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At least 685 records · Page 38

Box codes of lengths 48 and 72

A self-dual code length 48, dimension 24, with Hamming distance essentially equal to 12 is constructed here. There are only six code words of weight eight. All the other code words have weights that are multiples of four and have a minimum weight equal to 12. This code may be encoded systematically and arises from a strict binary representation of the (8,4;5) Reed-Solomon (RS) code over GF (64). The code may be considered as six interrelated (8,7;2) codes. The Mattson-Solomon representation of the cyclic decomposition of these codes and their parity sums are used to detect an odd number of errors in any of the six codes. These may then be used in a correction algorithm for hard or soft decision decoding. A (72,36;15) box code was constructed from a (63,35;8) cyclic code. The theoretical justification is presented herein. A second (72,36;15) code is constructed from an inner (63,27;16) Bose Chaudhuri Hocquenghem (BCH) code and expanded to length 72 using box code algorithms for extension. This code was simulated and verified to have a minimum distance of 15 with even weight words congruent to zero modulo four. The decoding for hard and soft decision is still more complex than the first code constructed above. Finally, an (8,4;5) RS code over GF (512) in the binary representation of the (72,36;15) box code gives rise to a (72,36;16*) code with nine words of weight eight, and all the rest have weights greater than or equal to 16.

Solomon, G.↗

The Communication Link and Error ANalysis (CLEAN) simulator

During the period July 1, 1993 through December 30, 1993, significant developments to the Communication Link and Error ANalysis (CLEAN) simulator were completed and include: (1) Soft decision Viterbi decoding; (2) node synchronization for the Soft decision Viterbi decoder; (3) insertion/deletion error programs; (4) convolutional encoder; (5) programs to investigate new convolutional codes; (6) pseudo-noise sequence generator; (7) soft decision data generator; (8) RICE compression/decompression (integration of RICE code generated by Pen-Shu Yeh at Goddard Space Flight Center); (9) Markov Chain channel modeling; (10) percent complete indicator when a program is executed; (11) header documentation; and (12) help utility. The CLEAN simulation tool is now capable of simulating a very wide variety of satellite communication links including the TDRSS downlink with RFI. The RICE compression/decompression schemes allow studies to be performed on error effects on RICE decompressed data. The Markov Chain modeling programs allow channels with memory to be simulated. Memory results from filtering, forward error correction encoding/decoding, differential encoding/decoding, channel RFI, nonlinear transponders and from many other satellite system processes. Besides the development of the simulation, a study was performed to determine whether the PCI provides a performance improvement for the TDRSS downlink. There exist RFI with several duty cycles for the TDRSS downlink. We conclude that the PCI does not improve performance for any of these interferers except possibly one which occurs for the TDRS East. Therefore, the usefulness of the PCI is a function of the time spent transmitting data to the WSGT through the TDRS East transponder.

Ebel, William J.↗

Non-orthogonal subband/transform coder

The present invention is directed to a simplified digital subband coder/decoder. In the present invention a signal is fed into a coder. The coder uses a non-orthogonal algorithm that is simply implemented in the coder hardware. The simple non-orthogonal design is then used in the implementation of the decoder to decode the signal.

Glover, Daniel R.↗

Convolutional encoding of self-dual codes

There exist almost complete convolutional encodings of self-dual codes, i.e., block codes of rate 1/2 with weights w, w = 0 mod 4. The codes are of length 8m with the convolutional portion of length 8m-2 and the nonsystematic information of length 4m-1. The last two bits are parity checks on the two (4m-1) length parity sequences. The final information bit complements one of the extended parity sequences of length 4m. Solomon and van Tilborg have developed algorithms to generate these for the Quadratic Residue (QR) Codes of lengths 48 and beyond. For these codes and reasonable constraint lengths, there are sequential decodings for both hard and soft decisions. There are also possible Viterbi-type decodings that may be simple, as in a convolutional encoding/decoding of the extended Golay Code. In addition, the previously found constraint length K = 9 for the QR (48, 24;12) Code is lowered here to K = 8.

