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Report presents mathematical principles of Berlekamp bit serial multiplier algorithm and its application to design of very-large-scale integrated (VLSI) encoders for Reed-Solomon error-correcting codes. Structure made readily on single chip of negatively doped channel metal oxide semiconductor.
The capability of programmers and non-programmers to specify problem solutions by developing example-solutions and also for the programmers by writing computer programs was investigated; each method of specification was accomplished at various levels of problem complexity. The level of difficulty of each problem was reflected by the number of steps needed by the user to develop a solution. Machine processing of the user inputs permitted inferences to be developed about the algorithms required to solve a particular problem. The interactive feedback of processing results led users to a more precise definition of the desired solution. Two participant groups (programmers and bookkeepers/accountants) working with three levels of problem complexity and three levels of processor complexity were used. The experimental task employed required specification of a logic for solution of a Navy task force problem.
Fast Viterbi decoder with fully parallel, pipeline architecture implemented on two VLSI NMOS chips. Decoder used with constraint-length-7, rate-1/2, convolutional error-correcting code widely used by NASA for deepspace telemetry data. With this (7,1/2) code, bit stream contains 2 bits per original data bit, and information about 1 data bit distributed over 7 pairs of bits. Design principles of decoder also applicable to Viterbi codes of other lengths and rates.
Simplifications result from use of residue Fermat number systems. System of finite arithmetic over residue Fermat number systems enables calculation of discrete Fourier transform (DFT) of series of complex numbers with reduced number of multiplications. Computer architectures based on approach suitable for design of very-large-scale integrated (VLSI) circuits for computing DFT's. General approach not limited to DFT's; Applicable to decoding of error-correcting codes and other transform calculations. System readily implemented in VLSI.
The Galileo uplink Frame Erasure probability and Undetected Frame Error probability are derived. The performance meets desired specification under normal operations. The Galileo command system will work well even in an emergency condition, where the bit error rate into the command decoder is 1.00 X 0.001 (although Galileo's command threshold error rate is 1.00 X 0.00001).
Efficient parallel processing used to implement complex decoders. Hypercube multiprocessor connection scheme practical to decode long convolutional codes with efficient use of hardware. Hypercube design reduces both communication time among processors and space needed for interconnection. Decoding concept applicable to concurrent processing of digital signals using convolutional codes for error correction.
Improved algorithm reduces complexity of calculations that must precede design of Massey-Omura finite-field normal-basis multipliers, used in error-correcting-code equipment and cryptographic devices. Algorithm represents an extension of development reported in "Algorithm To Design Finite-Field Normal-Basis Multipliers" (NPO-17109), NASA Tech Briefs, Vol. 12, No. 5, page 82.
Lidar Atmospheric Wind Sounder (LAWS) Simulation Models (LSM) were developed to evaluate the potential impact of global wind observations on the basic understanding of the Earth's atmosphere and on the predictive skills of current forecast models (GCM and regional scale). Fully integrated top to bottom LAWS Simulation Models for global and regional scale simulations were developed. The algorithm development incorporated the effects of aerosols, water vapor, clouds, terrain, and atmospheric turbulence into the models. Other additions include a new satellite orbiter, signal processor, line of sight uncertainty model, new Multi-Paired Algorithm and wind error analysis code. An atmospheric wind field library containing control fields, meteorological fields, phenomena fields, and new European Center for Medium Range Weather Forecasting (ECMWF) data was also added. The LSM was used to address some key LAWS issues and trades such as accuracy and interpretation of LAWS information, data density, signal strength, cloud obscuration, and temporal data resolution.
An advanced satellite payload is proposed for single hop linking of mobile terminals of all classes as well as Very Small Aperture Terminal's (VSAT's). It relies on an intensive use of communications on-board processing and beam hopping for efficient link design to maximize capacity and a large satellite antenna aperture and high satellite transmitter power to minimize the cost of the ground terminals. Intersatellite links are used to improve the link quality and for high capacity relay. Power budgets are presented for links between the satellite and mobile, VSAT, and hub terminals. Defeating the effects of shadowing and fading requires the use of differentially coherent demodulation, concatenated forward error correction coding, and interleaving, all on a single link basis.
