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All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

Bilayer Protograph Codes for Half-Duplex Relay Channels

Direct to Earth return links are limited by the size and power of lander devices. A standard alternative is provided by a two-hops return link: a proximity link (from lander to orbiter relay) and a deep-space link (from orbiter relay to Earth). Although direct to Earth return links are limited by the size and power of lander devices, using an additional link and a proposed coding for relay channels, one can obtain a more reliable signal. Although significant progress has been made in the relay coding problem, existing codes must be painstakingly optimized to match to a single set of channel conditions, many of them do not offer easy encoding, and most of them do not have structured design. A high-performing LDPC (low-density parity-check) code for the relay channel addresses simultaneously two important issues: a code structure that allows low encoding complexity, and a flexible rate-compatible code that allows matching to various channel conditions. Most of the previous high-performance LDPC codes for the relay channel are tightly optimized for a given channel quality, and are not easily adapted without extensive re-optimization for various channel conditions. This code for the relay channel combines structured design and easy encoding with rate compatibility to allow adaptation to the three links involved in the relay channel, and furthermore offers very good performance. The proposed code is constructed by synthesizing a bilayer structure with a pro to graph. In addition to the contribution to relay encoding, an improved family of protograph codes was produced for the point-to-point AWGN (additive white Gaussian noise) channel whose high-rate members enjoy thresholds that are within 0.07 dB of capacity. These LDPC relay codes address three important issues in an integrative manner: low encoding complexity, modular structure allowing for easy design, and rate compatibility so that the code can be easily matched to a variety of channel conditions without extensive re-optimization. The main problem of half-duplex relay coding can be reduced to the simultaneous design of two codes at two rates and two SNRs (signal-to-noise ratios), such that one is a subset of the other. This problem can be addressed by forceful optimization, but a clever method of addressing this problem is via the bilayer lengthened (BL) LDPC structure. This method uses a bilayer Tanner graph to make the two codes while using a concept of "parity forwarding" with subsequent successive decoding that removes the need to directly address the issue of uneven SNRs among the symbols of a given codeword. This method is attractive in that it addresses some of the main issues in the design of relay codes, but it does not by itself give rise to highly structured codes with simple encoding, nor does it give rate-compatible codes. The main contribution of this work is to construct a class of codes that simultaneously possess a bilayer parity- forwarding mechanism, while also benefiting from the properties of protograph codes having an easy encoding, a modular design, and being a rate-compatible code.

Divsalar, Dariush↗
DOE OSTI2024

Impacts of Model Building Energy Codes

The Department of Energy (DOE) Building Energy Codes Program (BECP) periodically evaluates national and state-level impacts associated with energy codes in residential and commercial buildings. Pacific Northwest National Laboratory (PNNL), funded by DOE, conducted an assessment of the prospective impacts of national model building energy codes from 2010 through 2040. A previous PNNL study evaluated the impact of the Building Energy Codes Program. A 2016 study looked more broadly at overall code impacts and this report describes the methodology used for the assessment and presents the impacts in terms of energy savings, consumer cost savings, and reduced emissions at the state level and at aggregated levels. In 2021, DOE conducted an interim and limited update to its 2016 study to evaluate potential building code updates using the 2016 methodology. That interim update includes estimated savings resulting from updates to the model energy codes, including the ANSI/ASHRAE/IES Standard 90.1-2016 (ASHRAE 90.1-2016) and 2019 editions, as well as the 2018 and 2021 International Energy Conservation Code (IECC). In 2023, DOE developed a fully updated report that includes code updates (ASHRAE 90.1-2019 and 2021 IECC), as well as additional enhancements and updates, including updated energy prices, annual floorspace additions, state code adoption dates, and emission factors, among others. This current version is another fully updated report that includes code updates (ASHRAE 90.1-2022 and 2024 IECC), as well as additional enhancements and updates, including updated energy prices, state code adoption dates, emission factors, and renewable energy contribution among others. Energy codes follow a three-phase cycle that starts with the development of a new model code, proceeds with the adoption of the new code by states and local jurisdictions, and finishes when the new code is implemented and builders, architects, and engineers are required to comply with the new provisions. The development of new model code editions creates the potential for increased energy savings. After a new model code is adopted, potential savings are realized in the field when new buildings (or additions and alterations) are constructed to comply with the new code. The contributions of all three phases are crucial to the overall impact of codes and are considered in this assessment. Figure ES.1 schematically describes the analysis framework. Energy savings are expressed in terms of energy use intensity (EUI) in the figure.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