Solomon, G.↗

An efficient system for reliably transmitting image and video data over low bit rate noisy channels

This research project is intended to develop an efficient system for reliably transmitting image and video data over low bit rate noisy channels. The basic ideas behind the proposed approach are the following: employ statistical-based image modeling to facilitate pre- and post-processing and error detection, use spare redundancy that the source compression did not remove to add robustness, and implement coded modulation to improve bandwidth efficiency and noise rejection. Over the last six months, progress has been made on various aspects of the project. Through our studies of the integrated system, a list-based iterative Trellis decoder has been developed. The decoder accepts feedback from a post-processor which can detect channel errors in the reconstructed image. The error detection is based on the Huber Markov random field image model for the compressed image. The compression scheme used here is that of JPEG (Joint Photographic Experts Group). Experiments were performed and the results are quite encouraging. The principal ideas here are extendable to other compression techniques. In addition, research was also performed on unequal error protection channel coding, subband vector quantization as a means of source coding, and post processing for reducing coding artifacts. Our studies on unequal error protection (UEP) coding for image transmission focused on examining the properties of the UEP capabilities of convolutional codes. The investigation of subband vector quantization employed a wavelet transform with special emphasis on exploiting interband redundancy. The outcome of this investigation included the development of three algorithms for subband vector quantization. The reduction of transform coding artifacts was studied with the aid of a non-Gaussian Markov random field model. This results in improved image decompression. These studies are summarized and the technical papers included in the appendices.

Costello, Daniel J., Jr.↗

Convolutional encoding of self-dual block codes (2)

Solomon and van Tilborg have developed convolutional encoding algorithms for quadratic residue (QR) codes of lengths 47 and beyond. For these codes and reasonable constraint lengths, there are sequential decodings that may be simple, as in a convolutional encoding/decoding of the extended Golay Code. In addition, the previously found constraint length K = 9 for the (48, 24; 12) QR code was lower to K = 8 by Solomon. In our search for the smallest possible constraint lengths K for (80, 40; 16) self-dual quadratic residue and nonquadratic residue codes, we have found the constraint lengths K = 14 and K = 13, respectively. We have discovered a K = 21 convolutional encoding for the (104, 52; 20) QR code; there may be a smaller K for a (104, 52; 20) self-dual code that is not a quadratic residue code. The smaller the K, the less complex the sequential or Viterbi decoder.

Solomon, G.↗

Low-complexity wavelet filter design for image compression

Image compression algorithms based on the wavelet transform are an increasingly attractive and flexible alternative to other algorithms based on block orthogonal transforms. While the design of orthogonal wavelet filters has been studied in significant depth, the design of nonorthogonal wavelet filters, such as linear-phase (LP) filters, has not yet reached that point. Of particular interest are wavelet transforms with low complexity at the encoder. In this article, we present known and new parameterizations of the two families of LP perfect reconstruction (PR) filters. The first family is that of all PR LP filters with finite impulse response (FIR), with equal complexity at the encoder and decoder. The second family is one of LP PR filters, which are FIR at the encoder and infinite impulse response (IIR) at the decoder, i.e., with controllable encoder complexity. These parameterizations are used to optimize the subband/wavelet transform coding gain, as defined for nonorthogonal wavelet transforms. Optimal LP wavelet filters are given for low levels of encoder complexity, as well as their corresponding integer approximations, to allow for applications limited to using integer arithmetic. These optimal LP filters yield larger coding gains than orthogonal filters with an equivalent complexity. The parameterizations described in this article can be used for the optimization of any other appropriate objective function.

Majani, E.↗

Multiple turbo codes for deep-space communications

In this article, we introduce multiple turbo codes and a suitable decoder structure derived from an approximation to the maximum a posteriori probability (MAP) decision rule, which is substantially different from the decoder for two-code-based encoders. We analyze the effect of interleaver choice on the weight distribution of the code, and we describe simulation results on the improved performance of these new codes.

