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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Future capabilities for the Deep Space Network

This paper will look at three new capabilities that are in different stages of development. First, turbo decoding, which provides improved telemetry performance for data rates up to about 1 Mbps, will be discussed. Next, pseudo-noise ranging will be presented. Pseudo-noise ranging has several advantages over the current sequential ranging, anmely easier operations, improved performance, and the capability to be used in a regenerative implementation on a spacecraft. Finally, Low Density Parity Check decoding will be discussed. LDPC codes can provide performance that matches or slightly exceed turbo codes, but are designed for use in the 10 Mbps range.

turbo code↗
NASA NTRSDate not supplied

Improvements on Low-Density Parity-Check (LDPC) Codes and High-Performance Neuromorphic Engineering for Communication Systems

Belief propagation (BP) on LDPC codes is an iterative decoding algorithm that performs information transfer on the Tanner graph, which represents the code. In each iteration, the algorithm exchanges information (LLR) between variable nodes and check nodes through the edges of the graph. LLR values represent the probability that a given bit in a transmitted codeword equals 0 or 1, given a received word. In the hardware part, recent advancements in intelligent technologies, such as artificial intelligence, big data analytics, autonomous vehicles, and speech/image recognition, have heightened the demand for faster calculations and reduced energy consumption.

Danilo Barrionuevo↗
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)↗
NASA NTRS2004

Accumulate Repeat Accumulate Coded Modulation

In this paper we propose an innovative coded modulation scheme called 'Accumulate Repeat Accumulate Coded Modulation' (ARA coded modulation). This class of codes can be viewed as serial turbo-like codes, or as a subclass of Low Density Parity Check (LDPC) codes that are combined with high level modulation. Thus at the decoder belief propagation can be used for iterative decoding of ARA coded modulation on a graph, provided a demapper transforms the received in-phase and quadrature samples to reliability of the bits.

coded modulation↗
NASA NTRS2004

Accumulate-Repeat-Accumulate-Accumulate-Codes

Inspired by recently proposed Accumulate-Repeat-Accumulate (ARA) codes [15], in this paper we propose a channel coding scheme called Accumulate-Repeat-Accumulate-Accumulate (ARAA) codes. These codes can be seen as serial turbo-like codes or as a subclass of Low Density Parity Check (LDPC) codes, and they have a projected graph or protograph representation; this allows for a high-speed iterative decoder implementation using belief propagation. An ARAA code can be viewed as a precoded Repeat-and-Accumulate (RA) code with puncturing in concatenation with another accumulator, where simply an accumulator is chosen as the precoder; thus ARAA codes have a very fast encoder structure. Using density evolution on their associated protographs, we find examples of rate-lJ2 ARAA codes with maximum variable node degree 4 for which a minimum bit-SNR as low as 0.21 dB from the channel capacity limit can be achieved as the block size goes to infinity. Such a low threshold cannot be achieved by RA or Irregular RA (IRA) or unstructured irregular LDPC codes with the same constraint on the maximum variable node degree. Furthermore by puncturing the accumulators we can construct families of higher rate ARAA codes with thresholds that stay close to their respective channel capacity thresholds uniformly. Iterative decoding simulation results show comparable performance with the best-known LDPC codes but with very low error floor even at moderate block sizes.

density evolution↗
NASA NTRS2003

Upper bounds to error probabilities of coded systems beyond the cutoff rate

A family of upper bounds to error probabilities of coded systems was recently proposed by Divsalar. These bounds are valid for transmission over the additive white Gaussian noise channel, and require only the knowledge of the weight spectrum of the code words. After illustrating these bounds, we extend them to fading channels. Contrary to the union bound, our bounds maintain their effectiveness below the signal-to-noise ratio (SNR)at which the cutoff rate of the channel equals the rate of the code. Some applications are shown. First, we derive upper bounds to the minimum SNR necessary to achieve zero error probability as the code block length increases to infinity. Next, we use our bounds to predict the performance of turbo codes and low-density parity-check codes.

