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NASA NTRS1988

A long constraint length VLSI Viterbi decoder for the DSN

A Viterbi decoder, capable of decoding convolutional codes with constraint lengths up to 15, is under development for the Deep Space Network (DSN). The objective is to complete a prototype of this decoder by late 1990, and demonstrate its performance using the (15, 1/4) encoder in Galileo. The decoder is expected to provide 1 to 2 dB improvement in bit SNR, compared to the present (7, 1/2) code and existing Maximum Likelihood Convolutional Decoder (MCD). The decoder will be fully programmable for any code up to constraint length 15, and code rate 1/2 to 1/6. The decoder architecture and top-level design are described.

Statman, J. I.↗

NASA NTRS1989

An algorithm for computing the distance spectrum of trellis codes

A class of quasiregular codes is defined for which the distance spectrum can be calculated from the codeword corresponding to the all-zero information sequence. Convolutional codes and regular codes are both quasiregular, as well as most of the best known trellis codes. An algorithm to compute the distance spectrum of linear, regular, and quasiregular trellis codes is presented. In particular, it can calculate the weight spectrum of convolutional (linear trellis) codes and the distance spectrum of most of the best known trellis codes. The codes do not have to be linear or regular, and the signals do not have to be used with equal probabilities. The algorithm is derived from a bidirectional stack algorithm, although it could also be based on the Viterbi algorithm. The algorithm is used to calculate the beginning of the distance spectrum of some of the best known trellis codes and to compute tight estimates on the first-event-error probability and on the bit-error probability.

Rouanne, Marc↗

NASA NTRS1989

Optimal focal-plane restoration

Image restoration can be implemented efficiently by calculating the convolution of the digital image and a small kernel during image acquisition. Processing the image in the focal-plane in this way requires less computation than traditional Fourier-transform-based techniques such as the Wiener filter and constrained least-squares filter. Here, the values of the convolution kernel that yield the restoration with minimum expected mean-square error are determined using a frequency analysis of the end-to-end imaging system. This development accounts for constraints on the size and shape of the spatial kernel and all the components of the imaging system. Simulation results indicate the technique is effective and efficient.

Reichenbach, Stephen E.↗

NASA NTRS1990

A combined finite element-boundary element formulation for solution of two-dimensional problems via CGFFT

A method for the computation of electromagnetic scattering from arbitrary two-dimensional bodies is presented. The method combines the finite element and boundary element methods leading to a system for solution via the conjugate gradient Fast Fourier Transform (FFT) algorithm. Two forms of boundaries aimed at reducing the storage requirement of the boundary integral are investigated. It is shown that the boundary integral becomes convolutional when a circular enclosure is chosen, resulting in reduced storage requirement when the system is solved via the conjugate gradient FFT method. The same holds for the ogival enclosure, except that some of the boundary integrals are not convolutional and must be carefully treated to maintain O(N) memory requirement. Results for several circular and ogival structures are presented and shown to be in excellent agreement with those obtained by traditional methods.

Collins, Jeffery D.↗

NASA NTRS1990

A VLSI decomposition of the deBruijn graph

A new Viterbi decoder for convolutional codes with constraint lengths up to 15, called the Big Viterbi Decoder, is under development for the Deep Space Network. It will be demonstrated by decoding data from the Galileo spacecraft, which has a rate 1/4, constraint-length 15 convolutional encoder on board. Here, the mathematical theory underlying the design of the very-large-scale-integrated (VLSI) chips that are being used to build this decoder is explained. The deBruijn graph B sub n describes the topology of a fully parallel, rate 1/v, constraint length n+2 Viterbi decoder, and it is shown that B sub n can be built by appropriately wiring together (i.e., connecting together with extra edges) many isomorphic copies of a fixed graph called a B sub n building block. The efficiency of such a building block is defined as the fraction of the edges in B sub n that are present in the copies of the building block. It is shown, among other things, that for any alpha less than 1, there exists a graph G which is a B sub n building block of efficiency greater than alpha for all sufficiently large n. These results are illustrated by describing a special hierarchical family of deBruijn building blocks, which has led to the design of the gate-array chips being used in the Big Viterbi Decoder.