An Energy Codes Gap Analysis Field Study in the Southwest (Final Technical Report)

The primary goal of the “An Energy Codes Gap Analysis Field Study in the Southwest” project was to improve housing through strengthened building energy code implementation in two states, Colorado and Nevada, leading to greater energy and utility bill savings for households. Colorado is a home rule state. Nevada adopts a statewide code, but cities and counties must also adopt the code, making the state function like a home rule state. To broaden the impact of the project, an additional goal was to share and amplify project experiences, findings, and lessons that can be applied in other states. To achieve these goals, the project’s key objectives were to examine how residential energy codes are implemented in partner states; to use these findings to strengthen codes implementation through enhanced education, training, and outreach; and to enhance energy code technical assistance capabilities in the two partner states. In both partner states, the project led to the creation of a quantitative baseline understanding of compliance with high-impact energy code requirements, such as foundation, wall, and ceiling R-value; window U-factor and SHGC; envelope air tightness; duct tightness; and high-efficiency lighting. It then applied this baseline information to directly inform training in geographic areas with high levels of building and construction activity. The project has placed Colorado and Nevada among 23 states across the country that have conducted a single-family residential field study based on the established U.S. Department of Energy (DOE) methodology since 2014. It has also helped each State Energy Office test models for partnership- and relationship-building among government agencies and key stakeholder groups, including the State Energy Office and relevant code administration and professional licensing agencies, building officials, designers, builders, trades and utilities. At the national level, the project helped educate and inform State and Territory Energy Offices on a replicable methodology to assess energy code construction practices, effective stakeholder engagement strategies, and tailored energy code education and training. These findings are particularly pertinent for home-rule states, such as Colorado and Nevada, which rely on local government awareness and action to advance and implement building energy codes. By raising awareness of code adoption and compliance, this project has helped to equip each partner state with data on code compliance, strategies, education, and partnership models to advance building energy codes. This in turn will have an important impact on new construction practices in Colorado and Nevada, leading to more energy efficient and affordable housing. Currently, more than 62 percent of Colorado’s population lives in one of the 55 jurisdictions that have adopted the 2021 IECC to date, while nearly 95 percent of the state's population lives in one of the 208 jurisdictions that have adopted a code at 2015 IECC levels or higher. In Nevada, the 2018 IECC was adopted by the Governor’s Office of Energy in July 2018. By July 2020, 47 percent of the adopted energy code in the state was 2018 IECC which covers 96.5 percent of Nevada’s population. The training materials funded by this project focus on the 2021 IECC and will continue to be relevant in the two states as additional jurisdictions update their building energy codes.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Engineering 3D Floquet Codes by Rewinding

Floquet codes are a novel class of quantum error-correcting codes with dynamically generated logical qubits arising from a periodic schedule of noncommuting measurements. We utilize the interpretation of measurements in terms of condensation of topological excitations and the rewinding of measurement sequences to engineer new examples of Floquet codes. In particular, rewinding is advantageous for obtaining a desired set of instantaneous stabilizer groups on both toric and planar layouts. Our first example is a Floquet code with instantaneous stabilizer codes that have the same topological order as the three-dimensional (3D) toric code(s). This Floquet code also exhibits a splitting of the topological order of the 3D toric code under the associated sequence of measurements, i.e., an instantaneous stabilizer group of a single copy of the 3D toric code in one round transforms into an instantaneous stabilizer group of two copies of the 3D toric code up to nonlocal stabilizers in the following round. We further construct boundaries for this 3D code and argue that stacking it with two copies of the 3D subsystem toric code allows for a transversal implementation of the logical non-Clifford controlled-controlled- Z gate. We also show that the coupled-layer construction of the X-cube Floquet code can be modified by a rewinding schedule such that each of the instantaneous stabilizer codes is finite depth equivalent to the X-cube model up to toric codes; the X-cube Floquet code exhibits a splitting of the X-cube model into a copy of the X-cube model and toric codes under the measurement sequence. Our final 3D example is a generalization of the 2D Floquet toric code on the honeycomb lattice to three dimensions, which has instantaneous stabilizer codes with the same topological order as the 3D fermionic toric code. Published by the American Physical Society2024

