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At least 199 records · Page 11

Error-Rate Bounds for Coded PPM on a Poisson Channel

Equations for computing tight bounds on error rates for coded pulse-position modulation (PPM) on a Poisson channel at high signal-to-noise ratio have been derived. These equations and elements of the underlying theory are expected to be especially useful in designing codes for PPM optical communication systems. The equations and the underlying theory apply, more specifically, to a case in which a) At the transmitter, a linear outer code is concatenated with an inner code that includes an accumulator and a bit-to-PPM-symbol mapping (see figure) [this concatenation is known in the art as "accumulate-PPM" (abbreviated "APPM")]; b) The transmitted signal propagates on a memoryless binary-input Poisson channel; and c) At the receiver, near-maximum-likelihood (ML) decoding is effected through an iterative process. Such a coding/modulation/decoding scheme is a variation on the concept of turbo codes, which have complex structures, such that an exact analytical expression for the performance of a particular code is intractable. However, techniques for accurately estimating the performances of turbo codes have been developed. The performance of a typical turbo code includes (1) a "waterfall" region consisting of a steep decrease of error rate with increasing signal-to-noise ratio (SNR) at low to moderate SNR, and (2) an "error floor" region with a less steep decrease of error rate with increasing SNR at moderate to high SNR. The techniques used heretofore for estimating performance in the waterfall region have differed from those used for estimating performance in the error-floor region. For coded PPM, prior to the present derivations, equations for accurate prediction of the performance of coded PPM at high SNR did not exist, so that it was necessary to resort to time-consuming simulations in order to make such predictions. The present derivation makes it unnecessary to perform such time-consuming simulations.

Moision, Bruce

Accumulate-Repeat-Accumulate-Accumulate Codes

Accumulate-repeat-accumulate-accumulate (ARAA) codes have been proposed, inspired by the recently proposed accumulate-repeat-accumulate (ARA) codes. These are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. ARAA codes can be regarded as serial turbolike codes or as a subclass of low-density parity-check (LDPC) codes, and, like ARA codes they have projected graph or protograph representations; these characteristics make it possible to design high-speed iterative decoders that utilize belief-propagation algorithms. The objective in proposing ARAA codes as a subclass of ARA codes was to enhance the error-floor performance of ARA codes while maintaining simple encoding structures and low maximum variable node degree.

Divsalar, Dariush

Coding for Communication Channels with Dead-Time Constraints

Coding schemes have been designed and investigated specifically for optical and electronic data-communication channels in which information is conveyed via pulse-position modulation (PPM) subject to dead-time constraints. These schemes involve the use of error-correcting codes concatenated with codes denoted constrained codes. These codes are decoded using an interactive method. In pulse-position modulation, time is partitioned into frames of Mslots of equal duration. Each frame contains one pulsed slot (all others are non-pulsed). For a given channel, the dead-time constraints are defined as a maximum and a minimum on the allowable time between pulses. For example, if a Q-switched laser is used to transmit the pulses, then the minimum allowable dead time is the time needed to recharge the laser for the next pulse. In the case of bits recorded on a magnetic medium, the minimum allowable time between pulses depends on the recording/playback speed and the minimum distance between pulses needed to prevent interference between adjacent bits during readout. The maximum allowable dead time for a given channel is the maximum time for which it is possible to satisfy the requirement to synchronize slots. In mathematical shorthand, the dead-time constraints for a given channel are represented by the pair of integers (d,k), where d is the minimum allowable number of zeroes between ones and k is the maximum allowable number of zeroes between ones. A system of the type to which the present schemes apply is represented by a binary- input, real-valued-output channel model illustrated in the figure. At the transmitting end, information bits are first encoded by use of an error-correcting code, then further encoded by use of a constrained code. Several constrained codes for channels subject to constraints of (d,infinity) have been investigated theoretically and computationally. The baseline codes chosen for purposes of comparison were simple PPM codes characterized by M-slot PPM frames separated by d-slot dead times.

Moision, Bruce

Auto Code Generation for Simulink-Based Attitude Determination Control System

This paper details the work done to auto generate C code from a Simulink-Based Attitude Determination Control System (ADCS) to be used in target platforms. NASA Marshall Engineers have developed an ADCS Simulink simulation to be used as a component for the flight software of a satellite. This generated code can be used for carrying out Hardware in the loop testing of components for a satellite in a convenient manner with easily tunable parameters. Due to the nature of the embedded hardware components such as microcontrollers, this simulation code cannot be used directly, as it is, on the target platform and must first be converted into C code; this process is known as auto code generation. In order to generate C code from this simulation; it must be modified to follow specific standards set in place by the auto code generation process. Some of these modifications include changing certain simulation models into their atomic representations which can bring new complications into the simulation. The execution order of these models can change based on these modifications. Great care must be taken in order to maintain a working simulation that can also be used for auto code generation. After modifying the ADCS simulation for the auto code generation process, it is shown that the difference between the output data of the former and that of the latter is between acceptable bounds. Thus, it can be said that the process is a success since all the output requirements are met. Based on these results, it can be argued that this generated C code can be effectively used by any desired platform as long as it follows the specific memory requirements established in the Simulink Model.