Biglieri, Ezio↗
DOE OSTI2025

Fault Tolerant Decoding of QLDPC-GKP Codes with Circuit Level Soft Information

Concatenated bosonic-stabilizer codes have recently gained prominence as promising candidates for achieving low-overhead fault-tolerant quantum computing in the long term. In such systems, analog information obtained from the syndrome measurements of an inner bosonic code is used to inform decoding for an outer code layer consisting of a discrete-variable stabilizer code such as a surface code. The use of Quantum Low-Density Parity Check (QLDPC) codes as an outer code is of particular interest due to the significantly higher encoding rates offered by these code families, leading to a further reduction in overhead for large-scale quantum computing. Recent works have investigated the performance of QLDPC-GKP codes in detail, and the use of analog information from the inner code significantly boosts decoder performance. However, the noise models assumed in these works are typically limited to depolarizing or phenomenological noise. In this paper, we investigate the performance of QLDPC-GKP concatenated codes under circuit-level noise, based on a model introduced by Noh et al. in the context of the surface-GKP code. To demonstrate the performance boost from analog information, we investigate three scenarios: (a) decoding without soft information, (b) decoding with precomputed error probabilities but without real-time soft information, and (c) decoding with real-time soft information obtained from round-to-round decoding of the inner GKP code. Results show minimal improvement between (a) and (b), but a significant boost in (c), indicating that real-time soft information is critical for concatenated decoding under circuit-level noise. We also study the effect of measurement schedules with varying depths and show that using a schedule with minimum depth is essential for obtaining reliable soft information from the inner code.

Borah, Shantom K. [Arizona U. (main)]↗
NASA NTRS2006

Protograph LDPC Codes for the Erasure Channel

This viewgraph presentation reviews the use of protograph Low Density Parity Check (LDPC) codes for erasure channels. A protograph is a Tanner graph with a relatively small number of nodes. A "copy-and-permute" operation can be applied to the protograph to obtain larger derived graphs of various sizes. For very high code rates and short block sizes, a low asymptotic threshold criterion is not the best approach to designing LDPC codes. Simple protographs with much regularity and low maximum node degrees appear to be the best choices Quantized-rateless protograph LDPC codes can be built by careful design of the protograph such that multiple puncturing patterns will still permit message passing decoding to proceed

long erasure codes↗
DOE OSTI2026

Efficient Routing of Quantum LDPC Codes on Programmable 2D Toric Architectures

Quantum low-density parity-check codes are promising candidates towards scalable fault-tolerant quantum computation. Among these, bivariate bicycle (BB) codes offer superior encoding rates and large code distance compared to surface codes. However, their requirement on long-range stabilizer measurements poses significant challenges for implementation on realistic hardware with limited connectivity, such as superconducting circuit platforms. In this work, we introduce a novel hardware-software co-design that leverages a programmable communication network architecture to address these limitations. Our approach utilizes a 2D toric network of oscillators as a flexible communication fabric linking qubits at each site. Such architecture significantly reduces the number of long-range couplers required from O ( n ) to O (√ n ). Dual-rail qubits, along with native gates including Swap-Wait-Swap gates and beamsplitter SWAPs, ensure that long-range two-qubit gates can be executed with high fidelity and low latency. To further enhance performance, our qubit layout and routing algorithm utilize symmetries of the codes and enable maximum parallelism for long-range two-qubit gates, maintaining a low syndrome extraction cycle duration and scalability over the code length. We perform circuit-level simulation with realistic noise modeling based on experimental hardware parameters, observing an logical error rate per logical qubit per cycle of 3.06% for [[18,4,4]] BB code, 2.6× less than the existing experimental result. These findings provide a practical roadmap and identify key technological advancements needed to achieve low-overhead fault-tolerant quantum computing at scale.

Liu, Kun [Yale Univ., New Haven, CT (United States↗
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↗
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↗
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 NTRSDate not supplied

Flexible Data and Frame Synchronization Structure for the LunaNet PNT Signal

A LunaNet Lunar Augmented Navigation Service (LANS) is being developed to enable a position, navigation, and timing service for future Lunar operations. The signal includes two components. An in-phase data channel signal is spread by a 1.023 MCPS ranging code that provides a high-rate data message at 250 bps and is encoded by a strong Low Density Parity Check (LDPC) code. A pilot channel with a 5.115 MCPS spreading code is also provided. The pilot code is configured with a secondary (overlay) code that does not currently provide absolute time or frame Synchronization as is the case for L1C. This work shows the advantage of implementing an overlay structure that provides absolute time for the LunaNet LANS signal structure known as the Augmented Forward Signal (AFS). The LunaNet AFS structure was developed to service two classes of user receivers. The first class is a low-complexity user receiver that only receives the 1.023 MCPS signal and does not use the 5.115 MCPS pilot channel. For this class of user, a data frame Sync word is needed. The second class of receiver is a high-end receiver that can processes both data and pilot channels to take advantage of the higher chip rate pilot channel for enhanced robustness and improved accuracy. In the current draft LunaNet LANS AFS design, these users must employ the frame Sync word in the data channel and obtain absolute time after decoding the AFS navigation message. The signal structure would greatly benefit from the addition of a pilot overlay structure that provides absolute time and robust frame Sync for high-end users as done for L1C. To provide a more robust and interoperable AFS structure, this work summarizes a study and recommends alternatives for a new overlay code on the pilot channel that provides absolute time and a Sync word approach on the data channel. The overlay code and Sync word are designed to allow for flexible and robust data synchronization for both low- complexity and high-end user receivers. The new overlay code structure permits frame synchronization performance that is as good as or better than the L1 C signal, while enabling a determination of absolute time upon frame Sync to aid high-end assisted LANS AFS user receivers at low signal to noise levels. We also present the design of rate-matched 5G new radio (5GNR) LDPC codes that fit within the current 6000-symbol frame size along with a time of interval (TOI) word, frame ID (FID) word, and the remaining LunaNet AFS data message blocks. The paper describes and demonstrates robust frame Synchronization performance of the overlay code and Synch word approaches. The results are described in terms of probability of missed detection and probability of false alarm for a correct frame Synchronization at low Eb/No levels expected for decoding the TOI word and LDPC encoded data. Advantages of the proposed data Synchronization structure will be described along with use cases for low-end and high-end receivers. Practical implementation considerations will also be described.