Collins, O.↗

NASA NTRS1990

Modulation and coding for satellite and space communications

Several modulation and coding advances supported by NASA are summarized. To support long-constraint-length convolutional code, a VLSI maximum-likelihood decoder, utilizing parallel processing techniques, which is being developed to decode convolutional codes of constraint length 15 and a code rate as low as 1/6 is discussed. A VLSI high-speed 8-b Reed-Solomon decoder which is being developed for advanced tracking and data relay satellite (ATDRS) applications is discussed. A 300-Mb/s modem with continuous phase modulation (CPM) and codings which is being developed for ATDRS is discussed. Trellis-coded modulation (TCM) techniques are discussed for satellite-based mobile communication applications.

Yuen, Joseph H.↗

NASA NTRS1991

Frame error rate of the NASA concatenated coding system

For a concatenated coding system, the effect of interleaving depth on interleaved frame-error rate is compiled by simulation. Comparisons are made for three different inner convolutional codes; all three systems have a (255,223) 8-bit Reed-Solomon code as an outer code. For all the inner convolutional codes tested, an interleaving depth smaller that 4 causes substantial loss.

Swanson, L.↗

NASA NTRS1991

Development of a probabilistic analysis methodology for structural reliability estimation

The novel probabilistic analysis method for assessment of structural reliability presented, which combines fast-convolution with an efficient structural reliability analysis, can after identifying the most important point of a limit state proceed to establish a quadratic-performance function. It then transforms the quadratic function into a linear one, and applies fast convolution. The method is applicable to problems requiring computer-intensive structural analysis. Five illustrative examples of the method's application are given.

Torng, T. Y.↗

NASA NTRS1991

Fault-tolerant multichannel demultiplexer subsystems

Fault tolerance in future processing and switching communication satellites is addressed by showing new methods for detecting hardware failures in the first major subsystem, the multichannel demultiplexer. An efficient method for demultiplexing frequency slotted channels uses multirate filter banks which contain fast Fourier transform processing. All numerical processing is performed at a lower rate commensurate with the small bandwidth of each bandbase channel. The integrity of the demultiplexing operations is protected by using real number convolutional codes to compute comparable parity values which detect errors at the data sample level. High rate, systematic convolutional codes produce parity values at a much reduced rate, and protection is achieved by generating parity values in two ways and comparing them. Parity values corresponding to each output channel are generated in parallel by a subsystem, operating even slower and in parallel with the demultiplexer that is virtually identical to the original structure. These parity calculations may be time shared with the same processing resources because they are so similar.

Redinbo, Robert↗

NASA NTRS1992

Coded 16-CPFSK for downlink applications

A bandwidth-efficient constant-envelope Proof-of-Concept (POC) modem is described. The modem was developed on an Advanced Modulation Techniques Development contract for the NASA/Lewis Research Center. The POC modem employs 16-ary Continuous Phase Frequency Shift Keying (16-CPFSK) modulation. The 16 frequencies are spaced every 1/16th baud rate which produces a compact spectrum allowing 2 bits/sec/Hz operation. The modem is designed for 200 mb/s Time Division Multiple Access (TDMA) application with 100 MHz adjacent channel spacing. Overall rate 3.4 convolutional coding is incorporated. The demodulator differs significantly from typical quadrature phase detector approaches in that phase is coherently measured by processing the baseband output of a frequency discriminator. Baud rate phase samples for the baseband processor are subsequently decoded to yield the original data stream. The method of encoding onto the 16-ary symbol-ending phase nodes, together with convolutional coding gain, results in near Quadrature Phase Shift Keying (QPSK) theoretical performance. The modulated signal is of constant envelope; thus the power amplifier can be saturated for peak performance. The spectrum is inherently bandlimited and requires no RF filter for sidelobe containment. Two novel theoretical techniques are used in this 16-CPFSK modem: (1) coherent phase measurements are obtained by processing an FM discriminator baseband output; and (2) modulation is accomplished via a closed-loop-linearized voltage controlled oscillator (VCO).

