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DOE OSTI2016

The vertical-current approximation nonlinear force-free field code — Description, performance tests, and measurements of magnetic energies dissipated in solar flares

In this work we provide an updated description of the Vertical-Current Approximation Nonlinear Force-Free Field (VCA-NLFFF) code, which is designed to measure the evolution of the potential, non-potential, free energies, and the dissipated magnetic energies during solar flares. This code provides a complementary and alternative method to existing traditional NLFFF codes. The chief advantages of the VCA-NLFFF code over traditional NLFFF codes are the circumvention of the unrealistic assumption of a force-free photosphere in the magnetic field extrapolation method, the capability to minimize the misalignment angles between observed coronal loops (or chromospheric fibril structures) and theoretical model field lines, as well as computational speed. In performance tests of the VCA-NLFFF code, by comparing with the NLFFF code of Wiegelmann, we find agreement in the potential, non-potential, and free energy within a factor of ≲1.3, but the Wiegelmann code yields in the average a factor of 2 lower flare energies. The VCA-NLFFF code is found to detect decreases in flare energies in most X, M, and C-class flares. The successful detection of energy decreases during a variety of flares with the VCA-NLFFF code indicates that current-driven twisting and untwisting of the magnetic field is an adequate model to quantify the storage of magnetic energies in active regions and their dissipation during flares. The VCA-NLFFF code is also publicly available in the Solar SoftWare.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Spin-squeezed Gottesman-Kitaev-Preskill codes for quantum error correction in atomic ensembles

Gottesman-Kitaev-Preskill (GKP) codes encode a qubit in displaced phase-space combs of a continuous-variable (CV) quantum system and are useful for correcting a variety of high-weight photonic errors. Here we propose atomic ensemble analogs of the single-mode CV GKP code by using the quantum central limit theorem to pull back the phase-space structure of a CV system to the compact phase space of a quantum spin system. We study the optimal recovery performance of these codes under error channels described by stochastic relaxation and isotropic ballistic dephasing processes using the diversity combining approach for calculating channel fidelity. Additionally, we find that the spin GKP codes outperform other spin system codes such as cat codes or binomial codes. Our spin GKP codes based on the two-axis countertwisting interaction and superpositions of SU(2) coherent states are direct spin analogs of the finite-energy CV GKP codes, whereas our codes based on one-axis twisting do not yet have well-studied CV analogs. A state preparation scheme for the spin GKP codes is proposed which uses the linear-combination-of-unitaries method, applicable to both the CV and spin GKP settings. Finally, we discuss a fault-tolerant approximate gate set for quantum computing with spin-GKP-encoded qubits, obtained by translating gates from the CV GKP setting using the quantum central limit theorem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Single-shot quantum error correction in intertwined toric codes

We construct a subsystem code in three dimensions that exhibits single-shot error correction in a user-friendly and transparent way. As this code is a subsystem version of coupled toric codes, we call it the intertwined toric code (ITC). Although previous codes share the property of single-shot error correction, the ITC is distinguished by its physically motivated origin, geometrically straightforward logical operators and errors, and a simple phase diagram. The code arises from three-dimensional (3D) stabilizer toric codes in a way that emphasizes the physical origin of the single-shot property. In particular, starting with two copies of the 3D toric code, we add check operators that provide for the confinement of pointlike excitations without condensing the loop excitations. Geometrically, the bare and dressed logical operators in the ITC derive from logical operators in the underlying toric codes, creating a clear relationship between errors and measurement outcomes. The syndromes of the ITC resemble the syndromes of the single-shot code by Kubica and Vasmer, allowing us to use their decoding schemes. We also extract the phase diagram corresponding to ITC and show that it contains the phases found in the Kubica-Vasmer code. Lastly, we suggest various connections to Walker-Wang models and measurement-based quantum computation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Error-correcting codes for fermionic quantum simulation

Utilizing the framework of \mathbb{Z}_2 ℤ 2 lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic automorphisms of the Pauli module over the Laurent polynomial ring. This enables us to systematically increase the code distances of stabilizer codes while fixing the rate between encoded logical fermions and physical qubits. We identify a family of stabilizer codes suitable for fermion simulation, achieving code distances of d=2,3,4,5,6,7, allowing correction of any \lfloor \frac{d-1}{2} \rfloor ⌊ d − 1 2 ⌋ -qubit error. In contrast to the traditional code concatenation approach, our method can increase the code distances without decreasing the (fermionic) code rate. In particular, we explicitly show all stabilizers and logical operators for codes with code distances of d=3,4,5. We provide syndromes for all Pauli errors and invent a syndrome-matching algorithm to compute code distances numerically.

