SEARCH · Search NASA
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Published document discusses method for correcting errors. According to this method, computer operation becomes fault-tolerant, i.e., its operation is error-free in spite of single hardware element malfunction. Also, method provides for detection and correction of repetitive and spurious processing and transmission errors.
The various methods of high bit transition density encoding are presented, their relative performance is compared in so far as error propagation characteristics, transition properties and system constraints are concerned. A computer simulation of the system using the specific PN code recommended, is included.
A suitable constant "exclusive-Ored" with ECC to flag data without impairing detection of correctable errors.
Comma-free properties of any group code from simple observation of null space
With the development of new advanced instruments for remote sensing applications, sensor data will be generated at a rate that not only requires increased onboard processing and storage capability, but imposes demands on the space to ground communication link and ground data management-communication system. Data compression and error control codes provide viable means to alleviate these demands. Two types of data compression have been studied by many researchers in the area of information theory: a lossless technique that guarantees full reconstruction of the data, and a lossy technique which generally gives higher data compaction ratio but incurs some distortion in the reconstructed data. To satisfy the many science disciplines which NASA supports, lossless data compression becomes a primary focus for the technology development. While transmitting the data obtained by any lossless data compression, it is very important to use some error-control code. For a long time, convolutional codes have been widely used in satellite telecommunications. To more efficiently transform the data obtained by the Rice algorithm, it is required to meet the a posteriori probability (APP) for each decoded bit. A relevant algorithm for this purpose has been proposed which minimizes the bit error probability in the decoding linear block and convolutional codes and meets the APP for each decoded bit. However, recent results on iterative decoding of 'Turbo codes', turn conventional wisdom on its head and suggest fundamentally new techniques. During the past several months of this research, the following approaches have been developed: (1) a new lossless data compression algorithm, which is much better than the extended Rice algorithm for various types of sensor data, (2) a new approach to determine the generalized Hamming weights of the algebraic-geometric codes defined by a large class of curves in high-dimensional spaces, (3) some efficient improved geometric Goppa codes for disk memory systems and high-speed mass memory systems, and (4) a tree based approach for data compression using dynamic programming.
Several methods for increasing bit transition densities in a data stream are summarized, discussed in detail, and compared against constraints imposed by the 2 MHz data link of the space shuttle high rate multiplexer unit. These methods include use of alternate pulse code modulation waveforms, data stream modification by insertion, alternate bit inversion, differential encoding, error encoding, and use of bit scramblers. The psuedo-random cover sequence generator was chosen for application to the 2 MHz data link of the space shuttle high rate multiplexer unit. This method is fully analyzed and a design implementation proposed.
Report is reviewed which considers theoretical basis of groups, rings, fields, and vector spaces, and their relationship to algebraic coding theory. Report serves as summary for engineers and scientists involved in data handling and processing systems.
The design to achieve the required bit transition density for the Space Shuttle high rate multiplexes (HRM) data stream of the Space Laboratory Vehicle is reviewed. It contained a recommended circuit approach, specified the pseudo random (PN) sequence to be used and detailed the properties of the sequence. Calculations showing the probability of failing to meet the required transition density were included. A computer simulation of the data stream and PN cover sequence was provided. All worst case situations were simulated and the bit transition density exceeded that required. The Preliminary Design Review and the critical Design Review are documented. The Cover Sequence Generator (CSG) Encoder/Decoder design was constructed and demonstrated. The demonstrations were successful. All HRM and HRDM units incorporate the CSG encoder or CSG decoder as appropriate.
The use of PN sequence generators to create a minimum number of transitions in an NRZ bit stream is described. The CSG encoder/decoder design was constructed and demonstrated.
A communication system which would effect channel coding for frequency-hopped multiple-access is described. It is shown that in theory coding can increase the spectrum utilization efficiency of a system with mutual interference to 100 percent. Various coding strategies are discussed and some initial comparisons are given. Some of the problems associated with implementing the type of system described here are discussed.