Davis, Robert↗

NASA NTRS1992

Modulation and coding technology for deep space and satellite applications

Modulation and coding research and development at the Jet Propulsion Laboratory (JPL) currently emphasize Deep Space Communications Systems and advanced near earth Commercial Satellite Communications Systems. The Deep Space Communication channel is extremely signal to noise ratio limited and has long transmission delay. The near earth satellite channel is bandwidth limited with fading and multipath. Recent code search efforts at JPL have found a long constraint, low rate convolutional code (15, 1/6) which, when concatenated with a ten bit Reed-Solomon (RS) code, provides a 2.1 dB gain over that of the Voyager spacecraft - the current standard. The new code is only 2 dB from the theoretical Shannon limit. A flight qualified version of the (15, 1/6) convolutional encoder was implemented on the Galileo Spacecraft to be launched later this year. An L-band mobile link, use of the Ka-band for personal communications, and the development of subsystem technology for the interconnection of satellite resources by using high rate optical inter-satellite links are noted.

Yuen, J. H.↗

NASA NTRS1993

Algorithms For Detection Of Correlation Spots

Three algorithms provide for improved postprocessing of outputs of optical correlators based on binary phase-only filters. Detect correlation spots. Function in presence of noise and executed rapidly. First algorithm starts processing correlation-image data while data fed out of video camera and digitized for subsequent analysis. Second involves convolution of correlation image with small-window two-dimensional impulse-response function followed by threshold operation in which negative values of convolution integral set to zero. Third affects generation as well as postprocessing of correlation image.

Scholl, Marija S.↗

NASA NTRS1991

An investigation of error correcting techniques for OMV and AXAF

The original objectives of this project were to build a test system for the NASA 255/223 Reed/Solomon encoding/decoding chip set and circuit board. This test system was then to be interfaced with a convolutional system at MSFC to examine the performance of the concantinated codes. After considerable work, it was discovered that the convolutional system could not function as needed. This report documents the design, construction, and testing of the test apparatus for the R/S chip set. The approach taken was to verify the error correcting behavior of the chip set by injecting known error patterns onto data and observing the results. Error sequences were generated using pseudo-random number generator programs, with Poisson time distribution between errors and Gaussian burst lengths. Sample means, variances, and number of un-correctable errors were calculated for each data set before testing.

Ingels, Frank↗

NASA NTRS1992

High-speed architecture for the decoding of trellis-coded modulation

Since 1971, when the Viterbi Algorithm was introduced as the optimal method of decoding convolutional codes, improvements in circuit technology, especially VLSI, have steadily increased its speed and practicality. Trellis-Coded Modulation (TCM) combines convolutional coding with higher level modulation (non-binary source alphabet) to provide forward error correction and spectral efficiency. For binary codes, the current stare-of-the-art is a 64-state Viterbi decoder on a single CMOS chip, operating at a data rate of 25 Mbps. Recently, there has been an interest in increasing the speed of the Viterbi Algorithm by improving the decoder architecture, or by reducing the algorithm itself. Designs employing new architectural techniques are now in existence, however these techniques are currently applied to simpler binary codes, not to TCM. The purpose of this report is to discuss TCM architectural considerations in general, and to present the design, at the logic gate level, or a specific TCM decoder which applies these considerations to achieve high-speed decoding.

