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NASA NTRS2025

The Design of a Flexible, Interoperable Navigation Signal for Future Lunar Missions

The LunaNet Interoperability Specification (LNIS) is a set of standards currently under development by NASA, ESA, and JAXA, which define a common, interoperable set of services and interfaces for lunar communication and navigation. The LNIS includes specifications for the GNSS-like Augmented Forward Signal (AFS). The LANS (Lunar Augmented Navigation Service) will be comprised of Multiple LunaNet Service Provider (LNSP) nodes broadcasting the AFS, such as NASA’s LCRNS (Lunar Communications Relay and Navigation Systems), ESA’s Moonlight LCNS (Lunar Communication and Navigation Services) and the Japan LNSS (Lunar Navigation Satellite System). The LANS will provide a GNSS-like capability enabling orbiting and surface users in lunar space (such as Artemis) to estimate their position, velocity and time as described in Giordano et al., (2023). Initial capabilities will focus on providing service to the lunar South pole region. The specification of AFS defines two orthogonal signal components on a single carrier, with the in-phase component (AFS-I) being a lower-chip-rate data channel tailored for applications where low SWaP is critical (e.g., IoT devices or search and rescue), and the quadrature component (AFS-Q) being a high-chip-rate data-less pilot signal for high-precision, robust lunar navigation and positioning applications. An initial description of AFS was provided in the LNIS, (2023), and initial analysis results were shown in Dafesh, et al., (2024). In this work, we provide rationale for updates to the LNIS that define key aspects of the signal including the primary spreading code designs for the data and pilot channels, and a three-tiered overlay code approach for the pilot channel that provides flexible signal acquisition alternatives, rapid time dissemination and robust frame Sync. The paper also describes a robust data sync word that is designed to enable frame Sync. for low-SWaP receivers that only use the I channel, as well as a low-density parity check code (LDPC) data message encoding design and interleaving definition. The work further describes the impact of the updated AFS design in terms of improved acquisition performance, interference resistance, navigation message capabilities and rapid absolute time dissemination for users able to access clock and ephemeris data over an external network. The cross-correlation and synchronization performance of the AFS design is also compared to potential alternatives, further providing rationale for the final signal design configuration.

LunaNet↗
NASA NTRS2010

Short-Block Protograph-Based LDPC Codes

Short-block low-density parity-check (LDPC) codes of a special type are intended to be especially well suited for potential applications that include transmission of command and control data, cellular telephony, data communications in wireless local area networks, and satellite data communications. [In general, LDPC codes belong to a class of error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels.] The codes of the present special type exhibit low error floors, low bit and frame error rates, and low latency (in comparison with related prior codes). These codes also achieve low maximum rate of undetected errors over all signal-to-noise ratios, without requiring the use of cyclic redundancy checks, which would significantly increase the overhead for short blocks. These codes have protograph representations; this is advantageous in that, for reasons that exceed the scope of this article, the applicability of protograph representations makes it possible to design highspeed iterative decoders that utilize belief- propagation algorithms.

Divsalar, Dariush↗
NASA NTRS2009

Rate-Compatible LDPC Codes with Linear Minimum Distance

A recently developed method of constructing protograph-based low-density parity-check (LDPC) codes provides for low iterative decoding thresholds and minimum distances proportional to block sizes, and can be used for various code rates. A code constructed by this method can have either fixed input block size or fixed output block size and, in either case, provides rate compatibility. The method comprises two submethods: one for fixed input block size and one for fixed output block size. The first mentioned submethod is useful for applications in which there are requirements for rate-compatible codes that have fixed input block sizes. These are codes in which only the numbers of parity bits are allowed to vary. The fixed-output-blocksize submethod is useful for applications in which framing constraints are imposed on the physical layers of affected communication systems. An example of such a system is one that conforms to one of many new wireless-communication standards that involve the use of orthogonal frequency-division modulation