NASA Lewis Research Center's Digital Systems Technology Branch has an ongoing program in modulation, coding, onboard processing, and switching. Recently, NASA completed a project to incorporate a time-shared decoder into the very-small-aperture terminal (VSAT) onboard-processing mesh architecture. The primary goal was to demonstrate a time-shared decoder for a regenerative satellite that uses asynchronous, frequency-division multiple access (FDMA) uplink channels, thereby identifying hardware and power requirements and fault-tolerant issues that would have to be addressed in a operational system. A secondary goal was to integrate and test, in a system environment, two NASA-sponsored, proof-of-concept hardware deliverables: the Harris Corp. high-speed Bose Chaudhuri-Hocquenghem (BCH) codec and the TRW multichannel demultiplexer/demodulator (MCDD). A beneficial byproduct of this project was the development of flexible, multichannel-uplink signal-generation equipment.
With the surging development of optical telecommunicationsfor space applications, the importance of errorcorrection has become more apparent than ever. Specifically,the exploration of forward error correction code (FEC) methodologieswill be instrumental in developing the standards foroptical communications in space. Despite the widespread useof low-density parity-check (LDPC) codes, alternate FEC codessuch as polar codes have shown immense promise in assistingspace communications error correction with their ability tobypass the error floors that plague LDPC codes. Extremelypromising techniques including cyclic redundancy checks (CRC),successive cancellation (SC), and successive cancellation lists(SCL) that assist polar coding in achieving the Shannon limitin a timely manner are evaluated. MATLAB simulations areconducted with AWGN and burst noise to test each technique'sability to handle noise typically encountered in space and eachtechnique's ability to correct unexpected errors. Results ofsimulations for different rates and message lengths are alsoreported to determine each technique's ability to handle largedata volumes and fix errors. Similar simulations are conductedfor LDPC codes with additional tests for convolutional and nointerleavers. Finally, a discussion regarding the future ability ofpolar codes to satisfy current missions in the place of, or inconjunction with, LDPC codes along with the merits of eachFEC technique's ability to process data efficiently and handledata while maintaining adequate performance will be provided.Preliminary recommendations will be made for each technique'seffectiveness for GEO related missions along with discussionsregarding each technique's ability to fit within the CCSDS standards for optical communications.
Algorithm for constructing random error correcting convolutional codes
Algorithm for constructing random error correcting convolutional codes
Shift register time-shared in proposed error-correcting code for tape-storage systems. Error-correcting code logic for blocks of 256-bit data words implemented by 14-stage-time-shared shift register, two 4,096bit RAM's and logic gates. Encoding and decoding logic implement generator polynomial that defines error-correcting code, and error correction based on algorithm also implemented by logic.
A quantum error-correcting code with a nonzero error threshold undergoes a mixed-state phase transition when the error rate reaches that threshold. We explore this phase transition for Haar-random quantum codes, in which the logical information is encoded in a random subspace of the physical Hilbert space. We focus on the spectrum of the encoded system density matrix as a function of the rate of uncorrelated, single-qudit errors. For low error rates, this spectrum consists of well-separated bands, representing errors of different weights. As the error rate increases, the bands for high-weight errors merge. The evolution of these bands with increasing error rate is well described by a simple analytic ansatz. Using this ansatz, as well as an explicit calculation, we show that the threshold for Haar-random quantum codes saturates the hashing bound, and thus coincides with that for random stabilizer codes. For error rates that exceed the hashing bound, typical errors are uncorrectable, but postselected error correction remains possible until a much higher detection threshold. Postselection can in principle be implemented by projecting onto subspaces corresponding to low-weight errors, which remain correctable past the hashing bound.
Abstract A potential platform for topological quantum computation is the Majorana-based tetron architecture. Its building blocks are superconducting islands called tetrons, which host four Majorana zero modes. Existing error correcting codes can correct even-weight errors on tetrons. In a previous proposal by us, we had shown that incorporating tetrons in the stabilizer group allows us to correct a combination of odd-weight errors and even-weight errors on tetrons. In this work, we show that inclusion of tetrons in the gauge group lets us create subsystem codes from conventional Pauli stabilizer codes, which can correct both kinds of errors. Compared to the previous approach, the current approach lets us construct codes with fewer stabilizer generators. This leads to shorter fault-tolerant sequence length, and improves the fault-tolerant pseudothreshold by as much as 84%.