Physics↗

DOE OSTI2020

Status Report on ASME Code Development for Nonmetallic Core Components in 2020

The purpose of this report is to provide a status update on the progress and ongoing activities of the current ASME Boiler Pressure Vessel (BPV) Code Section III, Division 5, on nonmetallic core components and assemblies which includes the design rules for graphite and ceramic composite materials. Section III is concerned with the design and construction of nuclear reactor components and Division 5 focuses on high temperature reactors (HTR). The ASME Section III Committee’s function for nuclear items other than pressure-retaining components, is to establish rules of safety related to structural integrity. The term “construction” refers to the all-inclusive effort comprising of materials, design, fabrication, examination, inspection, testing, certification, and pressure relief. The Department of Energy (DOE) supports industry codes and standards development through focused research providing the technical basis for new or modified codes and standards and the participation of subject matter experts in codes and standards committees. The activities for the nonmetallic core components and assemblies committees are the pursuit of two working groups that meet quarterly during ASME BPV Code Week meetings. The two working groups are General Requirements for Graphite and Ceramic Composite Core Components and Assemblies (GR GCCCCA) and Nonmetallic Design and Materials (NDM). The rules on general requirements for nonmetallic core components are discussed in the articles of Subsection HA subpart B. Ceramic composites were recently incorporated within the rules, and the GR GCCCCA working group is now in the process of aligning the requirements with the subsections and articles of ASME BPV Code Section III NCA, the general requirements for Division 1 and 2 of the code. The NDM working group is concerned with the design rules for graphite and composite materials for core components and assemblies discussed in Subsection HH (Class SN Nonmetallic Core Components) subpart A and subpart B which reference graphite and composite materials respectively. The bulk of the progress and work is done within this working group. A significant undertaking, with discussion that started in 2015, is to gain endorsement of ASME Section III, Division 5, by the U.S. Nuclear Regulatory Commission (NRC). In June 2018, ASME formally recommended endorsement to the NRC. The NRC has since initiated the endorsement review process, which is to be concluded early in 2021. ASME task groups on metallic structures and components, as well as non-metallic core support structures, have been formed to define potential pathways and schedules for NRC endorsement of Division 5. NRC determined to perform a review on the 2017 edition of Section III Division 5 as a baseline. As a result, the use of graphite as nonmetallic core components formed part of the review, but it excluded composite materials (which were first introduced in the 2019 edition). This report documents progress in FY 2020 directed toward ASME’s efforts to develop design codes for graphite and composites. Progress includes a major code review by NRC, the first code enquiry, and its solution, an overhaul of the treatment of Weibull Statistics, and the addition of Nonmandatory Appendices to the composites code relating to carbon-carbon composite materials.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

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 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 NTRS1988

A concatenated coded modulation scheme for error control

A concatenated coded modulation scheme for error control in data communications is presented. The scheme is achieved by concatenating a Reed-Solomon outer code and a bandwidth efficient block inner code for M-ary PSK modulation. Error performance of the scheme is analyzed for an AWGN channel. It is shown that extremely high reliability can be attained by using a simple M-ary PSK modulation inner code and a relatively powerful Reed-Solomon outer code. Furthermore, if an inner code of high effective rate is used, the bandwidth expansion required by the scheme due to coding will be greatly reduced. The proposed scheme is very effective for high speed satellite communications for large file transfer where high reliability is required. A simple method is also presented for constructing codes for M-ary PSK modulation. Some short M-ary PSK codes with good minimum squared Euclidean distance are constructed. These codes have trellis structure and hence can be decoded with a soft decision Viterbi decoding algorithm. Furthermore, some of these codes are phase invariant under multiples of 45 deg rotation.

Lin, Shu↗

NASA NTRS1988

A concatenated coded modulation scheme for error control (addition 2)

A concatenated coded modulation scheme for error control in data communications is described. The scheme is achieved by concatenating a Reed-Solomon outer code and a bandwidth efficient block inner code for M-ary PSK modulation. Error performance of the scheme is analyzed for an AWGN channel. It is shown that extremely high reliability can be attained by using a simple M-ary PSK modulation inner code and a relatively powerful Reed-Solomon outer code. Furthermore, if an inner code of high effective rate is used, the bandwidth expansion required by the scheme due to coding will be greatly reduced. The proposed scheme is particularly effective for high-speed satellite communications for large file transfer where high reliability is required. This paper also presents a simple method for constructing block codes for M-ary PSK modulation. Some short M-ary PSK codes with good minimum squared Euclidean distance are constructed. These codes have trellis structure and hence can be decoded with a soft-decision Viterbi decoding algorithm. Furthermore, some of these codes are phase invariant under multiples of 45 deg rotation.