LunaNet↗
NASA NTRSDate not supplied

Flexible Data and Frame Synchronization Structure for the LunaNet PNT Signal

A LunaNet Lunar Augmented Navigation Service (LANS) is being developed to enable a position, navigation, and timing service for future Lunar operations [1]. The signal includes two components. An in-phase data channel signal is spread by a 1.023 MCPS ranging code that provides a high-rate data message at 250 bps and is encoded by a strong Low Density Parity Check (LDPC) code. A pilot channel with a 5.115 MCPS spreading code is also provided. The pilot code is configured with a secondary (overlay) code that does not currently provide absolute time or frame Synchronization as is the case for L1C [2] [3]. This work shows the advantage of implementing an overlay structure that provides absolute time for the LunaNet LANS signal structure known as the Augmented Forward Signal (AFS). The LunaNet AFS structure was developed to service two classes of user receivers. The first class is a low-complexity user receiver that only receives the 1.023 MCPS signal and does not use the 5.115 MCPS pilot channel. For this class of user, a data frame Sync word is needed. The second class of receiver is a high-end receiver that can processes both data and pilot channels to take advantage of the higher chip rate pilot channel for enhanced robustness and improved accuracy. In the current draft LunaNet LANS AFS design, these users must employ the frame Sync word in the data channel and obtain absolute time after decoding the AFS navigation message [2]. The signal structure would greatly benefit from the addition of a pilot overlay structure that provides absolute time and robust frame Sync for high-end users as done for L1C [3]. To provide a more robust and interoperable AFS structure, this work summarizes a study and recommends alternatives for a new overlay code on the pilot channel that provides absolute time and a Sync word approach on the data channel. The overlay code and Sync word are designed to allow for flexible and robust data synchronization for both low- complexity and high-end user receivers. The new overlay code structure permits frame synchronization performance that is as good as or better than the L1 C signal, while enabling a determination of absolute time upon frame Sync to aid high-end assisted LANS AFS user receivers at low signal to noise levels. We also present the design of rate-matched 5G new radio (5GNR) LDPC codes that fit within the current 6000-symbol frame size along with a time of interval (TOI) word, frame ID (FID) word, and the remaining LunaNet AFS data message blocks. The paper describes and demonstrates robust frame Synchronization performance of the overlay code and Synch word approaches. The results are described in terms of probability of missed detection and probability of false alarm for a correct frame Synchronization at low Eb/No levels expected for decoding the TOI word and LDPC encoded data. Advantages of the proposed data Synchronization structure will be described along with use cases for low-end and high-end receivers. Practical implementation considerations will also be described.

Philip Dafesh↗
NASA NTRS2008

Direct-detection Free-space Laser Transceiver Test-bed

NASA Goddard Space Flight Center is developing a direct-detection free-space laser communications transceiver test bed. The laser transmitter is a master-oscillator power amplifier (MOPA) configuration using a 1060 nm wavelength laser-diode with a two-stage multi-watt Ytterbium fiber amplifier. Dual Mach-Zehnder electro-optic modulators provide an extinction ratio greater than 40 dB. The MOPA design delivered 10-W average power with low-duty-cycle PPM waveforms and achieved 1.7 kW peak power. We use pulse-position modulation format with a pseudo-noise code header to assist clock recovery and frame boundary identification. We are examining the use of low-density-parity-check (LDPC) codes for forward error correction. Our receiver uses an InGaAsP 1 mm diameter photocathode hybrid photomultiplier tube (HPMT) cooled with a thermo-electric cooler. The HPMT has 25% single-photon detection efficiency at 1064 nm wavelength with a dark count rate of 60,000/s at -22 degrees Celsius and a single-photon impulse response of 0.9 ns. We report on progress toward demonstrating a combined laser communications and ranging field experiment.

Krainak, Michael A.↗
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↗