MolinaFraticelli, Jose Carlos

The Performance of Current Atmospheric Radiation Codes in Phase I of CIRC

The Continual Intercomparison of Radiation Codes (CIRC) is intended as an evolving and regularly updated reference source for evaluation of radiative transfer (RT) codes used in Global Climate Models and other atmospheric applications. In our presentation we will discuss our evaluation of the performance of 13 shortwave and 11 longwave RT codes that participated in Phase I of CIRC. CIRC differs from previous intercomparisons in that it relies on an observationally validated catalogue of cases. The seven CIRC Phase I baseline cases, five cloud-free, and two with overcast liquid clouds, are built around observations by the Atmospheric Radiation Measurements (ARM) program that satisfy the goals .of Phase I, namely to examine RT model performance in realistic, yet not overly complex, atmospheric conditions. Besides the seven baseline cases, additional idealized "subcases" are also examined to facilitate interpretation of model errors. We will quantify individual model performance with respect to reference line-by-line calculations, and will also highlight RT code behavior for conditions of doubled CO2 , aspects of utilizing a spectral specification of surface albedo, and the impact of the inclusion of scattering in the thermal infrared. Our analysis suggests that RT codes should work towards improving their calculation of diffuse shortwave flux, shortwave absorption, treatment of spectral surface albedo, and shortwave CO2 forcing. Despite practical difficulties in comparing our results to previous results by the Intercomparison of Radiation Codes in Climate Models (ICRCCM) conducted about 20 years ago, it appears that the current generation of RT codes do indeed perform better than the codes of the ICRCCM era. By enhancing the range of conditions under which participating codes are tested, future CIRC phases will hopefully allow even more rigorous examination of RT code performance.

Oreopoulos, L.

The 'Brick Wall' radio loss approximation and the performance of strong channel codes for deep space applications at high data rates

In order to evaluate performance of strong channel codes in presence of imperfect carrier phase tracking for residual carrier BPSK modulation in this paper an approximate 'brick wall' model is developed which is independent of the channel code type for high data rates. It is shown that this approximation is reasonably accurate (less than 0.7dB for low FERs for (1784,1/6) code and less than 0.35dB for low FERs for (5920,1/6) code). Based on the approximation's accuracy, it is concluded that the effects of imperfect carrier tracking are more or less independent of the channel code type for strong channel codes. Therefore, the advantage that one strong channel code has over another with perfect carrier tracking translates to nearly the same advantage under imperfect carrier tracking conditions. This will allow the link designers to incorporate projected channel code performance of strong channel codes into their design tables without worrying about their behavior in the face of imperfect carrier phase tracking.

turbo codes

An analysis of the metabolic theory of the origin of the genetic code

A computer program was used to test Wong's coevolution theory of the genetic code. The codon correlations between the codons of biosynthetically related amino acids in the universal genetic code and in randomly generated genetic codes were compared. It was determined that many codon correlations are also present within random genetic codes and that among the random codes there are always several which have many more correlations than that found in the universal code. Although the number of correlations depends on the choice of biosynthetically related amino acids, the probability of choosing a random genetic code with the same or greater number of codon correlations as the universal genetic code was found to vary from 0.1% to 34% (with respect to a fairly complete listing of related amino acids). Thus, Wong's theory that the genetic code arose by coevolution with the biosynthetic pathways of amino acids, based on codon correlations between biosynthetically related amino acids, is statistical in nature.

NASA Discipline Exobiology

Correlation approach to identify coding regions in DNA sequences

Recently, it was observed that noncoding regions of DNA sequences possess long-range power-law correlations, whereas coding regions typically display only short-range correlations. We develop an algorithm based on this finding that enables investigators to perform a statistical analysis on long DNA sequences to locate possible coding regions. The algorithm is particularly successful in predicting the location of lengthy coding regions. For example, for the complete genome of yeast chromosome III (315,344 nucleotides), at least 82% of the predictions correspond to putative coding regions; the algorithm correctly identified all coding regions larger than 3000 nucleotides, 92% of coding regions between 2000 and 3000 nucleotides long, and 79% of coding regions between 1000 and 2000 nucleotides. The predictive ability of this new algorithm supports the claim that there is a fundamental difference in the correlation property between coding and noncoding sequences. This algorithm, which is not species-dependent, can be implemented with other techniques for rapidly and accurately locating relatively long coding regions in genomic sequences.