Divsalar, D.↗

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.↗

Investigation of Near Shannon Limit Coding Schemes

Turbo codes can deliver performance that is very close to the Shannon limit. This report investigates algorithms for convolutional turbo codes and block turbo codes. Both coding schemes can achieve performance near Shannon limit. The performance of the schemes is obtained using computer simulations. There are three sections in this report. First section is the introduction. The fundamental knowledge about coding, block coding and convolutional coding is discussed. In the second section, the basic concepts of convolutional turbo codes are introduced and the performance of turbo codes, especially high rate turbo codes, is provided from the simulation results. After introducing all the parameters that help turbo codes achieve such a good performance, it is concluded that output weight distribution should be the main consideration in designing turbo codes. Based on the output weight distribution, the performance bounds for turbo codes are given. Then, the relationships between the output weight distribution and the factors like generator polynomial, interleaver and puncturing pattern are examined. The criterion for the best selection of system components is provided. The puncturing pattern algorithm is discussed in detail. Different puncturing patterns are compared for each high rate. For most of the high rate codes, the puncturing pattern does not show any significant effect on the code performance if pseudo - random interleaver is used in the system. For some special rate codes with poor performance, an alternative puncturing algorithm is designed which restores their performance close to the Shannon limit. Finally, in section three, for iterative decoding of block codes, the method of building trellis for block codes, the structure of the iterative decoding system and the calculation of extrinsic values are discussed.

Kwatra, S. C.↗

Low Density Parity Check Codes Based on Finite Geometries: A Rediscovery and More

Low density parity check (LDPC) codes with iterative decoding based on belief propagation achieve astonishing error performance close to Shannon limit. No algebraic or geometric method for constructing these codes has been reported and they are largely generated by computer search. As a result, encoding of long LDPC codes is in general very complex. This paper presents two classes of high rate LDPC codes whose constructions are based on finite Euclidean and projective geometries, respectively. These classes of codes a.re cyclic and have good constraint parameters and minimum distances. Cyclic structure adows the use of linear feedback shift registers for encoding. These finite geometry LDPC codes achieve very good error performance with either soft-decision iterative decoding based on belief propagation or Gallager's hard-decision bit flipping algorithm. These codes can be punctured or extended to obtain other good LDPC codes. A generalization of these codes is also presented.

Kou, Yu↗

The Use of Large Lithium-Drifted, Germanium Diodes for Gamma-Ray Spectral Measurements at Balloon Altitudes

A series of balloon-borne experiments has been initiated at the Oak Ridge National Laboratory (ORNL) in cooperation with the Space Sciences Laboratory of the NASA G. C. Marshall Space Flight Center to determine the feasibility of using large (greater than 20 cc) lithium-drifted, germanium diodes to investigate the spectrum of atmospheric gamma rays (60 keV < E < 1.5 MeV) at altitudes corresponding to a few grams per cm (sup 2) residual atmosphere. The results of these measurements will also provide a basis for designing an appropriate shield for a multi-diode, highly directional gamma-ray spectrometer for use in astrophysical measurements. Two flights were accomplished during 1967 using the same two diodes and basic instrument package. Both flights were launched at the NCAR Scientific Balloon Flight Base, Palestine, Texas, and attained a float altitude of 117, 000 ft. The measured atmospheric gamma-ray spectrum shows at least one distinct line at 511 keV (annihilation radiation) superimposed on a continuous distribution of gamma rays attributable to both energy-degraded gamma rays and brems-strahlung photons. A second diode, encased in a passive shield of plastic and lead, shows the expected lines resulting from both neutron inelastic scattering and capture in the germanium. Data acquisition was accomplished on an event-by-event basis through the use of 512-channel, on-board ADC and word-generator circuits and a ground-based, on-line telemetry decoder. The decoder makes it possible to store the data in the memory of a modified pulse-height analyzer simultaneously with storage on magnetic tape. This provides a real-time visual observation of the data as it is accumulated and greatly facilitates preflight calibrations.