NASA's Advanced Communications Technology Satellite (ACTS) provides an ideal spaced-based platform for analyzing the Ka-band mobile satellite channel. This paper reports on the results of the Ka-band mobile propagation analysis campaign using the ACTS Mobile Terminal (AMT) developed by the Jet Propulsion Laboratory (JPL). The objectives of the mobile propagation experiments were to measure and analyze the fading characteristics of the Ka-band channel. The analysis involved examining pilot tone tests in three environments: lightly shadowed suburban, moderately shadowed suburban, and heavily shadowed suburban. The results indicate that Ka-band pilot tones experience significant multipath and fading effects. It may be possible to design link margins to provide reliable service for the lightly shadowed suburban environment at Ka-band. However, for areas with moderate and heavy shadowing, the link margin required to realize reliable communications with 99% availability is excessive (26 dB for moderate shadowing, and greater then 30 dB for heavy shadowing). An alternate approach would be to use shadowing/fading countermeasures (e.g., interleaved error control coding and antenna diversity). Such mitigation techniques, necessary for reliable Ka-band mobile communication within a suburban environment, are currently being considered within the NASA program.
The Advanced Communications Technology Satellite (ACTS) was developed by NASA as an experimental platform to demonstrate to industry the high risk technologies need for the next generation of communication satellites. The ACTS contains many state-of-the-art technologies including time division multiple accessing, adaptive error correction coding, multiple electronically steerable hopping beam antennas, spectrally efficient SMSK modulation, demand assignment multiple access protocol and on-board baseband circuit switching. An integral part of this testbed is the ACTS T1-very small aperture terminal (VSAT). The requirements imposed on the T1-VSAT demanded numerous design tradeoffs; balancing risk, cost, and implementation. Some of these considerations include: the method used for determining link quality, the development of a low cost and reliable Ka-band high power amplifier, the integration and testing environment for use in development and production and the low cost signal processing solution to high rate burst data. This paper discusses the tradeoffs considered in the selected implementation and the results obtained over the past two years of operation. Recommendations for improvements are also included.
Following the deployment failure of Galileo's high gain antenna, the downlink had to be redesigned so as to effectively use the low gain antenna. The downlink was redesigned to maximize the data return and increase the reliability which required the reconfiguration of the onboard software and the deep space network. The revised downlink features: data compression; antenna arraying; the recoding and reprocessing of telemetry; suppressed carrier tracking, and error-correction coding. The deep space network Galileo telemetry (DGT) subsystem was developed and deployed at three sites in Australia, Spain and the U.S. The DGT was designed as an automated system that continuously monitors and adjusts its parameters and environment in response to either pre-loaded sequences or changes in the internal status.
In the first of this pair of papers, it was proven that there cannot be a physical computer to which one can properly pose any and all computational tasks concerning the physical universe. It was then further proven that no physical computer C can correctly carry out all computational tasks that can be posed to C. As a particular example, this result means that no physical computer that can, for any physical system external to that computer, take the specification of that external system's state as input and then correctly predict its future state before that future state actually occurs; one cannot build a physical computer that can be assured of correctly "processing information faster than the universe does". These results do not rely on systems that are infinite, and/or non-classical, and/or obey chaotic dynamics. They also hold even if one uses an infinitely fast, infinitely dense computer, with computational powers greater than that of a Turing Machine. This generality is a direct consequence of the fact that a novel definition of computation - "physical computation" - is needed to address the issues considered in these papers, which concern real physical computers. While this novel definition does not fit into the traditional Chomsky hierarchy, the mathematical structure and impossibility results associated with it have parallels in the mathematics of the Chomsky hierarchy. This second paper of the pair presents a preliminary exploration of some of this mathematical structure. Analogues of Chomskian results concerning universal Turing Machines and the Halting theorem are derived, as are results concerning the (im)possibility of certain kinds of error-correcting codes. In addition, an analogue of algorithmic information complexity, "prediction complexity", is elaborated. A task-independent bound is derived on how much the prediction complexity of a computational task can differ for two different reference universal physical computers used to solve that task, a bound similar to the "encoding" bound governing how much the algorithm information complexity of a Turing machine calculation can differ for two reference universal Turing machines. Finally, it is proven that either the Hamiltonian of our universe proscribes a certain type of computation, or prediction complexity is unique (unlike algorithmic information complexity), in that there is one and only version of it that can be applicable throughout our universe.
