LDPC Research Articles

Near regular LDPC codes based on combinatorial designs

Some new approaches for constructing near regular binary low-density parity-check (LDPC) codes free of 4-cycles are proposed using dual of certain combinatorial designs which are [Formula: see text]-configurations. The present constructions further broaden the class of code lengths. The present constructions give higher code rates of near regular LDPC codes compared to the earlier codes with respect to same code length.

List-Based Optimization of Proximal Decoding for LDPC Codes

List-Based Optimization of Proximal Decoding for LDPC Codes

Improved rate-distance trade-offs for quantum codes with restricted connectivity

Abstract For quantum error-correcting codes to be realizable, it is important that the qubits subject to the code constraints exhibit some form of limited connectivity. The works of Bravyi and Terhal (2009 New J. Phys. 11 043029) (BT) and Bravyi et al (2010 Phys. Rev. Lett. 104 050503) (BPT) established that geometric locality constrains code properties—for instance [ [ n , k , d ] ] quantum codes defined by local checks on the D-dimensional lattice must obey k d 2 / ( D − 1 ) ⩽ O ( n ) . Baspin and Krishna (2022 Quantum 6 711) studied the more general question of how the connectivity graph associated with a quantum code constrains the code parameters. These trade-offs apply to a richer class of codes compared to the BPT and BT bounds, which only capture geometrically-local codes. We extend and improve this work, establishing a tighter dimension-distance trade-off as a function of the size of separators in the connectivity graph. We also obtain a distance bound that covers all stabilizer codes with a particular separation profile, rather than only LDPC codes.

Two-Phase Globally Coupled Low-Density Parity Check Decoding Aided with Early Termination and Forced Convergence.

To enhance the decoding efficiency of Globally Coupled (GC) LDPC codes, we incorporated Early Termination (ET) and Forced Convergence (FC) into the local/global two-phase decoding algorithm to expedite the decoding process. The two-phase decoding scheme integrates the ET technique to halt unnecessary iterations in the local decoding phase while employing the FC technique to accelerate convergence in the global phase decoding. The application of ET technology in the local decoding of GC-LDPC codes will not cause performance loss as in traditional block codes and will cause considerable complexity gains. For a longer code length and larger convergence differences between nodes' global codes, the FC technique operates more efficiently in global code than local code. Two variants are proposed for the ET scheme in the local decoding, namely ET-1 and ET-2. The initial variant, ET-1, predicts whether local decoding can be successful according to data characteristics and stop the local decoding iteration that is not expected to be successful in time. In the case of ET-2, the saved local iterations are transformed to global decoding equally. The results show that ET-1 saves considerable decoding time complexity and ET-2 improves the performance of the GC-LDPC code with the same decoding time complexity. The combined approach of ET-1 with FC reduces the decoding time complexity up to 42% at a low Signal Noise Rate region while maintaining its performance; ET-2-FC two-phase decoding saves approximately 25% decoding time complexity while improving the BER by about 0.18 dB and FER by about 0.23 dB.

Decoding LDPC Codes with a Regular Check Matrix Structure Using the Bit Flip Method

Problem statement: low-density LDPC codes have become very popular in modern communication systems, which make it possible to implement decoders for them in practice. In conditions of severe limitations of equipment performance, the task of searching and researching the characteristics of decoding algorithms for these codes is urgent. The aim of the work is to find a simplified algorithm for decoding LDPC codes and to study the noise immunity of the proposed algorithm. The methods used: to solve this problem computer simulation is used to compare the noise immunity of known decoding algorithms and the proposed algorithm. Scientific novelty: the noise immunity characteristics of the proposed Bit Flip algorithm for decoding LDPC code with a regular structure of the check matrix using gradient descent and the procedure for escaping the local minimum are investigated. Result: a specific variant of the Bit Flip algorithm for LDPC code with a regular structure check matrix using gradient descent and a procedure for escaping the local minimum is proposed. The results of computer simulation are presented. Theoretical significance: the characteristics of noise immunity for the proposed variant of the LDPC code decoding algorithm with a regular structure of the check matrix are investigated. Practical significance: when using the proposed LDPC code decoding algorithm in the receiver, it is possible to calculate the parameters of the communication system based on the available dependencies of the error coefficient on the signal-to-noise ratio.