Chapman, G. T.↗

UNICON Laser Memory: Interlaced Codes for Multi-burst-Error Correction

Interlaced binary BCH codes are described for multiple-burst-error correction for the UNICON 690 laser memory. Other multiple-burst-error-correcting codes, such as Reed-Solomon codes and Product codes, are also briefly mentioned. In particular, an interlaced (31, 21) t = 2 BCH code is selected as an outer code for UNICON double-burst-error correction. This code is shortened to (26,16) and interlaced to degree X = 16. Decoding is implemented by table lookup. This method not only avoids all computations in GF(2(exp 5)), it also offers a decoding time of less than 1 ps. The inner code is an existing (80,64) Fire code capable of correcting a single-burst error of length b less than or equal to 6.

Lim, R. S.↗

The NASA Spacecraft Transponding Modem

A new deep space transponder is being developed by the Jet Propulsion Laboratory for NASA. The Spacecraft Transponding Modem (STM) implements the standard transponder functions and the channel service functions that have previously resided in spacecraft Command/Data Subsystems. The STM uses custom ASICs, MMICs, and MCMs to reduce the active device parts count to 70, mass to I kg, and volume to 524 cc. The first STMs will be flown on missions launching in the 2003 time frame. The STM tracks an X-band uplink signal and provides both X-band and Ka-band downlinks, either coherent or non-coherent with the uplink. A NASA standard Command Detector Unit is integrated into the STM, along with a codeblock processor and a hardware command decoder. The decoded command codeblocks are output to the spacecraft command/data subsystem. Virtual Channel 0 (VC-0) (hardware) commands are processed and output as critical controller (CRC) commands. Downlink telemetry is received from the spacecraft data subsystem as telemetry frames. The STM provides the following downlink coding options: the standard CCSDS (7-1/2) convolutional coding, ReedSolomon coding with interleave depths one and five, (15-1/6) convolutional coding, and Turbo coding with rates 1/3 and 1/6. The downlink symbol rates can be linearly ramped to match the G/T curve of the receiving station, providing up to a 1 dB increase in data return. Data rates range from 5 bits per second (bps) to 24 Mbps, with three modulation modes provided: modulated subcarrier (3 different frequencies provided), biphase-L modulated direct on carrier, and Offset QPSK. Also, the capability to generate one of four non-harmonically related telemetry beacon tones is provided, to allow for a simple spacecraft status monitoring scheme for cruise phases of missions. Three ranging modes are provided: standard turn around ranging, regenerative pseudo-noise (PN) ranging, and Differential One-way Ranging (DOR) tones. The regenerative ranging provides the capability of increasing the ground received ranging SNR by up to 30 dB. Two different avionics interfaces to the command/data subsystem's data bus are provided: a MIL STD 1553B bus or an industry standard PCI interface. Digital interfaces provide the capability to control antenna selection (e.g., switching between high gain and low gain antennas) and antenna pointing (for future steered Ka-band antennas).

Berner, Jeff B.↗

Video Compression

Optivision developed two PC-compatible boards and associated software under a Goddard Space Flight Center Small Business Innovation Research grant for NASA applications in areas such as telerobotics, telesciences and spaceborne experimentation. From this technology, the company used its own funds to develop commercial products, the OPTIVideo MPEG Encoder and Decoder, which are used for realtime video compression and decompression. They are used in commercial applications including interactive video databases and video transmission. The encoder converts video source material to a compressed digital form that can be stored or transmitted, and the decoder decompresses bit streams to provide high quality playback.