Divsalar, Dariush↗
DOE OSTI2025

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 ↗
NASA NTRS2009

LDPC Codes with Minimum Distance Proportional to Block Size

Low-density parity-check (LDPC) codes characterized by minimum Hamming distances proportional to block sizes have been demonstrated. Like the codes mentioned in the immediately preceding article, the present codes are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. The previously mentioned codes have low decoding thresholds and reasonably low error floors. However, the minimum Hamming distances of those codes do not grow linearly with code-block sizes. Codes that have this minimum-distance property exhibit very low error floors. Examples of such codes include regular LDPC codes with variable degrees of at least 3. Unfortunately, the decoding thresholds of regular LDPC codes are high. Hence, there is a need for LDPC codes characterized by both low decoding thresholds and, in order to obtain acceptably low error floors, minimum Hamming distances that are proportional to code-block sizes. The present codes were developed to satisfy this need. The minimum Hamming distances of the present codes have been shown, through consideration of ensemble-average weight enumerators, to be proportional to code block sizes. As in the cases of irregular ensembles, the properties of these codes are sensitive to the proportion of degree-2 variable nodes. A code having too few such nodes tends to have an iterative decoding threshold that is far from the capacity threshold. A code having too many such nodes tends not to exhibit a minimum distance that is proportional to block size. Results of computational simulations have shown that the decoding thresholds of codes of the present type are lower than those of regular LDPC codes. Included in the simulations were a few examples from a family of codes characterized by rates ranging from low to high and by thresholds that adhere closely to their respective channel capacity thresholds; the simulation results from these examples showed that the codes in question have low error floors as well as low decoding thresholds. As an example, the illustration shows the protograph (which represents the blueprint for overall construction) of one proposed code family for code rates greater than or equal to 1.2. Any size LDPC code can be obtained by copying the protograph structure N times, then permuting the edges. The illustration also provides Field Programmable Gate Array (FPGA) hardware performance simulations for this code family. In addition, the illustration provides minimum signal-to-noise ratios (Eb/No) in decibels (decoding thresholds) to achieve zero error rates as the code block size goes to infinity for various code rates. In comparison with the codes mentioned in the preceding article, these codes have slightly higher decoding thresholds.

Divsalar, Dariush↗
NASA NTRS2014

Rate-Compatible Protograph LDPC Codes

Digital communication coding methods resulting in rate-compatible low density parity-check (LDPC) codes built from protographs. Described digital coding methods start with a desired code rate and a selection of the numbers of variable nodes and check nodes to be used in the protograph. Constraints are set to satisfy a linear minimum distance growth property for the protograph. All possible edges in the graph are searched for the minimum iterative decoding threshold and the protograph with the lowest iterative decoding threshold is selected. Protographs designed in this manner are used in decode and forward relay channels.

Nguyen, Thuy V.↗
NASA NTRS2009

Pilotless Frame Synchronization Using LDPC Code Constraints

A method of pilotless frame synchronization has been devised for low- density parity-check (LDPC) codes. In pilotless frame synchronization , there are no pilot symbols; instead, the offset is estimated by ex ploiting selected aspects of the structure of the code. The advantag e of pilotless frame synchronization is that the bandwidth of the sig nal is reduced by an amount associated with elimination of the pilot symbols. The disadvantage is an increase in the amount of receiver data processing needed for frame synchronization.

Jones, Christopher↗
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 NTRS2012

Rate-compatible protograph LDPC code families with linear minimum distance

Digital communication coding methods are shown, which generate certain types of low-density parity-check (LDPC) codes built from protographs. A first method creates protographs having the linear minimum distance property and comprising at least one variable node with degree less than 3. A second method creates families of protographs of different rates, all structurally identical for all rates except for a rate-dependent designation of certain variable nodes as transmitted or non-transmitted. A third method creates families of protographs of different rates, all structurally identical for all rates except for a rate-dependent designation of the status of certain variable nodes as non-transmitted or set to zero. LDPC codes built from the protographs created by these methods can simultaneously have low error floors and low iterative decoding thresholds.

Divsalar, Dariush↗
NASA NTRS2012

Measurement Techniques for Clock Jitter

NASA is in the process of modernizing its communications infrastructure to accompany the development of a Crew Exploration Vehicle (CEV) to replace the shuttle. With this effort comes the opportunity to infuse more advanced coded modulation techniques, including low-density parity-check (LDPC) codes that offer greater coding gains than the current capability. However, in order to take full advantage of these codes, the ground segment receiver synchronization loops must be able to operate at a lower signal-to-noise ratio (SNR) than supported by equipment currently in use.