Lin, Shu↗

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 NTRS1991

A bandwidth efficient coding scheme for the Hubble Space Telescope

As a demonstration of the performance capabilities of trellis codes using multidimensional signal sets, a Viterbi decoder was designed. The choice of code was based on two factors. The first factor was its application as a possible replacement for the coding scheme currently used on the Hubble Space Telescope (HST). The HST at present uses the rate 1/3 nu = 6 (with 2 (exp nu) = 64 states) convolutional code with Binary Phase Shift Keying (BPSK) modulation. With the modulator restricted to a 3 Msym/s, this implies a data rate of only 1 Mbit/s, since the bandwidth efficiency K = 1/3 bit/sym. This is a very bandwidth inefficient scheme, although the system has the advantage of simplicity and large coding gain. The basic requirement from NASA was for a scheme that has as large a K as possible. Since a satellite channel was being used, 8PSK modulation was selected. This allows a K of between 2 and 3 bit/sym. The next influencing factor was INTELSAT's intention of transmitting the SONET 155.52 Mbit/s standard data rate over the 72 MHz transponders on its satellites. This requires a bandwidth efficiency of around 2.5 bit/sym. A Reed-Solomon block code is used as an outer code to give very low bit error rates (BER). A 16 state rate 5/6, 2.5 bit/sym, 4D-8PSK trellis code was selected. This code has reasonable complexity and has a coding gain of 4.8 dB compared to uncoded 8PSK (2). This trellis code also has the advantage that it is 45 deg rotationally invariant. This means that the decoder needs only to synchronize to one of the two naturally mapped 8PSK signals in the signal set.

Pietrobon, Steven S.↗

NASA NTRS1991

Some partial-unit-memory convolutional codes

The results of a study on a class of error correcting codes called partial unit memory (PUM) codes are presented. This class of codes, though not entirely new, has until now remained relatively unexplored. The possibility of using the well developed theory of block codes to construct a large family of promising PUM codes is shown. The performance of several specific PUM codes are compared with that of the Voyager standard (2, 1, 6) convolutional code. It was found that these codes can outperform the Voyager code with little or no increase in decoder complexity. This suggests that there may very well be PUM codes that can be used for deep space telemetry that offer both increased performance and decreased implementational complexity over current coding systems.

Abdel-Ghaffar, K.↗

NASA NTRS1992

Bandwidth efficient CCSDS coding standard proposals

The basic concatenated coding system for the space telemetry channel consists of a Reed-Solomon (RS) outer code, a symbol interleaver/deinterleaver, and a bandwidth efficient trellis inner code. A block diagram of this configuration is shown. The system may operate with or without the outer code and interleaver. In this recommendation, the outer code remains the (255,223) RS code over GF(2 exp 8) with an error correcting capability of t = 16 eight bit symbols. This code's excellent performance and the existence of fast, cost effective, decoders justify its continued use. The purpose of the interleaver/deinterleaver is to distribute burst errors out of the inner decoder over multiple codewords of the outer code. This utilizes the error correcting capability of the outer code more efficiently and reduces the probability of an RS decoder failure. Since the space telemetry channel is not considered bursty, the required interleaving depth is primarily a function of the inner decoding method. A diagram of an interleaver with depth 4 that is compatible with the (255,223) RS code is shown. Specific interleaver requirements are discussed after the inner code recommendations.

Costello, Daniel J., Jr.↗

NASA NTRS1992

Self-dual (48,24;12) codes

Two self-dual (48,24;12) codes are constructed as 6 x 8 matrices whose columns add up to form an extended BCH-Hamming (8,4;4) code and whose rows sum to odd or even parity. The codes constructed have the identical weight structure of the extended quadratic residue code of length 48. Algebraic isomorphisms may exist between pairs of these three codes. However, because of their matrix form, the newly constructed codes are easily correctable for all five-error and many six-error patterns. The first code comes from restricting a binary cyclic (63,18;36) code to a 6 x 7 matrix and then adjoining six dimensions to the extended 6 x 8 matrix. These six dimensions are generated by linear combinations of row permutations of a 6 x 8 matrix of weight 12, whose sums of rows and columns add to one. The second code comes from a slight modification in the parity (eighth) dimension of the Reed-Solomon (8,4;5) code over GF(64). Error correction in both codes uses the row sum parity information to detect errors in the correction algorithm.