Physics↗
NASA NTRS1992

Bandwidth efficient coding for satellite communications

An error control coding scheme was devised to achieve large coding gain and high reliability by using coded modulation with reduced decoding complexity. To achieve a 3 to 5 dB coding gain and moderate reliability, the decoding complexity is quite modest. In fact, to achieve a 3 dB coding gain, the decoding complexity is quite simple, no matter whether trellis coded modulation or block coded modulation is used. However, to achieve coding gains exceeding 5 dB, the decoding complexity increases drastically, and the implementation of the decoder becomes very expensive and unpractical. The use is proposed of coded modulation in conjunction with concatenated (or cascaded) coding. A good short bandwidth efficient modulation code is used as the inner code and relatively powerful Reed-Solomon code is used as the outer code. With properly chosen inner and outer codes, a concatenated coded modulation scheme not only can achieve large coding gains and high reliability with good bandwidth efficiency but also can be practically implemented. This combination of coded modulation and concatenated coding really offers a way of achieving the best of three worlds, reliability and coding gain, bandwidth efficiency, and decoding complexity.

Lin, Shu↗
NASA NTRS2010

Optimal Codes for the Burst Erasure Channel

Deep space communications over noisy channels lead to certain packets that are not decodable. These packets leave gaps, or bursts of erasures, in the data stream. Burst erasure correcting codes overcome this problem. These are forward erasure correcting codes that allow one to recover the missing gaps of data. Much of the recent work on this topic concentrated on Low-Density Parity-Check (LDPC) codes. These are more complicated to encode and decode than Single Parity Check (SPC) codes or Reed-Solomon (RS) codes, and so far have not been able to achieve the theoretical limit for burst erasure protection. A block interleaved maximum distance separable (MDS) code (e.g., an SPC or RS code) offers near-optimal burst erasure protection, in the sense that no other scheme of equal total transmission length and code rate could improve the guaranteed correctible burst erasure length by more than one symbol. The optimality does not depend on the length of the code, i.e., a short MDS code block interleaved to a given length would perform as well as a longer MDS code interleaved to the same overall length. As a result, this approach offers lower decoding complexity with better burst erasure protection compared to other recent designs for the burst erasure channel (e.g., LDPC codes). A limitation of the design is its lack of robustness to channels that have impairments other than burst erasures (e.g., additive white Gaussian noise), making its application best suited for correcting data erasures in layers above the physical layer. The efficiency of a burst erasure code is the length of its burst erasure correction capability divided by the theoretical upper limit on this length. The inefficiency is one minus the efficiency. The illustration compares the inefficiency of interleaved RS codes to Quasi-Cyclic (QC) LDPC codes, Euclidean Geometry (EG) LDPC codes, extended Irregular Repeat Accumulate (eIRA) codes, array codes, and random LDPC codes previously proposed for burst erasure protection. As can be seen, the simple interleaved RS codes have substantially lower inefficiency over a wide range of transmission lengths.

Hamkins, Jon↗
NASA NTRS1993

Box codes of lengths 48 and 72

A self-dual code length 48, dimension 24, with Hamming distance essentially equal to 12 is constructed here. There are only six code words of weight eight. All the other code words have weights that are multiples of four and have a minimum weight equal to 12. This code may be encoded systematically and arises from a strict binary representation of the (8,4;5) Reed-Solomon (RS) code over GF (64). The code may be considered as six interrelated (8,7;2) codes. The Mattson-Solomon representation of the cyclic decomposition of these codes and their parity sums are used to detect an odd number of errors in any of the six codes. These may then be used in a correction algorithm for hard or soft decision decoding. A (72,36;15) box code was constructed from a (63,35;8) cyclic code. The theoretical justification is presented herein. A second (72,36;15) code is constructed from an inner (63,27;16) Bose Chaudhuri Hocquenghem (BCH) code and expanded to length 72 using box code algorithms for extension. This code was simulated and verified to have a minimum distance of 15 with even weight words congruent to zero modulo four. The decoding for hard and soft decision is still more complex than the first code constructed above. Finally, an (8,4;5) RS code over GF (512) in the binary representation of the (72,36;15) box code gives rise to a (72,36;16*) code with nine words of weight eight, and all the rest have weights greater than or equal to 16.

