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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Resilience of the surface code to error bursts

Quantum error correction works effectively only if the error rate of gate operations is sufficiently low. However, some rare physical mechanisms can cause a temporary increase in the error rate that affects many qubits; examples include ionizing radiation in superconducting hardware and large deviations in the global control of atomic systems. We refer to such rare transient spikes in the gate error rate as error bursts. In this work, we investigate the resilience of the rotated surface code to generic error bursts. We assume that, after appropriate mitigation strategies, the spike in the error rate lasts for only a single syndrome-extraction cycle; we also assume that the enhanced error rate is uniform across the code block. Under these assumptions, and for a circuit-level depolarizing noise model, we perform Monte Carlo simulations to determine the regime in burst error rate and background error rate for which the memory time becomes arbitrarily long as the code block size grows. Our results indicate that suitable hardware mitigation methods combined with standard decoding methods may suffice to protect against transient error bursts in the rotated surface code.

Quantum error correction↗
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 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 NTRS1975

On the effect of timing errors in run length codes

Many redundancy removal algorithms employ some sort of run length code. Blocks of timing words are coded with synchronization words inserted between blocks. The probability of incorrectly reconstructing a sample because of a channel error in the timing data is a monotonically nondecreasing function of time since the last synchronization word. In this paper we compute the 'probability that the accumulated magnitude of timing errors equal zero' as a function of time since the last synchronization word for a zero-order predictor (ZOP). The result is valid for any data source that can be modeled by a first-order Markov chain and any digital channel that can be modeled by a channel transition matrix. An example is presented.

Wilkins, L. C.↗
DOE OSTI2024

Gradient Coding With Iterative Block Leverage Score Sampling

Gradient coding is a method for mitigating straggling servers in a centralized computing network that uses erasure-coding techniques to distributively carry out first-order optimization methods. Randomized numerical linear algebra uses randomization to develop improved algorithms for large-scale linear algebra computations. In this study, we propose a method for distributed optimization that combines gradient coding and randomized numerical linear algebra. The proposed method uses a randomized ℓ 2 -subspace embedding and a gradient coding technique to distribute blocks of data to the computational nodes of a centralized network, and at each iteration the central server only requires a small number of computations to obtain the steepest descent update. The novelty of our approach is that the data is replicated according to importance scores, called block leverage scores, in contrast to most gradient coding approaches that uniformly replicate the data blocks. Furthermore, we do not require a decoding step at each iteration, avoiding a bottleneck in previous gradient coding schemes. We show that our approach results in a valid ℓ 2 -subspace embedding, and that our resulting approximation converges to the optimal solution.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

The trellis complexity of convolutional codes

It has long been known that convolutional codes have a natural, regular trellis structure that facilitates the implementation of Viterbi's algorithm. It has gradually become apparent that linear block codes also have a natural, though not in general a regular, 'minimal' trellis structure, which allows them to be decoded with a Viterbi-like algorithm. In both cases, the complexity of the Viterbi decoding algorithm can be accurately estimated by the number of trellis edges per encoded bit. It would, therefore, appear that we are in a good position to make a fair comparison of the Viterbi decoding complexity of block and convolutional codes. Unfortunately, however, this comparison is somewhat muddled by the fact that some convolutional codes, the punctured convolutional codes, are known to have trellis representations that are significantly less complex than the conventional trellis. In other words, the conventional trellis representation for a convolutional code may not be the minimal trellis representation. Thus, ironically, at present we seem to know more about the minimal trellis representation for block than for convolutional codes. In this article, we provide a remedy, by developing a theory of minimal trellises for convolutional codes. (A similar theory has recently been given by Sidorenko and Zyablov). This allows us to make a direct performance-complexity comparison for block and convolutional codes. A by-product of our work is an algorithm for choosing, from among all generator matrices for a given convolutional code, what we call a trellis-minimal generator matrix, from which the minimal trellis for the code can be directly constructed. Another by-product is that, in the new theory, punctured convolutional codes no longer appear as a special class, but simply as high-rate convolutional codes whose trellis complexity is unexpectedly small.

Mceliece, R. J.↗
NASA NTRS1979

Some optimal partial-unit-memory codes

A class of time-invariant binary convolutional codes is defined, called partial-unit-memory codes. These codes are optimal in the sense of having maximum free distance for given values of R, k (the number of encoder inputs), and mu (the number of encoder memory cells). Optimal codes are given for rates R = 1/4, 1/3, 1/2, and 2/3, with mu not greater than 4 and k not greater than mu + 3, whenever such a code is better than previously known codes. An infinite class of optimal partial-unit-memory codes is also constructed based on equidistant block codes.