Error rates of optically pre-amplified PPM wireless systems with coding and arbitrary optical filter response

We present novel results for the uncoded and coded bit-error probability (BEP) of optically pre-amplified pulse-position modulation (PPM) wireless systems. For uncoded systems, a novel analytic method for the evaluation of the BEP is derived. The method takes into account the non-ideal optical filter response and utilizes a finite Karhunen–Loève series expansion to calculate the BEP. Using the proposed approach, it is possible to accurately evaluate the PPM BEP for arbitrarily shaped filters where the well-established χ2 method only provides approximate results. Considering a Lorentzian filter response, the discrepancy between the two methods amounts to 0.5 dB in a variety of filter bandwidths and PPM modulation orders. The Lorentzian filter response was chosen as an illustrative practical example whose series can be calculated analytically. The proposed method is also valid for any type of optical filter for which the Karhunen–Loève series expansion can be calculated analytically or numerically. Due to the finite number of terms that are required irrespective of the signal energy level, the proposed method can also be applied without loss of accuracy to assess the system performance under the effects of turbulence and adverse weather conditions. For coded systems with Lorentzian filters, Monte-Carlo simulations are utilized to evaluate the BEP performance of the 5G LDPC codes, and it is demonstrated that they impart an energy gain up to 3.3 dB for 4–PPM and 2.3 dB for 16–PPM at a target BEP of 10−5. The optimal code rates are also discussed for several combinations of the optical filter bandwidth and PPM modulation order and it is shown that in almost all of the cases the optimal code rate is 11/13. Moreover, the sum-product and min-sum decoders perform within 0.1 dB from each other for the best code rates, which points towards the utilization of the min-sum decoder in all settings, since its operation does not require knowledge of the filter parameters. Finally, the comparison between the coded systems with Lorentzian and ideal passband filters exhibits the same 0.5 dB discrepancy that was observed for uncoded systems.

Improving Threshold for Fault-Tolerant Color-Code Quantum Computing by Flagged Weight Optimization

Color codes are promising quantum error-correction (QEC) codes because they have an advantage over surface codes in that all Clifford gates can be implemented transversally. However, the thresholds of color codes under circuit-level noise are relatively low, mainly because measurements of their high-weight stabilizer generators cause an increase in the circuit depth and, thus, substantial errors are introduced. This makes color codes not the best candidate for fault-tolerant quantum computing. Here, we propose a method to suppress the impact of such errors by optimizing weights of decoders using conditional error probabilities conditioned on the measurement outcomes of flag qubits. In numerical simulations, we improve the threshold of the (4.8.8) color code under circuit-level noise from 0.14% to around 0.27%, which is calculated by using an integer programming decoder. Furthermore, in the (6.6.6) color code, we achieve a circuit-level threshold of around 0.36%, which is almost the same value as the highest value in the previous studies employing the same noise model. In both cases, the effective code distance is also improved compared to a conventional method that uses a single ancilla qubit for each stabilizer measurement. Thereby, the achieved logical error rates at low physical error rates are almost one order of magnitude lower than those of the conventional method with the same code distance. Even when compared to the single-ancilla method with a higher code distance, considering the increased number of qubits used in our method, we achieve lower logical error rates in most cases. This method can also be applied to other weight-based decoders, making the color codes more promising as candidates for the experimental implementation of QEC. Furthermore, one can utilize this approach to improve a threshold of wider classes of QEC codes, such as high-rate quantum low-density parity-check codes. Published by the American Physical Society 2024