Solomon, G.↗
NASA NTRS2009

Constructing LDPC Codes from Loop-Free Encoding Modules

A method of constructing certain low-density parity-check (LDPC) codes by use of relatively simple loop-free coding modules has been developed. The subclasses of LDPC codes to which the method applies includes accumulate-repeat-accumulate (ARA) codes, accumulate-repeat-check-accumulate codes, and the codes described in Accumulate-Repeat-Accumulate-Accumulate Codes (NPO-41305), NASA Tech Briefs, Vol. 31, No. 9 (September 2007), page 90. All of the affected codes can be characterized as serial/parallel (hybrid) concatenations of such relatively simple modules as accumulators, repetition codes, differentiators, and punctured single-parity check codes. These are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. These codes can also be characterized as hybrid turbolike codes that have projected graph or protograph representations (for example see figure); these characteristics make it possible to design high-speed iterative decoders that utilize belief-propagation algorithms. The present method comprises two related submethods for constructing LDPC codes from simple loop-free modules with circulant permutations. The first submethod is an iterative encoding method based on the erasure-decoding algorithm. The computations required by this method are well organized because they involve a parity-check matrix having a block-circulant structure. The second submethod involves the use of block-circulant generator matrices. The encoders of this method are very similar to those of recursive convolutional codes. Some encoders according to this second submethod have been implemented in a small field-programmable gate array that operates at a speed of 100 megasymbols per second. By use of density evolution (a computational- simulation technique for analyzing performances of LDPC codes), it has been shown through some examples that as the block size goes to infinity, low iterative decoding thresholds close to channel capacity limits can be achieved for the codes of the type in question having low maximum variable node degrees. The decoding thresholds in these examples are lower than those of the best-known unstructured irregular LDPC codes constrained to have the same maximum node degrees. Furthermore, the present method enables the construction of codes of any desired rate with thresholds that stay uniformly close to their respective channel capacity thresholds.

Divsalar, Dariush↗
NASA NTRS1990

New multi-level codes over GF(q)

Set partitioning to multi-dimensional signal spaces over GF(q), particularly GF sup q-1(q) and GF sup q (q), and show how to construct both multi-level block codes and multi-level trellis codes over GF(q). Two classes of multi-level (n, k, d) block codes over GF(q) with block length n, number of information symbols k, and minimum distance d sub min greater than or = d, are presented. These two classes of codes use Reed-Solomon codes as component codes. They can be easily decoded as block length q-1 Reed-Solomon codes or block length q or q + 1 extended Reed-Solomon codes using multi-stage decoding. Many of these codes have larger distances than comparable q-ary block codes, as component codes. Low rate q-ary convolutional codes, work error correcting convolutional codes, and binary-to-q-ary convolutional codes can also be used to construct multi-level trellis codes over GF(q) or binary-to-q-ary trellis codes, some of which have better performance than the above block codes. All of the new codes have simple decoding algorithms based on hard decision multi-stage decoding.

Wu, Jiantian↗
NASA NTRS1992

New multilevel codes over GF(q)

Set partitioning to multi-dimensional signal spaces over GF(q), particularly GF sup q-1(q) and GF sup q (q), and show how to construct both multi-level block codes and multi-level trellis codes over GF(q). Two classes of multi-level (n, k, d) block codes over GF(q) with block length n, number of information symbols k, and minimum distance d sub min greater than or = d, are presented. These two classes of codes use Reed-Solomon codes as component codes. They can be easily decoded as block length q-1 Reed-Solomon codes or block length q or q + 1 extended Reed-Solomon codes using multi-stage decoding. Many of these codes have larger distances than comparable q-ary block codes, as component codes. Low rate q-ary convolutional codes, work error correcting convolutional codes, and binary-to-q-ary convolutional codes can also be used to construct multi-level trellis codes over GF(q) or binary-to-q-ary trellis codes, some of which have better performance than the above block codes. All of the new codes have simple decoding algorithms based on hard decision multi-stage decoding.