Non-NASA Center

RASPA3

RASPA3, a molecular simulation code for computing adsorption and diffusion in nanoporous materials and thermodynamic and transport properties of fluids. It implements force field based classical Monte Carlo/molecular dynamics in various ensembles. RASPA3 is rewritten from the ground up in C++23 with speed and code readability in mind. Transition-matrix Monte Carlo is added to compute the density of states and free energies. The Monte Carlo code for rigid molecules is based on quaternions, and the atomic positions needed in the energy evaluation are recreated from the center of mass position and quaternion orientation. The expanded ensemble methodology for fractional molecules, with a scaling parameter λ between 0 and 1, now also keeps track of analytic expressions of dU/dλ, allowing independent verification of the chemical potential using thermodynamic integration. The source code is freely available under the MIT license on GitHub.

Dubbeldam, David

Fracton models from product codes

We explore a deep connection between fracton order and product codes. In particular, we propose and analyze conditions on classical seed codes which lead to fracton order in the resulting quantum product codes. Depending on the properties of the input codes, product codes can realize either Type-I or Type-II fracton models, in both nonlocal and local constructions. For the nonlocal case, we show that a recently proposed model of lineons on nonlocal graphs can be obtained as a hypergraph product code. Interestingly, constrained mobility in this model arises only from energy barriers associated with the graph. For the local case, we introduce a novel type of classical LDPC code defined on a planar aperiodic tiling. By considering the specific example of the pinwheel tiling, we demonstrate the systematic construction of local Type-I and Type-II fracton models as product codes. Our work establishes product codes as a natural setting for exploring fracton order.

Fractons

Extracting Topological Orders of Generalized Pauli Stabilizer Codes in Two Dimensions

In this paper, we introduce an algorithm for extracting topological data from translation invariant generalized Pauli stabilizer codes in two-dimensional systems, focusing on the analysis of anyon excitations and string operators. The algorithm applies to Z d qudits, including instances where d is a nonprime number. This capability allows the identification of topological orders that differ from the Z d toric codes. It extends our understanding beyond the established theorem that Pauli stabilizer codes for Z p qudits (with p being a prime) are equivalent to finite copies of Z p toric codes and trivial stabilizers. The algorithm is designed to determine all anyons and their string operators, enabling the computation of their fusion rules, topological spins, and braiding statistics. The method converts the identification of topological orders into computational tasks, including Gaussian elimination, the Hermite normal form, and the Smith normal form of truncated Laurent polynomials. Furthermore, the algorithm provides a systematic approach for studying quantum error-correcting codes. We apply it to various codes, such as self-dual CSS quantum codes modified from the two-dimensional honeycomb color code and non-CSS quantum codes that contain the double semion topological order or the six-semion topological order. Published by the American Physical Society 2024

Physics

Building Performance Standards and Energy Code Alignment - Technical Brief

Building energy codes focus on building design, construction and renovation and have significantly increased building efficiency since the first national energy code was published in 1975. Most jurisdictions have energy codes based on ANSI/ASHRAE/IES Standard 90.1 (hereto referred to as Standard 90.1) and the International Energy Conservation Code (IECC). Compliance options available in these model energy codes include a prescriptive path, whole building performance paths – including IECC Total Building Performance (TBP), Standard 90.1 Energy Cost Budget (ECB) method and Performance Rating Method (PRM) – and system performance paths for envelope and heating, ventilation, and air-conditioning systems. Building performance standard (BPS) policies are an emerging policy tool used by jurisdictions to reduce the operational energy use or greenhouse gas (GHG) emissions of the existing commercial building stock. BPS policies vary widely between jurisdictions and are tailored to each location’s climate and energy goals. Intuitively, projects that met a recent edition of the energy code should comply with the BPS targets. However, some new buildings may struggle with meeting the BPS for the following reasons: 1. Energy codes focus on the design of the building and its projected ability to perform efficiently, while BPS compliance is dependent on the actual ongoing performance of the building, considering variables like occupancy, operation, and maintenance. 2. There are significant differences in the methodologies used to determine BPS compliance versus code compliance, including how each handles compliance metrics, handling of building amenities, and renewable energy generation. 3. The prescriptive compliance path in the energy code is based on performance of individual building components, as opposed to the performance compliance path which accounts for holistic building design strategies and interdependent building systems. This can result in a significant variability in post-occupancy performance for buildings built using the prescriptive path. Designs on the lower end of the permitted efficiency range may struggle with meeting the BPS.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI

