given.

Liu, K. Y.↗

NASA NTRS1981

On the error statistics of Viterbi decoding and the performance of concatenated codes

Miller, R. L.↗

NASA NTRS1981

Fast polynomial transform and its implementation by computer

A fast polynomial transform (FPT) algorithm for computing two-dimensional cyclic convolutions on a general-purpose computer is demonstrated and compared with the FFT approach. An FPT program for two-dimensional convolutions written in FORTRAN is shown to be 20% faster than the conventional FFT algorithm. This higher speed advantage makes the FPT algorithm a candidate for many two-dimensional digital image filtering applications.

Reed, I. S.↗

NASA NTRS1981

Alternative methods to smooth the Earth's gravity field

Convolutions on the sphere with corresponding convolution theorems are developed for one and two dimensional functions. Some of these results are used in a study of isotropic smoothing operators or filters. Well known filters in Fourier spectral analysis, such as the rectangular, Gaussian, and Hanning filters, are adapted for data on a sphere. The low-pass filter most often used on gravity data is the rectangular (or Pellinen) filter. However, its spectrum has relatively large sidelobes; and therefore, this filter passes a considerable part of the upper end of the gravity spectrum. The spherical adaptations of the Gaussian and Hanning filters are more efficient in suppressing the high-frequency components of the gravity field since their frequency response functions are strongly field since their frequency response functions are strongly tapered at the high frequencies with no, or small, sidelobes. Formulas are given for practical implementation of these new filters.

Jekeli, C.↗

NASA NTRS1982

A parallel VLSI architecture for a digital filter of arbitrary length using Fermat number transforms

A parallel architecture for computation of the linear convolution of two sequences of arbitrary lengths using the Fermat number transform (FNT) is described. In particular a pipeline structure is designed to compute a 128-point FNT. In this FNT, only additions and bit rotations are required. A standard barrel shifter circuit is modified so that it performs the required bit rotation operation. The overlap-save method is generalized for the FNT to compute a linear convolution of arbitrary length. A parallel architecture is developed to realize this type of overlap-save method using one FNT and several inverse FNTs of 128 points. The generalized overlap save method alleviates the usual dynamic range limitation in FNTs of long transform lengths. Its architecture is regular, simple, and expandable, and therefore naturally suitable for VLSI implementation.

Truong, T. K.↗

NASA NTRS1981

Capacity, cutoff rate, and coding for a direct-detection optical channel

It is shown that when Pierce's pulse-position modulation scheme with 2 to the L power positions (where L is some positive integer) is used on a self-noise-limited direct-detection optical communication channel, there results a (2 to the L power)-ary erasure channel that is equivalent to the parallel combination of L completely correlated binary erasure channels. The capacity of the full channel is the sum of the capacities of the component channels, but the cutoff rate of the full channel is shown to be much smaller than the sum of the cutoff rates. An interpretation of the cutoff rate is given that suggests a complexity advantage in coding separately on the component channels. It is shown that if short-constraint length convolutional codes with Viterbi decoders are used on the component channels, then the performance and complexity compare favorably with the Reed-Solomon coding system proposed by McEliece (1979) for the full channel. The reasons for this unexpectedly fine performance by the convolutional code system are explored in detail, as are various facets of the channel structure.

Massey, J. L.↗

NASA NTRS1980

The effects of receiver tracking phase error on the performance of the concatenated Reed-Solomon Viterbi channel coding system

In connection with attempts to achieve very low error probabilities, Odenwalder (1970) proposed a concatenated coding system using the Viterbi-decoded convolutional codes as the inner code and Reed-Solomon (RS) codes as the outer code. Analytical and experimental results are presented concerning the effects of the receiver tracking phase error on the performance of the concatenated RS/Viterbi channel coding system. On the basis of these results it is concluded that certain problems regarding communication operations on deep-space missions can be alleviated by employing the RS/Viterbi coding system. In one-way communication, an employment of RS/Viterbi coding will also provide greater data protection than the Viterbi-decoded convolutional-only coding system.

Liu, K. Y.↗

NASA NTRS1982

Viterbi decoder node synchronization losses in the Reed-Solomon/Veterbi concatenated channel

The Viterbi decoders currently used by the Deep Space Network (DSN) employ an algorithm for maintaining node synchronization that significantly degrades at bit signal-to-noise ratios (SNRs) of below 2.0 dB. In a recent report by the authors, it was shown that the telemetry receiving system, which uses a convolutionally encoded downlink, will suffer losses of 0.85 dB and 1.25 dB respectively at Voyager 2 Uranus and Neptune encounters. This report extends the results of that study to a concatenated (255,223) Reed-Solomon/(7, 1/2) convolutionally coded channel, by developing a new radio loss model for the concatenated channel. It is shown here that losses due to improper node synchronization of 0.57 dB at Uranus and 1.0 dB at Neptune can be expected if concatenated coding is used along with an array of one 64-meter and three 34-meter antennas.

Deutsch, L. J.↗

NASA NTRS1985

Parallel VLSI Architecture

Fermat number transformation convolutes two digital data sequences. Very-large-scale integration (VLSI) applications, such as image and radar signal processing, X-ray reconstruction, and spectrum shaping, linear convolution of two digital data sequences of arbitrary lenghts accomplished using Fermat number transform (ENT).

Truong, T. K.↗

NASA NTRS1983

LANDSAT-4 thematic mapper Modulation Transfer Function (MTF) evaluation

A power spectrum (PS) analysis technique was used to compare thematic mapper (TM) A and P-tape data for a Washington, DC scene in two orthogonal directions, along scan and along track. The resulting effective modulation transfer functions (MTF) between the A and P data are repeatable from area to area and consistent with theoretical expectations. The average x-direction (along scan) MTF calculated with the PS technique is compared to the MTF of the cubic convolution resampling function used to create P data from A data. The two curves are nearly identical, indicating that the major factor affecting the image quality of P data relative to A data is the cubic convolution resampling.

Schowengerdt, R.↗

NASA NTRS1983

Relationship of strength of turbulence to received power

Because of contributions due to reflection, the determination of the turbulence refractive index structure constant may be affected. For pure scattering from turbulence in the inertial subrange, the radar echo power can be used to calculate the refractive index structure constant. The radar power is determined by a convolution integral. If the antenna beam is swung to sufficiently large off-zenith angles ( 12.5 deg) so that a quasi-isotropic response from the tail ends of the Gaussian angular distribution can be anticipated, the evaluation of the convolution integral depends only on the known antenna pattern of the radar. This procedure, swinging the radar beam to attenuate the reflected component, may be called angular or direction filtering. The tilted antenna also may be pick up reflected components from near the zenith through the sidelobes. This can be tested by the evaluation of the correlation function. This method applies a time domain filtering of the intensity time series but needs a very careful selection of the high pass filters.

Rottger, J.↗