A Low-Complexity Security Scheme for Drone Communication Based on PUF and LDPC

Due to the limited payload and power of drones, the computational overhead, storage overhead and communication overhead that can be used for secure communication are restricted, making it difficult to apply some complex but fairly secure authentication protocols on drones. In this paper, we propose a low-complexity protocol for storing identity information in a resource-unconstrained device that does not require the UAV to store the information, thereby enhancing the UAV’s resistance to capture. The protocol in this paper mainly consists of quasi-cyclic low-density parity-check (QC-LDPC) codes, physical unclonable functions (PUFs) based on random-access memory (RAM), “XOR” operations, and hash computation. The protocol in this paper is an authentication architecture in which the drone is guided by the ground station to read its identity information, and the drone does not store any identity information in advance. The protocol is divided into two phases: 1. fuzzy authentication of fingerprint PUF and 2. uniqueness authentication accomplished while guiding the recovery of identity PUF. Recovering identity PUF in this paper, QC-LDPC is used as the error control module, and the optimization of bit-flip decoding significantly reduces the probability of decoding failure. After the comparative security analysis and comparative overhead analysis of this paper’s protocol, it can be concluded that this paper’s protocol can withstand common attacks (including attacks attempting to pass authentication, attacks attempting to interfere with authentication, and physical capture attacks), and the storage and communication overhead is small in the case of large time overhead.

On Construction of Low-Density Parity-Check Codes for Ultra-Reliable and Low Latency Communications

On Construction of Low-Density Parity-Check Codes for Ultra-Reliable and Low Latency Communications

Fast erasure decoder for hypergraph product codes

We propose a decoder for the correction of erasures with hypergraph product codes, which form one of the most popular families of quantum LDPC codes. Our numerical simulations show that this decoder provides a close approximation of the maximum likelihood decoder that can be implemented in O(N2) bit operations where N is the length of the quantum code. A probabilistic version of this decoder can be implemented in O(N1.5) bit operations.

Estimation of the Impulse Response of the AWGN Channel with ISI within an Iterative Equalization and Decoding System That Uses LDPC Codes.

In this paper, new schemes have been proposed for the estimation of the additive white Gaussian noise (AWGN) channel with intersymbol interference (ISI) in an iterative equalization and decoding system using low-density parity check (LDPC) codes. This article explores the use of the least squares algorithm in various scenarios. For example, the impulse response of the AWGN channel h was initially estimated using a training sequence. Subsequently, the impulse response was calculated based on the training sequence and then re-estimated once using the sequence estimated from the output of the LDPC decoder. Lastly, the impulse response was calculated based on the training sequence and re-estimated twice using the sequence estimated from the output of the LDPC decoder. Comparisons were made between the performances of the three mentioned situations, with the situation in which a perfect estimate of the impulse response of the channel is assumed. The performance analysis focused on how the bit error rate changes in relation to the signal-to-noise ratio. The BER performance comes close to the scenario of having a perfect estimate of the impulse response when the estimation is performed based on the training sequence and then re-estimated twice from the sequence obtained from the output of the LDPC decoder.

A History of Channel Coding in Aeronautical Mobile Telemetry and Deep-Space Telemetry.

This paper presents a history of the development of channel codes in deep-space telemetry and aeronautical mobile telemetry. The history emphasizes "firsts" and other remarkable achievements. Because coding was used first in deep-space telemetry, the history begins with the codes used for Mariner and Pioneer. History continues with the international standard for concatenated coding developed for the Voyager program and the remarkable role channel coding played in rescuing the nearly-doomed Galileo mission. The history culminates with the adoption of turbo codes and LDPC codes and the programs that relied on them. The history of coding in aeronautical mobile telemetry is characterized by a number of "near misses" as channel codes were explored, sometimes tested, and rarely adopted. Aeronautical mobile telemetry is characterized by bandwidth constraints that make use of low-rate codes and their accompanying bandwidth expansion, an unattractive option. The emergence of a family of high-rate LDPC codes coupled with a bandwidth-efficient modulation has nudged the aeronautical mobile telemetry community to adopt the codes in their standards.

