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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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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

The Limits of Coding with Joint Constraints on Detected and Undetected Error Rates

We develop a remarkably tight upper bound on the performance of a parameterized family of bounded angle maximum-likelihood (BA-ML) incomplete decoders. The new bound for this class of incomplete decoders is calculated from the code's weight enumerator, and is an extension of Poltyrev-type bounds developed for complete ML decoders. This bound can also be applied to bound the average performance of random code ensembles in terms of an ensemble average weight enumerator. We also formulate conditions defining a parameterized family of optimal incomplete decoders, defined to minimize both the total codeword error probability and the undetected error probability for any fixed capability of the decoder to detect errors. We illustrate the gap between optimal and BA-ML incomplete decoding via simulation of a small code.

Undetected Error Rate↗
NASA NTRS1983

Automatic-repeat-request error control schemes

Error detection incorporated with automatic-repeat-request (ARQ) is widely used for error control in data communication systems. This method of error control is simple and provides high system reliability. If a properly chosen code is used for error detection, virtually error-free data transmission can be attained. Various types of ARQ and hybrid ARQ schemes, and error detection using linear block codes are surveyed.

Lin, S.↗
NASA NTRS1978

A packet telemetry system employing ARQ error control

A proposed packet telemetry system employing automatic retransmission request (ARQ) mode of error control is characterized. Limitations of the present multiplexing/demultiplexing approach are considered, and the use of the proposed system in near-earth satellites in the 1980s is suggested. Onboard processing and an adaptive multiplexing technique are described, as is an elastic buffer, required because the instantaneous data rate will be different from the telemetry transmission rate. The telemetry packets would be encoded into a powerful error-detection block code. A mechanism involving temporary buffering in a long shift register will permit retransmission request from the ground station for packets received in error. The ARQ mode of operation should ensure essentially error-free transmission at lower signal-to-noise ratios and at considerably higher transmission rates than are usually used.

Greene, E. P.↗
NASA NTRS1992

Least Reliable Bits Coding (LRBC) for high data rate satellite communications

An analysis and discussion of a bandwidth efficient multi-level/multi-stage block coded modulation technique called Least Reliable Bits Coding (LRBC) is presented. LRBC uses simple multi-level component codes that provide increased error protection on increasingly unreliable modulated bits in order to maintain an overall high code rate that increases spectral efficiency. Further, soft-decision multi-stage decoding is used to make decisions on unprotected bits through corrections made on more protected bits. Using analytical expressions and tight performance bounds it is shown that LRBC can achieve increased spectral efficiency and maintain equivalent or better power efficiency compared to that of Binary Phase Shift Keying (BPSK). Bit error rates (BER) vs. channel bit energy with Additive White Gaussian Noise (AWGN) are given for a set of LRB Reed-Solomon (RS) encoded 8PSK modulation formats with an ensemble rate of 8/9. All formats exhibit a spectral efficiency of 2.67 = (log2(8))(8/9) information bps/Hz. Bit by bit coded and uncoded error probabilities with soft-decision information are determined. These are traded with with code rate to determine parameters that achieve good performance. The relative simplicity of Galois field algebra vs. the Viterbi algorithm and the availability of high speed commercial Very Large Scale Integration (VLSI) for block codes indicates that LRBC using block codes is a desirable method for high data rate implementations.

Vanderaar, Mark↗
NASA NTRS1974

Performance of convolutional codes on fading channels typical of planetary entry missions

The performance of convolutional codes in fading channels typical of the planetary entry channel is examined in detail. The signal fading is due primarily to turbulent atmospheric scattering of the RF signal transmitted from an entry probe through a planetary atmosphere. Short constraint length convolutional codes are considered in conjunction with binary phase-shift keyed modulation and Viterbi maximum likelihood decoding, and for longer constraint length codes sequential decoding utilizing both the Fano and Zigangirov-Jelinek (ZJ) algorithms are considered. Careful consideration is given to the modeling of the channel in terms of a few meaningful parameters which can be correlated closely with theoretical propagation studies. For short constraint length codes the bit error probability performance was investigated as a function of E sub b/N sub o parameterized by the fading channel parameters. For longer constraint length codes the effect was examined of the fading channel parameters on the computational requirements of both the Fano and ZJ algorithms. The effects of simple block interleaving in combatting the memory of the channel is explored, using the analytic approach or digital computer simulation.

Modestino, J. W.↗
NASA NTRS1983

An extended d(min) = 4 RS code

A minimum distance d sub m - 4 extended Reed - Solomon (RS) code over GF (2 to the b power) was constructed. This code is used to correct any single byte error and simultaneously detect any double byte error. Features of the code; including fast encoding and decoding, are presented.