Lauer, G. S.↗
NASA NTRS1992

Visual information processing; Proceedings of the Meeting, Orlando, FL, Apr. 20-22, 1992

Topics discussed in these proceedings include nonlinear processing and communications; feature extraction and recognition; image gathering, interpolation, and restoration; image coding; and wavelet transform. Papers are presented on noise reduction for signals from nonlinear systems; driving nonlinear systems with chaotic signals; edge detection and image segmentation of space scenes using fractal analyses; a vision system for telerobotic operation; a fidelity analysis of image gathering, interpolation, and restoration; restoration of images degraded by motion; and information, entropy, and fidelity in visual communication. Attention is also given to image coding methods and their assessment, hybrid JPEG/recursive block coding of images, modified wavelets that accommodate causality, modified wavelet transform for unbiased frequency representation, and continuous wavelet transform of one-dimensional signals by Fourier filtering.

Huck, Friedrich O.↗
NASA NTRS1974

Upper bounds on sequential decoding performance parameters

This paper presents the best obtainable random coding and expurgated upper bounds on the probabilities of undetectable error, of t-order failure (advance to depth t into an incorrect subset), and of likelihood rise in the incorrect subset, applicable to sequential decoding when the metric bias G is arbitrary. Upper bounds on the Pareto exponent are also presented. The G-values optimizing each of the parameters of interest are determined, and are shown to lie in intervals that in general have nonzero widths. The G-optimal expurgated bound on undetectable error is shown to agree with that for maximum likelihood decoding of convolutional codes, and that on failure agrees with the block code expurgated bound. Included are curves evaluating the bounds for interesting choices of G and SNR for a binary-input quantized-output Gaussian additive noise channel.

Jelinek, F.↗
NASA NTRS1988

Further results on finite-state codes

A general construction for finite-state (FS) codes is applied to some well-known block codes. Subcodes of the (24,12) Golay code are used to generate two optimal FS codes with d sub free = 12 and 16. A partition of the (16,8) Nordstrom-Robinson code yields a d sub free = 10 FS code. Simulation results are shown and decoding algorithms are briefly discussed.

Pollara, F.↗
NASA NTRS2006

General Solution for Theoretical Packet Data Loss Rate

Communications systems which transfer blocks ("frames") of data must use a marker ("frame synchronization pattern") for identifying where a block begins. A technique ("frame synchronization strategy") is used to locate the start of each frame and maintain synchronization as additional blocks are processed. A device which strips out the frame synchronization pattern [FSP] and provides an "end of frame" pulse is called a frame synchronizer. As clock and data errors are introduced into the system, the start-of-block marker becomes displaced and/or corrupted. The capability of the frame synchronizer to stay locked to the pattern under these conditions is a figure of merit for the frame synchronization strategy. It is important to select a strategy which will stay locked nearly all the time at bit error rates where the data is usable. ("Bit error rate" [BER] is the fraction of binary bits which are inverted by passage through a communication system.) The fraction of frames that are discarded because the frame synchronizer is not locked is called "Percent Data Loss" or "Packet Data Loss rate" [PDL]. A general approach for accurately predicting PDL given BER was developed in Theoretical Percent Data Loss Calculation and Measurement Accuracy, T. P. Kelly, LESC-30554, December 1992. Kelly gave a solution in terms of matrix equations, and only addressed "level" channel encoding. This paper goes on to give a closed-form polynomial solution for the most common class of frame synchronizer strategies, and will also address "mark" and "space" (differential) channel encoding, and burst error environments. The paper is divided into four sections and follows a logically ordered presentation, with results developed before they are evaluated. However, most readers will derive the greatest benefit from this paper by treating the results as reference material. The result developed for differential encoding can be extended to other applications (like block codes) where the probability is needed that a block contains only a certain number of errors.

Lansdowne, Chatwin↗
NASA NTRS1979

A connection between block and convolutional codes

Convolutional codes of any rate and any constraint length give rise to a sequence of quasi-cyclic codes. Conversely, any quasi-cyclic code may be convolutionally encoded. Among the quasi-cyclic codes are the quadratic residue codes, Reed-Solomon codes and optimal BCH codes. The constraint length K for the convolutional encoding of many of these codes (Golay, (48, 24) QR, etc.) turns out to be surprisingly small. Thus using the soft decoding techniques for convolutional decoding, a new maximum likelihood decoding algorithm for many block codes is established. Conversely an optimal quasi-cyclic code will yield a convolutional encoding with optimal local properties and therefore with good infinite convolutional coding properties.

Solomon, G.↗
NASA NTRS1974

Evaluation of three coding schemes designed for improved data communication

Three coding schemes designed for improved data communication are evaluated. Four block codes are evaluated relative to a quality function, which is a function of both the amount of data rejected and the error rate. The Viterbi maximum likelihood decoding algorithm as a decoding procedure is reviewed. This evaluation is obtained by simulating the system on a digital computer. Short constraint length rate 1/2 quick-look codes are studied, and their performance is compared to general nonsystematic codes.

Snelsire, R. W.↗