Lansdowne, Chatwin↗
NASA NTRS2012

Rate-compatible protograph LDPC code families with linear minimum distance

Digital communication coding methods are shown, which generate certain types of low-density parity-check (LDPC) codes built from protographs. A first method creates protographs having the linear minimum distance property and comprising at least one variable node with degree less than 3. A second method creates families of protographs of different rates, all having the linear minimum distance property, and structurally identical for all rates except for a rate-dependent designation of certain variable nodes as transmitted or non-transmitted. A third method creates families of protographs of different rates, all having the linear minimum distance property, and structurally identical for all rates except for a rate-dependent designation of the status of certain variable nodes as non-transmitted or set to zero. LDPC codes built from the protographs created by these methods can simultaneously have low error floors and low iterative decoding thresholds, and families of such codes of different rates can be decoded efficiently using a common decoding architecture.

Divsalar, Dariush↗
NASA NTRS2007

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↗
NASA NTRS2012

Replacing the CCSDS Telecommand Protocol with the Next Generation Uplink (NGU)

The current CCSDS Telecommand (TC) Recommendations 1-3 have essentially been in use since the early 1960s. The purpose of this paper is to propose a successor protocol to TC. The current CCSDS recommendations can only accommodate telecommand rates up to approximately 1 mbit/s. However today's spacecraft are storehouses for software including software for Field Programmable Gate Arrays (FPGA) which are rapidly replacing unique hardware systems. Changes to flight software occasionally require uplinks to deliver very large volumes of data. In the opposite direction, high rate downlink missions that use acknowledged CCSDS File Delivery Protocol (CFDP)4 will increase the uplink data rate requirements. It is calculated that a 5 mbits/s downlink could saturate a 4 kbits/s uplink with CFDP downlink responses: negative acknowledgements (NAKs), FINISHs, End-of-File (EOF), Acknowledgements (ACKs). Moreover, it is anticipated that uplink rates of 10 to 20 mbits/s will be required to support manned missions. The current TC recommendations cannot meet these new demands. Specifically, they are very tightly coupled to the Bose-Chaudhuri-Hocquenghem (BCH) code in Ref. 2. This protocol requires that an uncorrectable BCH codeword delimit the TC frame and terminate the randomization process. This method greatly limits telecom performance since only the BCH code can support the protocol. More modern techniques such as the CCSDS Low Density Parity Check (LDPC)5 codes can provide a minimum performance gain of up to 6 times higher command data rates as long as sufficient power is available in the data. This paper will describe the proposed protocol format, trade-offs, and advantages offered, along with a discussion of how reliable communications takes place at higher nominal rates.

Consultative Committee for Space Data Systems (CCS↗
NASA NTRS2008

Using LDPC Code Constraints to Aid Recovery of Symbol Timing

A method of utilizing information available in the constraints imposed by a low-density parity-check (LDPC) code has been proposed as a means of aiding the recovery of symbol timing in the reception of a binary-phase-shift-keying (BPSK) signal representing such a code in the presence of noise, timing error, and/or Doppler shift between the transmitter and the receiver. This method and the receiver architecture in which it would be implemented belong to a class of timing-recovery methods and corresponding receiver architectures characterized as pilotless in that they do not require transmission and reception of pilot signals. Acquisition and tracking of a signal of the type described above have traditionally been performed upstream of, and independently of, decoding and have typically involved utilization of a phase-locked loop (PLL). However, the LDPC decoding process, which is iterative, provides information that can be fed back to the timing-recovery receiver circuits to improve performance significantly over that attainable in the absence of such feedback. Prior methods of coupling LDPC decoding with timing recovery had focused on the use of output code words produced as the iterations progress. In contrast, in the present method, one exploits the information available from the metrics computed for the constraint nodes of an LDPC code during the decoding process. In addition, the method involves the use of a waveform model that captures, better than do the waveform models of the prior methods, distortions introduced by receiver timing errors and transmitter/ receiver motions. An LDPC code is commonly represented by use of a bipartite graph containing two sets of nodes. In the graph corresponding to an (n,k) code, the n variable nodes correspond to the code word symbols and the n-k constraint nodes represent the constraints that the code places on the variable nodes in order for them to form a valid code word. The decoding procedure involves iterative computation of values associated with these nodes. A constraint node represents a parity-check equation using a set of variable nodes as inputs. A valid decoded code word is obtained if all parity-check equations are satisfied. After each iteration, the metrics associated with each constraint node can be evaluated to determine the status of the associated parity check. Heretofore, normally, these metrics would be utilized only within the LDPC decoding process to assess whether or not variable nodes had converged to a codeword. In the present method, it is recognized that these metrics can be used to determine accuracy of the timing estimates used in acquiring the sampled data that constitute the input to the LDPC decoder. In fact, the number of constraints that are satisfied exhibits a peak near the optimal timing estimate. Coarse timing estimation (or first-stage estimation as described below) is found via a parametric search for this peak. The present method calls for a two-stage receiver architecture illustrated in the figure. The first stage would correct large time delays and frequency offsets; the second stage would track random walks and correct residual time and frequency offsets. In the first stage, constraint-node feedback from the LDPC decoder would be employed in a search algorithm in which the searches would be performed in successively narrower windows to find the correct time delay and/or frequency offset. The second stage would include a conventional first-order PLL with a decision-aided timing-error detector that would utilize, as its decision aid, decoded symbols from the LDPC decoder. The method has been tested by means of computational simulations in cases involving various timing and frequency errors. The results of the simulations ined in the ideal case of perfect timing in the receiver.