Deng, H.↗
NASA NTRS1999

An Interactive Concatenated Turbo Coding System

This paper presents a concatenated turbo coding system in which a Reed-Solomon outer code is concatenated with a binary turbo inner code. In the proposed system, the outer code decoder and the inner turbo code decoder interact to achieve both good bit error and frame error performances. The outer code decoder helps the inner turbo code decoder to terminate its decoding iteration while the inner turbo code decoder provides soft-output information to the outer code decoder to carry out a reliability-based soft- decision decoding. In the case that the outer code decoding fails, the outer code decoder instructs the inner code decoder to continue its decoding iterations until the outer code decoding is successful or a preset maximum number of decoding iterations is reached. This interaction between outer and inner code decoders reduces decoding delay. Also presented in the paper are an effective criterion for stopping the iteration process of the inner code decoder and a new reliability-based decoding algorithm for nonbinary codes.

Liu, Ye↗
NASA NTRS2002

Constrained coding for the deep-spaced optical channel

In this paper, we demonstrate a class of low-complexity modulation codes satisfying the (d,k) constraint that offer throughput gains over M-PPM on the order of 10-15%, which translate into SNR gains of .4 - .6 dB.

constrained coding optical communications error-co↗
NASA NTRS1999

Punctured Parallel and Serial Concatenated Convolutional Codes for BPSK/QPSK Channels

As available bandwidth for communication applications becomes scarce, bandwidth-efficient modulation and coding schemes become ever important. Since their discovery in 1993, turbo codes (parallel concatenated convolutional codes) have been the center of the attention in the coding community because of their bit error rate performance near the Shannon limit. Serial concatenated convolutional codes have also been shown to be as powerful as turbo codes. In this dissertation, we introduce algorithms for designing bandwidth-efficient rate r = k/(k + 1),k = 2, 3,..., 16, parallel and rate 3/4, 7/8, and 15/16 serial concatenated convolutional codes via puncturing for BPSK/QPSK (Binary Phase Shift Keying/Quadrature Phase Shift Keying) channels. Both parallel and serial concatenated convolutional codes have initially, steep bit error rate versus signal-to-noise ratio slope (called the -"cliff region"). However, this steep slope changes to a moderate slope with increasing signal-to-noise ratio, where the slope is characterized by the weight spectrum of the code. The region after the cliff region is called the "error rate floor" which dominates the behavior of these codes in moderate to high signal-to-noise ratios. Our goal is to design high rate parallel and serial concatenated convolutional codes while minimizing the error rate floor effect. The design algorithm includes an interleaver enhancement procedure and finds the polynomial sets (only for parallel concatenated convolutional codes) and the puncturing schemes that achieve the lowest bit error rate performance around the floor for the code rates of interest.

Acikel, Omer Fatih↗
NASA NTRS1990

On complexity of trellis structure of linear block codes

The trellis structure of linear block codes (LBCs) is discussed. The state and branch complexities of a trellis diagram (TD) for a LBC is investigated. The TD with the minimum number of states is said to be minimal. The branch complexity of a minimal TD for a LBC is expressed in terms of the dimensions of specific subcodes of the given code. Then upper and lower bounds are derived on the number of states of a minimal TD for a LBC, and it is shown that a cyclic (or shortened cyclic) code is the worst in terms of the state complexity among the LBCs of the same length and dimension. Furthermore, it is shown that the structural complexity of a minimal TD for a LBC depends on the order of its bit positions. This fact suggests that an appropriate permutation of the bit positions of a code may result in an equivalent code with a much simpler minimal TD. Boolean polynomial representation of codewords of a LBC is also considered. This representation helps in study of the trellis structure of the code. Boolean polynomial representation of a code is applied to construct its minimal TD. Particularly, the construction of minimal trellises for Reed-Muller codes and the extended and permuted binary primitive BCH codes which contain Reed-Muller as subcodes is emphasized. Finally, the structural complexity of minimal trellises for the extended and permuted, and double-error-correcting BCH codes is analyzed and presented. It is shown that these codes have relatively simple trellis structure and hence can be decoded with the Viterbi decoding algorithm.

Lin, Shu↗
NASA NTRS1972

Design of communication systems using short-constraint-length convolutional codes.

A method is presented for calculating the effect of carrier-phase reference error in a receiver phase-locked loop on bit error rates in convolutionally coded data, for the practical design of systems using short-constraint-length convolutional codes. A set of design curves shows the relation between design bit error rate, uplink carrier tracking loop SNR, downlink total SNR, and downlink modulation index. These curves make possible rapid and simple system optimization.

Merrill, H. M.↗
NASA NTRS1990

On linear structure and phase rotation invariant properties of block 2(sup l)-PSK modulation codes

Two important structural properties of block 2(l)-ary PSK (phase shift keying) modulation codes, linear structure and phase symmetry, are investigated. For an additive white Gaussian noise (AWGN) channel, the error performance of a modulation code depends on its squared Euclidean distance distribution. Linear structure of a code makes the error performance analysis much easier. Phase symmetry of a code is important in resolving carrier phase ambiguity and ensuring rapid carrier phase resynchronization after temporary loss of synchronization. It is desirable for a code to have as many phase symmetries as possible. A 2(l)-ary modulation code is represented here as a code with symbols from the integer group. S sub 2(l) PSK = (0,1,2,...,2(l)-1), under the modulo-2(l) addition. The linear structure of block 2(l)-ary PSK modulation codes over S sub 2(l)-ary PSK with respect to the modulo-2(l) vector addition is defined, and conditions under which a block 2(l)-ary PSK modulation code is linear are derived. Once the linear structure is developed, phase symmetry of a block 2(l)-ary PSK modulation code is studied. It is a necessary and sufficient condition for a block 2(l)-PSK modulation code, which is linear as a binary code, to be invariant under 180 deg/2(l-h) phase rotation, for 1 is less than or equal to h is less than or equal to l. A list of short 8-PSK and 16-PSK modulation codes is given, together with their linear structure and the smallest phase rotation for which a code is invariant.