Hierarchical memories: Simulating quantum LDPC codes with local gates

Constant-rate low-density parity-check (LDPC) codes are promising candidates for constructing efficient fault-tolerant quantum memories. However, if physical gates are subject to geometric-locality constraints, it becomes challenging to realize these codes. In this paper, we construct a new family of [[N,K,D]] codes, referred to as hierarchical codes, that encode a number of logical qubits K=Ω(N/log(N) 2 ). The N th element of this code family is obtained by concatenating a constant-rate quantum LDPC code with a surface code; nearest-neighbor gates in two dimensions are sufficient to implement the corresponding syndrome-extraction circuit and achieve a threshold. Below threshold the logical failure rate vanishes superpolynomially as a function of the distance D(N). We present a bilayer architecture for implementing the syndrome-extraction circuit, and estimate the logical failure rate for this architecture. Under conservative assumptions, we find that the hierarchical code outperforms the basic encoding where all logical qubits are encoded in the surface code.

Pattison, Christopher A. [California Institute of

Diffusion Codes: Self-Correction from Small(er)-Set Expansion with Tunable Non-locality

Optimal constructions of classical LDPC codes can be obtained by choosing the Tanner graph uniformly at random among biregular graphs. We introduce a class of codes that we call ``diffusion codes'', defined by placing each edge connecting bits and checks on some graph, and acting on that graph with a random SWAP network. By tuning the depth of the SWAP network, we can tune a tradeoff between the amount of randomness -- and hence the optimality of code parameters -- and locality with respect to the underlying graph. For diffusion codes defined on the cycle graph, if the SWAP network has depth $\sim Tn$ with $T> n^{2β}$ for arbitrary $β>0$, then we prove that almost surely the Tanner graph is a lossless ``smaller set'' vertex expander for small sets up size $δ\sim \sqrt T \sim n^β$, with bounded bit and check degree. At the same time, the geometric size of the largest stabilizer is bounded by $\sqrt T$ in graph distance. We argue, based on physical intuition, that this result should hold more generally on arbitrary graphs. By taking hypergraph products of these classical codes we obtain quantum LDPC codes defined on the torus with smaller-set boundary and co-boundary expansion and the same expansion/locality tradeoffs as for the classical codes. These codes are self-correcting and admit single-shot decoding, while having the geometric size of the stabilizer growing as an arbitrarily small power law. Our proof technique establishes mixing of a random SWAP network on small subsystems at times scaling with only the subsystem size, which may be of independent interest.

Combinatorics (math.CO)

The effects of receiver tracking phase error on the performance of the concatenated Reed-Solomon Viterbi channel coding system

In connection with attempts to achieve very low error probabilities, Odenwalder (1970) proposed a concatenated coding system using the Viterbi-decoded convolutional codes as the inner code and Reed-Solomon (RS) codes as the outer code. Analytical and experimental results are presented concerning the effects of the receiver tracking phase error on the performance of the concatenated RS/Viterbi channel coding system. On the basis of these results it is concluded that certain problems regarding communication operations on deep-space missions can be alleviated by employing the RS/Viterbi coding system. In one-way communication, an employment of RS/Viterbi coding will also provide greater data protection than the Viterbi-decoded convolutional-only coding system.

Liu, K. Y.

Rate 3/4 16-PSK phase codes

An investigation is carried out of convolutional-coding coupled with 16-PSK modulation for bandwidth efficient transmission. Small memory codes (rate three-fourths) are found that are optimum in the free-distance sense on the Gaussian channel. These codes furnish up to 4.8 dB of coding gain with 32 states over uncoded 8-PSK, a scheme having the same spectral efficiency as the codes described. The performance is compared with the earlier findings of Ungerboeck (1976, 1982) and certain recent results on R = 2/3 coded 8-PSK. It is shown that with 4 decoder states the coding gain is 3.5 dB and with 32 states it is 4.8 dB. What is more, the codes compare favorably with coded 16-QASK when envelope variations and peak energy constraints are considered.

Wilson, S. G.

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.

The undetected error probability for shortened hamming codes

Hamming or shortened Hamming codes are widely used for error detection in data communications. For example, the CCITT (International Telegraph and Telephone Consultative Committee) recommendation X.25 for packet-switched data networks adopts a distance-4 cyclic Hamming code with 16 parity-check bits for error detection. The natural length of this code is n = 2(15)-1 = 32,767. In practice the length of a data packet is no more than a few thousand bits which is much shorter than the natural length of the code. Consequently, a shortened version of thecode is used. Often the length of a data packet varies, say from a few hundred bits to a few thousand bits, hence the code must be shortened by various degrees. Shortening affects the performance of the code. The error-detection performance of shortened Hamming codes, particularly the codes obtained from the distance-4 Hamming codes adopted by CCITT recommendation X.25, is investigated. A method for computing the probability of an undetected error is presented.

Costello, D. J., Jr.