Security-based low-density parity check encoder for 5G communication

The fifth generation (5G) of mobile telecommunication standards is intended to offer better performance and efficiency. One of the most significant difficulties in delivering safe data transfer through the transmission channel in the emerging 5G technology is channel-coding security. This research primarily focused on offering information transmission that is secure in the place of novel assaults such as side-channel attacks. In this research, we present a low-density parity check (LDPC) encoder that is constructed using the multiplicative masking method to overcome side-channel attacks, one of the most significant security concerns for the upcoming 5G system. As a result, it offers greater security, reduced complexity, and higher performance. Power, area, and delay can all be calculated using LDPC codes. Comparing multiplicative masking implemented LDPC encoders to ordinary channel coding techniques in terms of security seen that multiplicative masking implemented LDPC encoders offer more security. The program Xilinx ISE 14.7 can synthesize the analysis. The advantage of multiplicative masking is that it offers a promising level of security through the principle of randomization, which is the foundation of the procedure. According to the analysis, the secured transmission of the data by the proposed multiplicative masking implemented LDPC encoder is increased.

An Optimization Model for Offline Scheduling Policy of Low-Density Parity-Check Codes

An Optimization Model for Offline Scheduling Policy of Low-Density Parity-Check Codes

Protograph LDPC Code and Shaped Index Modulation Design for Multi-Mode OAM Systems

Protograph LDPC Code and Shaped Index Modulation Design for Multi-Mode OAM Systems

Quantum LDPC Codes From Intersecting Subsets

Quantum LDPC Codes From Intersecting Subsets

Triangle Projection Algorithm in ADMM-LP Decoding of LDPC Codes

Triangle Projection Algorithm in ADMM-LP Decoding of LDPC Codes

Efficient LDPC Code Design based on Genetic Algorithm for IoT Applications

Efficient LDPC Code Design based on Genetic Algorithm for IoT Applications

Symmetry-Enforced Many-Body Separability Transitions

We study quantum many-body mixed states with a symmetry from the perspective of , i.e., whether a mixed state can be expressed as an ensemble of short-range-entangled symmetric pure states. We provide evidence for “symmetry-enforced separability transitions” in a variety of states, where in one regime the mixed state is expressible as a convex sum of symmetric short-range-entangled pure states, while in the other regime, such a representation is not feasible. We first discuss the Gibbs state of Hamiltonians that exhibit spontaneous breaking of a discrete symmetry, and argue that the associated thermal phase transition can be thought of as a symmetry-enforced separability transition. Next we study cluster states in various dimensions subjected to local decoherence, and identify several distinct mixed-state phases and associated separability phase transitions, which also provides an alternative perspective on recently discussed “average symmetry-protected topological order.” We also study decohered p+ip superconductors, and find that if the decoherence breaks the fermion parity explicitly, then the resulting mixed state can be expressed as a convex sum of nonchiral states, while a fermion parity–preserving decoherence results in a phase transition at a nonzero threshold that corresponds to spontaneous breaking of fermion parity. Finally, we briefly discuss systems that satisfy the no low-energy trivial state property, such as the recently discovered good low-density parity-check codes, and argue that the Gibbs state of such systems exhibits a temperature-tuned separability transition. Published by the American Physical Society 2024

A Low-Density Parity-Check Coding Scheme for LoRa Networking

This article presents a novel system, LLDPC , 1 which brings Low-Density Parity-Check (LDPC) codes into Long Range (LoRa) networks to improve Forward Error Correction, a task currently managed by less efficient Hamming codes. Three challenges in achieving this are addressed: First, Chirp Spread Spectrum (CSS) modulation used by LoRa produces only hard demodulation outcomes, whereas LDPC decoding requires Log-Likelihood Ratios (LLR) for each bit. We solve this by developing a CSS-specific LLR extractor. Second, we improve LDPC decoding efficiency by using symbol-level information to fine-tune LLRs of error-prone bits. Finally, to minimize the decoding latency caused by the computationally heavy Soft Belief Propagation (SBP) algorithm typically used in LDPC decoding, we apply graph neural networks to accelerate the process. Our results show that LLDPC extends default LoRa’s lifetime by 86.7% and reduces SBP algorithm decoding latency by 58.09×.