Jones, Christopher↗
NASA NTRS2009

Bounded-Angle Iterative Decoding of LDPC Codes

Bounded-angle iterative decoding is a modified version of conventional iterative decoding, conceived as a means of reducing undetected-error rates for short low-density parity-check (LDPC) codes. For a given code, bounded-angle iterative decoding can be implemented by means of a simple modification of the decoder algorithm, without redesigning the code. Bounded-angle iterative decoding is based on a representation of received words and code words as vectors in an n-dimensional Euclidean space (where n is an integer).

Dolinar, Samuel↗
NASA NTRS2009

Structured Low-Density Parity-Check Codes with Bandwidth Efficient Modulation

In this work, we study the performance of structured Low-Density Parity-Check (LDPC) Codes together with bandwidth efficient modulations. We consider protograph-based LDPC codes that facilitate high-speed hardware implementations and have minimum distances that grow linearly with block sizes. We cover various higher- order modulations such as 8-PSK, 16-APSK, and 16-QAM. During demodulation, a demapper transforms the received in-phase and quadrature samples into reliability information that feeds the binary LDPC decoder. We will compare various low-complexity demappers and provide simulation results for assorted coded-modulation combinations on the additive white Gaussian noise and independent Rayleigh fading channels.

Crew Exploration Vehicle (CEV)↗
NASA NTRS2011

Coded Modulation in C and MATLAB

This software, written separately in C and MATLAB as stand-alone packages with equivalent functionality, implements encoders and decoders for a set of nine error-correcting codes and modulators and demodulators for five modulation types. The software can be used as a single program to simulate the performance of such coded modulation. The error-correcting codes implemented are the nine accumulate repeat-4 jagged accumulate (AR4JA) low-density parity-check (LDPC) codes, which have been approved for international standardization by the Consultative Committee for Space Data Systems, and which are scheduled to fly on a series of NASA missions in the Constellation Program. The software implements the encoder and decoder functions, and contains compressed versions of generator and parity-check matrices used in these operations.

Hamkins, Jon↗
NASA NTRS2019

Polar Coding For Forward Error Correction In Space Communications With LDPC Comparisons

With the surging development of optical telecommunicationsfor space applications, the importance of errorcorrection has become more apparent than ever. Specifically,the exploration of forward error correction code (FEC) methodologieswill be instrumental in developing the standards foroptical communications in space. Despite the widespread useof low-density parity-check (LDPC) codes, alternate FEC codessuch as polar codes have shown immense promise in assistingspace communications error correction with their ability tobypass the error floors that plague LDPC codes. Extremelypromising techniques including cyclic redundancy checks (CRC),successive cancellation (SC), and successive cancellation lists(SCL) that assist polar coding in achieving the Shannon limitin a timely manner are evaluated. MATLAB simulations areconducted with AWGN and burst noise to test each technique'sability to handle noise typically encountered in space and eachtechnique's ability to correct unexpected errors. Results ofsimulations for different rates and message lengths are alsoreported to determine each technique's ability to handle largedata volumes and fix errors. Similar simulations are conductedfor LDPC codes with additional tests for convolutional and nointerleavers. Finally, a discussion regarding the future ability ofpolar codes to satisfy current missions in the place of, or inconjunction with, LDPC codes along with the merits of eachFEC technique's ability to process data efficiently and handledata while maintaining adequate performance will be provided.Preliminary recommendations will be made for each technique'seffectiveness for GEO related missions along with discussionsregarding each technique's ability to fit within the CCSDS standards for optical communications.

Polar Coding↗