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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

High-order neural models for error correcting code

The decoding and error-correction of data transmitted over a noisy channel is in principle equivalent to the operation of a neural network performing as a content-addressable memory. For a successful application, however, the neural network has to be capable of storing arbitrary words, and it has to be guaranteed that the stored words represent the only stable attractors of the memory. This paper presents a novel high-order neural network architecture that has these characteristics. The analog nature of the network can be used to perform soft-decision decoding with any block code. The performance in terms of postdecoding bit error rate versus SNR is demonstrated for two exemplary block codes. The comparison with a conventional decoding algorithm for a (15,5) cyclic redundancy code shows, for example, that the bit error rate at 7dB SNR can be decreased by two orders of magnitude.

Jeffries, Clark↗
NASA NTRS1984

Reed Solomon codes for error control in byte organized computer memory systems

A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. In LSI and VLSI technology, memories are often organized on a multiple bit (or byte) per chip basis. For example, some 256K-bit DRAM's are organized in 32Kx8 bit-bytes. Byte oriented codes such as Reed Solomon (RS) codes can provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. Some special decoding techniques for extended single-and-double-error-correcting RS codes which are capable of high speed operation are presented. These techniques are designed to find the error locations and the error values directly from the syndrome without having to use the iterative algorithm to find the error locator polynomial.

Lin, S.↗
NASA NTRS1987

Cyclic unequal error protection codes constructed from cyclic codes of composite length

The distance structure of cyclic codes of composite length was investigated. A lower bound on the minimum distance for this class of codes is derived. In many cases, the lower bound gives the true minimum distance of a code. Then the distance structure of the direct sum of two cyclic codes of composite length were investigated. It was shown that, under certain conditions, the direct-sum code provides two levels of error correcting capability, and hence is a two-level unequal error protection (UEP) code. Finally, a class of two-level UEP cyclic direct-sum codes and a decoding algorithm for a subclass of these codes are presented.

Lin, Shu↗
NASA NTRS1984

On the undetected error probability of a concatenated coding scheme for error control

Consider a concatenated coding scheme for error control on a binary symmetric channel, called the inner channel. The bit error rate (BER) of the channel is correspondingly called the inner BER, and is denoted by Epsilon (sub i). Two linear block codes, C(sub f) and C(sub b), are used. The inner code C(sub f), called the frame code, is an (n,k) systematic binary block code with minimum distance, d(sub f). The frame code is designed to correct + or fewer errors and simultaneously detect gamma (gamma +) or fewer errors, where + + gamma + 1 = to or d(sub f). The outer code C(sub b) is either an (n(sub b), K(sub b)) binary block with a n(sub b) = mk, or an (n(sub b), k(Sub b) maximum distance separable (MDS) code with symbols from GF(q), where q = 2(b) and the code length n(sub b) satisfies n(sub)(b) = mk. The integerim is the number of frames. The outercode is designed for error detection only.

Deng, H.↗
NASA NTRS1996

Introduction to Forward-Error-Correcting Coding

This reference publication introduces forward error correcting (FEC) and stresses definitions and basic calculations for use by engineers. The seven chapters include 41 example problems, worked in detail to illustrate points. A glossary of terms is included, as well as an appendix on the Q function. Block and convolutional codes are covered.

Freeman, Jon C.↗
NASA NTRS1996

Testing and Performance Analysis of the Multichannel Error Correction Code Decoder

This report provides the test results and performance analysis of the multichannel error correction code decoder (MED) system for a regenerative satellite with asynchronous, frequency-division multiple access (FDMA) uplink channels. It discusses the system performance relative to various critical parameters: the coding length, data pattern, unique word value, unique word threshold, and adjacent-channel interference. Testing was performed under laboratory conditions and used a computer control interface with specifically developed control software to vary these parameters. Needed technologies - the high-speed Bose Chaudhuri-Hocquenghem (BCH) codec from Harris Corporation and the TRW multichannel demultiplexer/demodulator (MCDD) - were fully integrated into the mesh very small aperture terminal (VSAT) onboard processing architecture and were demonstrated.

Soni, Nitin J.↗
NASA NTRS1989

Bandwidth efficient coding for error control

One of the dramatic developments in bandwidth-efficient communications over the past few years is the introduction and rapid applications of combined coding and bandwidth efficient modulation, known as coded modulation, for error control. Using coded modulation, reliable data transmission can be attained without compromising bandwidth efficiency. Presented here are the basic concepts of coded modulation. Two simple examples are used to demonstrate how significant coding gains can be achieved without bandwidth expansion.

Lin, Shu↗
NASA NTRS1990

Tutorial on Reed-Solomon error correction coding

This tutorial attempts to provide a frank, step-by-step approach to Reed-Solomon (RS) error correction coding. RS encoding and RS decoding both with and without erasing code symbols are emphasized. There is no need to present rigorous proofs and extreme mathematical detail. Rather, the simple concepts of groups and fields, specifically Galois fields, are presented with a minimum of complexity. Before RS codes are presented, other block codes are presented as a technical introduction into coding. A primitive (15, 9) RS coding example is then completely developed from start to finish, demonstrating the encoding and decoding calculations and a derivation of the famous error-locator polynomial. The objective is to present practical information about Reed-Solomon coding in a manner such that it can be easily understood.

Geisel, William A.↗
NASA NTRS1996

Communications and information research: Improved space link performance via concatenated forward error correction coding

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.

Rao, T. R. N.↗
NASA NTRS1996

Error-correction coding

This report describes the progress made towards the completion of a specific task on error-correcting coding. The proposed research consisted of investigating the use of modulation block codes as the inner code of a concatenated coding system in order to improve the overall space link communications performance. The study proposed to identify and analyze candidate codes that will complement the performance of the overall coding system which uses the interleaved RS (255,223) code as the outer code.

Hinds, Erold W.↗
NASA NTRS1992

Links between N-modular redundancy and the theory of error-correcting codes

N-Modular Redundancy (NMR) is one of the best known fault tolerance techniques. Replication of a module to achieve fault tolerance is in some ways analogous to the use of a repetition code where an information symbol is replicated as parity symbols in a codeword. Linear Error-Correcting Codes (ECC) use linear combinations of information symbols as parity symbols which are used to generate syndromes for error patterns. These observations indicate links between the theory of ECC and the use of hardware redundancy for fault tolerance. In this paper, we explore some of these links and show examples of NMR systems where identification of good and failed elements is accomplished in a manner similar to error correction using linear ECC's.

Bobin, V.↗
NASA NTRS1979

Concurrent error detecting codes for arithmetic processors

A method of concurrent error detection for arithmetic processors is described. Low-cost residue codes with check-length l and checkbase m = 2 to the l power - 1 are described for checking arithmetic operations of addition, subtraction, multiplication, division complement, shift, and rotate. Of the three number representations, the signed-magnitude representation is preferred for residue checking. Two methods of residue generation are described: the standard method of using modulo m adders and the method of using a self-testing residue tree. A simple single-bit parity-check code is described for checking the logical operations of XOR, OR, and AND, and also the arithmetic operations of complement, shift, and rotate. For checking complement, shift, and rotate, the single-bit parity-check code is simpler to implement than the residue codes.

Lim, R. S.↗
NASA NTRS1977

Efficient bit-error detecting code

Two highly reliable codes termed "Modified b-adjacent interleaving codes" provide fail-safe operation of launch processing and control system in which common memory is coordination point for interconnection of up to 64 minicomputers. Codes detect and correct bit errors in computer data transmission.

Hockenberger, R. W.↗