Source record↗

Low Density Parity Check Codes: Bandwidth Efficient Channel Coding

Low Density Parity Check (LDPC) Codes provide near-Shannon Capacity performance for NASA Missions. These codes have high coding rates R=0.82 and 0.875 with moderate code lengths, n=4096 and 8176. Their decoders have inherently parallel structures which allows for high-speed implementation. Two codes based on Euclidean Geometry (EG) were selected for flight ASIC implementation. These codes are cyclic and quasi-cyclic in nature and therefore have a simple encoder structure. This results in power and size benefits. These codes also have a large minimum distance as much as d,,, = 65 giving them powerful error correcting capabilities and error floors less than lo- BER. This paper will present development of the LDPC flight encoder and decoder, its applications and status.

Fong, Wai↗

Reduction of ETS-VI Laser Communication Equipment Optical-Downlink Telemetry Collected During GOLD

Free-space laser communications experiments were conducted between the laser communication equipment (LCE) on board the Japanese Engineering Test Satellite VI (ETS-VI) and the ground station located at the Table Mountain Facility (TMF) during late 1995 and early 1996. This article describes the on-line data reduction process used to decode LCE telemetry (called E2) downlinked on the optical carrier during the Ground/Orbiter Lasercomm Demonstration (GOLD) experiments. The LCE has the capability of transmitting real-time sensor and status information at 128 kbps by modulating the onboard diode laser. The optical downlink was detected on the ground, bit synchronized, and the resulting data stream stored on a data recorder. The recorded data were subsequently decoded by on-line data processing that included cross-correlation of the known telemetry data format and the downlink data stream. Signals obtained from the processing can be useful not only in evaluating the characteristics of the LCE but also in understanding uplink and downlink signal quality.

Toyoshima, M.↗

Evaluation of Open-Source Hard Real Time Software Packages

Reliable software is, at times, hard to find. No piece of software can be guaranteed to work in every situation that may arise during its use here at Glenn Research Center or in space. The job of the Software Assurance (SA) group in the Risk Management Office is to rigorously test the software in an effort to ensure it matches the contract specifications. In some cases the SA team also researches new alternatives for selected software packages. This testing and research is an integral part of the department of Safety and Mission Assurance. Real Time operation in reference to a computer system is a particular style of handing the timing and manner with which inputs and outputs are handled. A real time system executes these commands and appropriate processing within a defined timing constraint. Within this definition there are two other classifications of real time systems: hard and soft. A soft real time system is one in which if the particular timing constraints are not rigidly met there will be no critical results. On the other hand, a hard real time system is one in which if the timing constraints are not met the results could be catastrophic. An example of a soft real time system is a DVD decoder. If the particular piece of data from the input is not decoded and displayed to the screen at exactly the correct moment nothing critical will become of it, the user may not even notice it. However, a hard real time system is needed to control the timing of fuel injections or steering on the Space Shuttle; a delay of even a fraction of a second could be catastrophic in such a complex system. The current real time system employed by most NASA projects is Wind River's VxWorks operating system. This is a proprietary operating system that can be configured to work with many of NASA s needs and it provides very accurate and reliable hard real time performance. The down side is that since it is a proprietary operating system it is also costly to implement. The prospect of replacing this somewhat costly implementation is the focus of one of the SA group s current research projects. The explosion of open source software in the last ten years has led to the development of a multitude of software solutions which were once only produced by major corporations. The benefits of these open projects include faster release and bug patching cycles as well as inexpensive if not free software solutions. The main packages for hard real time solutions under Linux are Real Time Application Interface (RTAI) and two varieties of Real Time Linux (RTL), RTLFree and RTLPro. During my time here at NASA I have been testing various hard real time solutions operating as layers on the Linux Operating System. All testing is being run on an Intel SBC 2590 which is a common embedded hardware platform. The test plan was provided to me by the Software Assurance group at the start of my internship and my job has been to test the systems by developing and executing the test cases on the hardware. These tests are constructed so that the Software Assurance group can get hard test data for a comparison between the open source and proprietary implementations of hard real time solutions.

Mattei, Nicholas S.↗