Solomon, G.↗

NASA NTRS1993

Advanced coding and modulation schemes for TDRSS

This paper describes the performance of the Ungerboeck and pragmatic 8-Phase Shift Key (PSK) Trellis Code Modulation (TCM) coding techniques with and without a (255,223) Reed-Solomon outer code as they are used for Tracking Data and Relay Satellite System (TDRSS) S-Band and Ku-Band return services. The performance of these codes at high data rates is compared to uncoded Quadrature PSK (QPSK) and rate 1/2 convolutionally coded QPSK in the presence of Radio Frequency Interference (RFI), self-interference, and hardware distortions. This paper shows that the outer Reed-Solomon code is necessary to achieve a 10(exp -5) Bit Error Rate (BER) with an acceptable level of degradation in the presence of RFI. This paper also shows that the TCM codes with or without the Reed-Solomon outer code do not perform well in the presence of self-interference. In fact, the uncoded QPSK signal performs better than the TCM coded signal in the self-interference situation considered in this analysis. Finally, this paper shows that the E(sub b)/N(sub 0) degradation due to TDRSS hardware distortions is approximately 1.3 dB with a TCM coded signal or a rate 1/2 convolutionally coded QPSK signal and is 3.2 dB with an uncoded QPSK signal.

Harrell, Linda↗

NASA NTRS1993

Evaluation of the efficiency and fault density of software generated by code generators

Flight computers and flight software are used for GN&C (guidance, navigation, and control), engine controllers, and avionics during missions. The software development requires the generation of a considerable amount of code. The engineers who generate the code make mistakes and the generation of a large body of code with high reliability requires considerable time. Computer-aided software engineering (CASE) tools are available which generates code automatically with inputs through graphical interfaces. These tools are referred to as code generators. In theory, code generators could write highly reliable code quickly and inexpensively. The various code generators offer different levels of reliability checking. Some check only the finished product while some allow checking of individual modules and combined sets of modules as well. Considering NASA's requirement for reliability, an in house manually generated code is needed. Furthermore, automatically generated code is reputed to be as efficient as the best manually generated code when executed. In house verification is warranted.

Schreur, Barbara↗

NASA NTRS1994

Error coding simulations in C

When data is transmitted through a noisy channel, errors are produced within the data rendering it indecipherable. Through the use of error control coding techniques, the bit error rate can be reduced to any desired level without sacrificing the transmission data rate. The Astrionics Laboratory at Marshall Space Flight Center has decided to use a modular, end-to-end telemetry data simulator to simulate the transmission of data from flight to ground and various methods of error control. The simulator includes modules for random data generation, data compression, Consultative Committee for Space Data Systems (CCSDS) transfer frame formation, error correction/detection, error generation and error statistics. The simulator utilizes a concatenated coding scheme which includes CCSDS standard (255,223) Reed-Solomon (RS) code over GF(2(exp 8)) with interleave depth of 5 as the outermost code, (7, 1/2) convolutional code as an inner code and CCSDS recommended (n, n-16) cyclic redundancy check (CRC) code as the innermost code, where n is the number of information bits plus 16 parity bits. The received signal-to-noise for a desired bit error rate is greatly reduced through the use of forward error correction techniques. Even greater coding gain is provided through the use of a concatenated coding scheme. Interleaving/deinterleaving is necessary to randomize burst errors which may appear at the input of the RS decoder. The burst correction capability length is increased in proportion to the interleave depth. The modular nature of the simulator allows for inclusion or exclusion of modules as needed. This paper describes the development and operation of the simulator, the verification of a C-language Reed-Solomon code, and the possibility of using Comdisco SPW(tm) as a tool for determining optimal error control schemes.

Noble, Viveca K.↗

NASA NTRS1995

On the design of turbo codes

In this article, we design new turbo codes that can achieve near-Shannon-limit performance. The design criterion for random interleavers is based on maximizing the effective free distance of the turbo code, i.e., the minimum output weight of codewords due to weight-2 input sequences. An upper bound on the effective free distance of a turbo code is derived. This upper bound can be achieved if the feedback connection of convolutional codes uses primitive polynomials. We review multiple turbo codes (parallel concatenation of q convolutional codes), which increase the so-called 'interleaving gain' as q and the interleaver size increase, and a suitable decoder structure derived from an approximation to the maximum a posteriori probability decision rule. We develop new rate 1/3, 2/3, 3/4, and 4/5 constituent codes to be used in the turbo encoder structure. These codes, for from 2 to 32 states, are designed by using primitive polynomials. The resulting turbo codes have rates b/n (b = 1, 2, 3, 4 and n = 2, 3, 4, 5, 6), and include random interleavers for better asymptotic performance. These codes are suitable for deep-space communications with low throughput and for near-Earth communications where high throughput is desirable. The performance of these codes is within 1 dB of the Shannon limit at a bit-error rate of 10(exp -6) for throughputs from 1/15 up to 4 bits/s/Hz.

Divsalar, D.↗