Osborne, William P.↗

NASA NTRS1993

Preliminary Studies Leading Toward the Development of a LIDAR Bathymetry Mapping Instrument

The National Aeronautics and Space Administration (NASA) at Goddard Space Flight Center (GSFC) has developed a laser ranging device (LIDAR) which provides accurate and timely data of earth features. NASA/GSFC recently modified the sensor to include a scanning capability to produce LIDAR swaths. They have also integrated a Global Positioning System (GPS) and an Inertial Navigation System (INS) to accurately determine the absolute aircraft location and aircraft attitude (pitch, yaw, and roll), respectively. The sensor has been flown in research mode by NASA for many years. The LIDAR has been used in different configurations or modes to acquire such data as altimetry (topography), bathymetry (water depth), laser-induced fluorosensing (tracer dye movements, oil spills and oil thickness, chlorophyll and plant stress identification), forestry, and wetland discrimination studies. NASA and HARC are developing a commercial version of the instrument for topographic mapping applications. The next phase of the commercialization project will be to investigate other applications such as wetlands mapping and coastal bathymetry. In this paper we report on preliminary laboratory measurements to determine the feasibility of making accurate depth measurements in relatively shallow water (approximately 2 to 6 feet deep) using a LIDAR system. The LIDAR bathymetry measurements are relatively simple in theory. The water depth is determined by measuring the time interval between the water surface reflection and the bottom surface reflection signals. Depth is then calculated by dividing by the index of refraction of water. However, the measurements are somewhat complicated due to the convolution of the water surface return signal with the bottom surface return signal. Therefore in addition to the laboratory experiments, computer simulations of the data were made to show these convolution effects in the return pulse waveform due to: (1) water depth, and (2) changes in bottom surface reflectivity.

Hill, John M.↗

NASA NTRS1992

Computational modeling of femtosecond optical solitons from Maxwell's equations

An algorithm is developed that permits the direct time integration of full-vector nonlinear Maxwell's equations. This capability permits the modeling of both linear and nonlinear instantaneous and dispersive effects in the electric polarization in material media. The modeling of the optical carrier is retained. The fundamental innovation is to notice that it is possible to treat the linear and nonlinear convolution integrals, which describe the dispersion, as new dependent variables. A coupled system of nonlinear second-order ordinary differential equations can then be derived for the linear and nonlinear convolution integrals, by differentiating them in the time domain. These equations, together with Maxwell's equations, are solved to determine the electromagnetic fields in nonlinear dispersive media. Results are presented of calculations in one dimension of the propagation and collision of femtosecond electromagnetic solitons that retain the optical carrier, taking into account as the Kerr and Raman interactions.

Goorjian, Peter M.↗

NASA NTRS1992

Matrix-vector multiplication using digital partitioning for more accurate optical computing

Digital partitioning offers a flexible means of increasing the accuracy of an optical matrix-vector processor. This algorithm can be implemented with the same architecture required for a purely analog processor, which gives optical matrix-vector processors the ability to perform high-accuracy calculations at speeds comparable with or greater than electronic computers as well as the ability to perform analog operations at a much greater speed. Digital partitioning is compared with digital multiplication by analog convolution, residue number systems, and redundant number representation in terms of the size and the speed required for an equivalent throughput as well as in terms of the hardware requirements. Digital partitioning and digital multiplication by analog convolution are found to be the most efficient alogrithms if coding time and hardware are considered, and the architecture for digital partitioning permits the use of analog computations to provide the greatest throughput for a single processor.

Gary, C. K.↗

NASA NTRS1993

Direct time integration of Maxwell's equations in two-dimensional dielectric waveguides for propagation and scattering of femtosecond electromagnetic solitons

We present what are to our knowledge first-time calculations from vector nonlinear Maxwell's equations of femtosecond soliton propagation and scattering, including carrier waves, in two-dimensional dielectric waveguides. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and the nonlinear convolution accounts for two quantum effects, the Kerr and Raman interactions. By retaining the optical carrier, the new method solves for fundamental quantities - optical electric and magnetic fields in space and time - rather than a nonphysical envelope function. It has the potential to provide an unprecedented two- and three-dimensional modeling capability for millimeter-scale integrated-optical circuits with submicrometer engineered inhomogeneities.

Joseph, Rose M.↗