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ave been developed to get as much data as possible from the Galileo spacecraft even without the high gain antenna. These methods include extensive data compression, a new packetized telemetry format, new error-correcting codes, new modulation, new ground receivers, and antenna arraying. (abstract only).
Gigabit-per-second communications have been a desired target for future NASA Earth science missions, and for potential manned lunar missions. Frequency bandwidth at S-band and X-band is typically insufficient to support missions at these high data rates. In this paper, we present the results of a 1 Gbps 32-QAM end-to-end experiment at Ka-band using a reconfigurable Field Programmable Gate Array (FPGA) baseband modulator board. Bit error rate measurements of the received signal using a software receiver demonstrate the feasibility of using ultra-high data rates at Ka-band, although results indicate that error correcting coding and/or modulator predistortion must be implemented in addition. Also, results of the demonstration validate the low-cost, MOS-based reconfigurable modulator approach taken to development of a high rate modulator, as opposed to more expensive ASIC or pure analog approaches.
An architecture has been designed that integrates formation estimation methodologies, precision formation sensing, and high-bandwidth formation communication into a robust, strap-on system that meets knowledge and communication requirements for the majority of planned, precision formation missions. Specifically, the integrated system supports (a) sub-millimeter metrology, (b) multiple greater than 10 Mbps communication channels over a large, 10 deg field-of-view (FOV), and (c) generalized formation estimation methodologies. The sensing sub-system consists of several absolute, metrology gauges with up to 0.1 mm precision that use amplitude-modulated lasers and a LISA-heritage phase meter. Since amplitude modulation is used, inexpensive and robust diode lasers may be used instead of complex, frequency-stabilized lasers such as for nanometer-level metrology. The metrology subsystem laser transceivers consist of a laser diode, collecting optics, and an avalanche photo diode (APD) for detecting incoming laser signals. The APD is necessary since received power is small due to the large (for optical applications) FOV. The phase meter determines the phase of the incoming amplitude modulations as measured by the APD. This phase is equivalent to time-of-flight and, therefore, distance. By placing three laser transceivers on each spacecraft, 18 clock-offset-corrupted distances are calculated. These measurements are communicated and averaged to obtain nine correct distances between the transceivers. From these correct distances, the range and bearing between spacecraft and their relative attitude are determined. Next, communication is integrated on the laser carrier through spectral separation. Metrology amplitude modulations are limited to the 45-50 MHz band, leaving 0-45 MHz for communication. Through careful design of coding scheme, error correction, and filters, six independent 10 Mbps receive channels are possible. Hence, a spacecraft can simultaneously broadcast at 10 Mbps and listen to six other spacecraft. The integrated sensing and communication architecture has been developed, as have formation estimation methodologies that allow the sensing topology to reconfigure as spacecraft maneuver. A bench-top implementation of the integrated sensing and communication architecture is in progress. The final, multiple sensing/communication systems will be tied together via formation estimation algorithms that are also undergoing further development.
Techniques for filtering clock jitter measurements are developed, in the context of controlling data modulation jitter on an RF carrier to accommodate low signal-to-noise ratio thresholds of high-performance error correction codes. Measurement artifacts from sampling are considered, and a tutorial on interpretation of direct readings is included.