Wu, Jiantian↗
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 NTRS1999

Investigation of Near Shannon Limit Coding Schemes

Turbo codes can deliver performance that is very close to the Shannon limit. This report investigates algorithms for convolutional turbo codes and block turbo codes. Both coding schemes can achieve performance near Shannon limit. The performance of the schemes is obtained using computer simulations. There are three sections in this report. First section is the introduction. The fundamental knowledge about coding, block coding and convolutional coding is discussed. In the second section, the basic concepts of convolutional turbo codes are introduced and the performance of turbo codes, especially high rate turbo codes, is provided from the simulation results. After introducing all the parameters that help turbo codes achieve such a good performance, it is concluded that output weight distribution should be the main consideration in designing turbo codes. Based on the output weight distribution, the performance bounds for turbo codes are given. Then, the relationships between the output weight distribution and the factors like generator polynomial, interleaver and puncturing pattern are examined. The criterion for the best selection of system components is provided. The puncturing pattern algorithm is discussed in detail. Different puncturing patterns are compared for each high rate. For most of the high rate codes, the puncturing pattern does not show any significant effect on the code performance if pseudo - random interleaver is used in the system. For some special rate codes with poor performance, an alternative puncturing algorithm is designed which restores their performance close to the Shannon limit. Finally, in section three, for iterative decoding of block codes, the method of building trellis for block codes, the structure of the iterative decoding system and the calculation of extrinsic values are discussed.

Kwatra, S. C.↗
NASA NTRS2004

Accumulate repeat accumulate codes

In this paper we propose an innovative channel coding scheme called 'Accumulate Repeat Accumulate codes' (ARA). This class of codes can be viewed as serial turbo-like codes, or as a subclass of Low Density Parity Check (LDPC) codes, thus belief propagation can be used for iterative decoding of ARA codes on a graph. The structure of encoder for this class can be viewed as precoded Repeat Accumulate (RA) code or as precoded Irregular Repeat Accumulate (IRA) code, where simply an accumulator is chosen as a precoder. Thus ARA codes have simple, and very fast encoder structure when they representing LDPC codes. Based on density evolution for LDPC codes through some examples for ARA codes, we show that for maximum variable node degree 5 a minimum bit SNR as low as 0.08 dB from channel capacity for rate 1/2 can be achieved as the block size goes to infinity. Thus based on fixed low maximum variable node degree, its threshold outperforms not only the RA and IRA codes but also the best known LDPC codes with the dame maximum node degree. Furthermore by puncturing the accumulators any desired high rate codes close to code rate 1 can be obtained with thresholds that stay close to the channel capacity thresholds uniformly. Iterative decoding simulation results are provided. The ARA codes also have projected graph or protograph representation that allows for high speed decoder implementation.

Low Density Parity Check codes (LDPC)↗
DOE OSTI2020

Local Truncation Error-Informed Code Verification

The method of manufactured solutions (MMS) has become increasingly popular in conducting code verification studies on predictive codes, such as nuclear power system codes and computational fluid dynamic codes. The reason for the popularity of this approach is that it can be used when an analytical solution is not available. Using MMS, code developers are able to verify that their code is free of coding errors that impact the observed order of accuracy. While MMS is still an excellent tool for code verification, it does not identify coding errors that are of the same order as the numerical method. This paper presents a method that combines MMS with modified equation analysis (MEA), which calculates the local truncation error (LTE) to identify coding error up to and including the order of the numerical method. This method is referred to as modified equation analysis methd of manufactured solutions (MEAMMS). MEAMMS is then applied to a custom-built code, which solves the shallow water equations, to test the performance of the code verification method. MEAMMS is able to detect all coding errors that impact the implementation of the numerical scheme. To show how MEAMMS is different than MMS, they are both applied to the same first-order numerical method test problem with a first-order coding error. When there are first-order coding errors, only MEAMMS is able to identify them. Finally, this shows that MEAMMS is able to identify a larger set of coding errors while still being able to identify the coding errors MMS is able to identify.