Lin, Shu↗
NASA NTRS1990

Performance comparison of combined ECC/RLL codes

In this paper, we present a performance comparison of several combined error correcting/run-lenth limited (ECC/RLL) codes created by concatenating a convolutional code with a run-length limited code. In each case, encoding and decoding are accomplished using a single trellis based on the combined code. Half of the codes under investigation use conventionally (d,k) run-length limited codes, where d is the minimum and k is the maximum allowable run of 0's between 1's. The other half of the combined codes use a special class of (d,k) codes known as distance preserving codes. These codes have the property that pairwise Hamming distances out of the (d,k) encoder are at least as large as the corresponding distances into the encoder (i.e., the codes preserve distance). Thus a combined code, created using a convolutional code concatenated with a distance preserving (d,k) code, will have a free distance (dfree) no smaller than the free distance of the original convolutional code. It should be noted that this does not hold if the (d,k) code was not distance preserving. A computer simulation is used to compare the performance of these two types of codes over the binary symmetric channel for various (d,k) constraints, rates, free distances, and numbers of states. Of particular interest for magnetic recording applications are codes with run-length constraints (1,3), (1,7), and (2,7).

French, C.↗
NASA NTRS1987

Constructions for finite-state codes

A class of codes called finite-state (FS) codes is defined and investigated. These codes, which generalize both block and convolutional codes, are defined by their encoders, which are finite-state machines with parallel inputs and outputs. A family of upper bounds on the free distance of a given FS code is derived from known upper bounds on the minimum distance of block codes. A general construction for FS codes is then given, based on the idea of partitioning a given linear block into cosets of one of its subcodes, and it is shown that in many cases the FS codes constructed in this way have a d sub free which is as large as possible. These codes are found without the need for lengthy computer searches, and have potential applications for future deep-space coding systems. The issue of catastropic error propagation (CEP) for FS codes is also investigated.

Pollara, F.↗
NASA NTRS2021

PolyFit: A C++ code for Polynomial Curve Fit with Calculation of Error Bars

In radiobiology, many dose-response results are modeled using the so-called linear-quadratic (LQ)model, which means that results are modeled as a function of dose Das 𝑅(𝐷)=𝛽0+𝛽1𝐷+𝛽2𝐷2. The coefficients 𝛽0, 𝛽1and 𝛽2are obtained from fitting a series of data points (𝑥𝑖, 𝑦𝑖), which is usually done using a least-square method. The LQ and more generally the polynomial fit capability is implemented in many software that analyzes data. However, there are some instances where the fitting needs to be done programmatically. Furthermore, depending on the software used, some features may not be implemented. In this mini-review, I discuss the basis of polynomial fitting, including the calculation of errors on the coefficients and results, use of weighting and fixing the intercept value (the coefficient 𝛽0). A simple C++ code to perform the polynomial curve fitting is also provided. This code should be useful not only in radiobiology but in other fields of science as well.

Ianik Plante↗
NASA NTRS2021

PolyFit: A C++ code for Polynomial Curve Fit with Calculation of Error Bars

In radiobiology, many dose-response results are modeled using the so-called linear-quadratic(LQ)model, which means that results are modeled as a function of dose Das 𝑅(𝐷)=𝛽0+𝛽1𝐷+𝛽2𝐷2. The coefficients 𝛽0, 𝛽1and 𝛽2are obtained from fitting a series of data points (𝑥𝑖,𝑦𝑖), which is usually done using a least-square method. The LQ and more generally the polynomial fit capability is implemented in many software that analyzes data. However, it is often convenient to do the fitting programmatically, especially when a large number of datasets should be analyzed. Furthermore, depending on the software used, some features may not be implemented. In this mini-review, I discuss the basis of polynomial fitting, including the calculation of errors on the coefficients and results, use of weighting and fixing the intercept value (the coefficient 𝛽0). A simple C++ code to perform the polynomial curve fitting is also provided. This code should be useful not only in radiobiology but in other fields of science as well.

Ianik Plante↗
NASA NTRS1981

Moments of inclination error distribution computer program

A FORTRAN coded computer program is described which calculates orbital inclination error statistics using a closed-form solution. This solution uses a data base of trajectory errors from actual flights to predict the orbital inclination error statistics. The Scott flight history data base consists of orbit insertion errors in the trajectory parameters - altitude, velocity, flight path angle, flight azimuth, latitude and longitude. The methods used to generate the error statistics are of general interest since they have other applications. Program theory, user instructions, output definitions, subroutine descriptions and detailed FORTRAN coding information are included.

Myler, T. R.↗