42 ENGINEERING↗
NASA NTRS2010

Performance Bounds on Two Concatenated, Interleaved Codes

A method has been developed of computing bounds on the performance of a code comprised of two linear binary codes generated by two encoders serially concatenated through an interleaver. Originally intended for use in evaluating the performances of some codes proposed for deep-space communication links, the method can also be used in evaluating the performances of short-block-length codes in other applications. The method applies, more specifically, to a communication system in which following processes take place: At the transmitter, the original binary information that one seeks to transmit is first processed by an encoder into an outer code (Co) characterized by, among other things, a pair of numbers (n,k), where n (n > k)is the total number of code bits associated with k information bits and n k bits are used for correcting or at least detecting errors. Next, the outer code is processed through either a block or a convolutional interleaver. In the block interleaver, the words of the outer code are processed in blocks of I words. In the convolutional interleaver, the interleaving operation is performed bit-wise in N rows with delays that are multiples of B bits. The output of the interleaver is processed through a second encoder to obtain an inner code (Ci) characterized by (ni,ki). The output of the inner code is transmitted over an additive-white-Gaussian- noise channel characterized by a symbol signal-to-noise ratio (SNR) Es/No and a bit SNR Eb/No. At the receiver, an inner decoder generates estimates of bits. Depending on whether a block or a convolutional interleaver is used at the transmitter, the sequence of estimated bits is processed through a block or a convolutional de-interleaver, respectively, to obtain estimates of code words. Then the estimates of the code words are processed through an outer decoder, which generates estimates of the original information along with flags indicating which estimates are presumed to be correct and which are found to be erroneous. From the perspective of the present method, the topic of major interest is the performance of the communication system as quantified in the word-error rate and the undetected-error rate as functions of the SNRs and the total latency of the interleaver and inner code. The method is embodied in equations that describe bounds on these functions. Throughout the derivation of the equations that embody the method, it is assumed that the decoder for the outer code corrects any error pattern of t or fewer errors, detects any error pattern of s or fewer errors, may detect some error patterns of more than s errors, and does not correct any patterns of more than t errors. Because a mathematically complete description of the equations that embody the method and of the derivation of the equations would greatly exceed the space available for this article, it must suffice to summarize by reporting that the derivation includes consideration of several complex issues, including relationships between latency and memory requirements for block and convolutional codes, burst error statistics, enumeration of error-event intersections, and effects of different interleaving depths. In a demonstration, the method was used to calculate bounds on the performances of several communication systems, each based on serial concatenation of a (63,56) expurgated Hamming code with a convolutional inner code through a convolutional interleaver. The bounds calculated by use of the method were compared with results of numerical simulations of performances of the systems to show the regions where the bounds are tight (see figure).

Moision, Bruce↗
DOE OSTI2018

Final Energy Savings Analysis of the Proposed NYStretch-Energy Code 2018

This study was conducted by the Pacific Northwest National Laboratory (PNNL) in support of the stretch energy code development led by the New York State Energy Research and Development Authority (NYSERDA). In 2017 NYSERDA developed its 2016 Stretch Code Supplement to the 2016 New York State Energy Conservation Construction Code (hereinafter referred to as “NYStretch-Energy”). NYStretch-Energy is intended as a model energy code for statewide voluntary adoption that anticipates other code advancements culminating in the goal of a statewide Net Zero Energy Code by 2028. Since then, NYSERDA continues to develop the NYStretch-Energy Code 2018 edition (NYSERDA 2018). To support the effort, PNNL conducted energy simulation analysis to quantify the energy savings of proposed commercial provisions of the NYStretch-Energy Code 2018 in New York. The focus of this project is to significantly improve the energy efficiency over existing commercial model energy codes. A key requirement of the proposed stretch code is that it be ‘adoptable’ as an energy code, meaning that it must align with current code scope and limitations, and primarily impact building components that are currently regulated by local building departments. It is largely limited to prescriptive measures, which are what most building departments and design projects are most familiar with. This report describes a set of energy-efficiency measures (EEMs) that demonstrate significant energy savings over ANSI/ASHRAE/IES Standard 90.1-2013 (ASHRAE 2013) across a broad range of commercial building types and all three climate zones in New York. In collaboration with New Building Institute, the EEMs were developed from national model codes and standards, high-performance building codes and standards, regional energy codes, and measures being proposed as part of the on-going code development process. PNNL analyzed these measures using whole building energy models for selected prototype commercial buildings and multifamily buildings representing buildings in New York.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS1994

Trace-shortened Reed-Solomon codes

Reed-Solomon (RS) codes have been part of standard NASA telecommunications systems for many years. RS codes are character-oriented error-correcting codes, and their principal use in space applications has been as outer codes in concatenated coding systems. However, for a given character size, say m bits, RS codes are limited to a length of, at most, 2(exp m). It is known in theory that longer character-oriented codes would be superior to RS codes in concatenation applications, but until recently no practical class of 'long' character-oriented codes had been discovered. In 1992, however, Solomon discovered an extensive class of such codes, which are now called trace-shortened Reed-Solomon (TSRS) codes. In this article, we will continue the study of TSRS codes. Our main result is a formula for the dimension of any TSRS code, as a function of its error-correcting power. Using this formula, we will give several examples of TSRS codes, some of which look very promising as candidate outer codes in high-performance coded telecommunications systems.

Mceliece, R. J.↗
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↗