Error-correcting Codes Research Articles

Robust image steganography against lossy JPEG compression based on embedding domain selection and adaptive error correction

Transmitting images for communication on social networks has become routine, which is helpful for covert communication. The traditional steganography algorithm is unable to successfully convey secret information since the social network channel will perform lossy operations on images, such as JPEG compression. Previous studies tried to solve this problem by enhancing the robustness or making the cover adapt to the channel processing. In this study, we proposed a robust image steganography method against lossy JPEG compression based on embedding domain selection and adaptive error correction. To improve anti-steganalysis performance, the embedding domain is selected adaptively. To increase robustness and lessen the impact on anti-steganalysis performance, the error correction capacity of the error correction code is adaptively adjusted to eliminate redundancy. The experimental results show that the proposed method achieves better anti-steganalysis and robustness.

T-depth-optimized quantum search with quantum data-access machine

Abstract Quantum search algorithms offer a remarkable advantage of quadratic reduction in query complexity using quantum superposition principle. However, how an actual architecture may access and handle the database in a quantum superposed state has been largely unexplored so far; the quantum state of data was simply assumed to be prepared and accessed by a black-box operation—so-called oracle, even though this process, if not appropriately designed, may adversely diminish the quantum query advantage. Here, we introduce an efficient quantum data-access process, dubbed as quantum data-access machine (QDAM), and present a general architecture for quantum search algorithm. We analyze the runtime of our algorithm in view of the fault-tolerant quantum computation (FTQC) consisting of logical qubits within an effective quantum error correction code. Specifically, we introduce a measure involving two computational complexities, i.e. quantum query and T-depth complexities, which can be critical to assess performance since the logical non-Clifford gates, such as the T (i.e. π / 8 rotation) gate, are known to be costliest to implement in FTQC. Our analysis shows that for N searching data, a QDAM model exhibiting a logarithmic, i.e. O ( log N ) , growth of the T-depth complexity can be constructed. Further analysis reveals that our QDAM-embedded quantum search requires O ( N × log N ) runtime cost. Our study thus demonstrates that the quantum data search algorithm can truly speed up over classical approaches with the logarithmic T-depth QDAM as a key component.

Quantum neural networks for the discovery and implementation of quantum error-correcting codes.

We implement and use quantum neural networks that exploit bit-flip quantum error-correcting codes that correct bit-flip errors in arbitrary logical qubit states. We introduce conjugate layer quantum autoencoders and use them in order to restore states impacted by amplitude damping through the utilization of an approximative four-qubit error-correcting codeword. Our specific implementation avoids barren plateaus of the cost function and improves the training time. Moreover, we propose a strategy that allows one to discover new encryption protocols tailored for specific quantum channels. This is exemplified by learning to generate logical qubits explicitly for the bit-flip channel. Our modified quantum neural networks consistently outperform the standard implementations across all tasks.

Designing an ultra-efficient Hamming code generator circuit for a secure nano-telecommunication network

Communication links forming secure telecommunications networks rely on various technologies such as message switching, circuit switching, or packet switching to transmit messages and data. Hamming codes, a family of linear error-correcting codes, are commonly used in communication networks to detect and correct one-bit and two-bit errors. However, reducing power consumption, occupied area, and latency in secure telecommunication networks remains a challenge for future information and communication technology. To address these challenges, emerging technologies like quantum dots offer potential solutions. Quantum-dot cellular automata (QCA) stands as a promising frontier in nanotechnology for enhancing secure telecommunications networks. It opens up the possibility of crafting high-performance, energy-efficient digital circuits. This research harnesses the potential of QCA and introduces groundbreaking innovations: a 3-8 decoder employing a single-layer layout and a 3-input XOR gate with a multi-layer configuration. These components are utilized in the design of an electronic circuit for Hamming codes, incorporating the QCA-based approach. It is important to note that practical implementation in real-world scenarios presents challenges due to the nature of QCA technology. As a result, the evaluation and validation of the proposed designs heavily rely on simulations using QCADesigner. While experimental validation in real-world scenarios is limited, the simulations provide insights into the functionality and feasibility of the suggested designs. By leveraging QCA, the proposed Hamming code circuit significantly enhances cell count, occupied area, and clock latency. The suggested design can be adapted to fit different generating matrices in Hamming codes without requiring drastic modifications to the underlying architecture.

New Structure of Channel Coding: Serial Concatenation of Polar Codes

In this paper, we introduce a new coding and decoding structure for enhancing the reliability and performance of polar codes, specifically at low error rates. We achieve this by concatenating two polar codes in series to create robust error-correcting codes. The primary objective here is to optimize the behavior of individual elementary codes within polar codes. In this structure, we incorporate interleaving, a technique that rearranges bits to maximize the separation between originally neighboring symbols. This rearrangement is instrumental in converting error clusters into distributed errors across the entire sequence. To evaluate their performance, we proposed to model a communication system with seven components: an information source, a channel encoder, a modulator, a channel, a demodulator, a channel decoder, and a destination. This work focuses on evaluating the bit error rate (BER) of codes for different block lengths and code rates. Next, we compare the bit error rate (BER) performance between our proposed method and polar codes.

A novel integrated signal structure of satellite navigation and communication system with plug-and-play capability

An integrated navigation/communication signal is proposed in our previous work. It considered Cyclic Code Shift Keying (CCSK) as a communication signal combined with traditional Global Navigation Satellite System (GNSS) signal, further the optimized cyclic shift set for communication signal was designed. Based on the previous research, a fuzzy judging algorithm is proposed to acquire the integrated signal in this paper. This algorithm adopts segmenting correlation domain to improve the integrated signal transmission robustness. Moreover, in order to solve incompatibility problem between the integrated signal and binary communication system, a strategy for optimizing cyclic shift set basing on dual-thresholds is proposed, in which interleaving coding is used to resist interference. The fault-tolerant rate of proposed algorithm is improved by about 87% compared with traditional algorithms. Based on the compatibility, the Bit Error Rate (BER) of the integrated signal decreases obviously, and the reliability of the communication system is improved greatly, benefiting from that interleaving technology and error correction coding is applied.

Multi‐Party Quantum Key Distribution Using Variational Quantum Eigensolvers

AbstractThe research paper introduces a novel approach to multi‐party quantum key distribution using variational quantum eigensolvers (VQEs). The protocol aims to establish secure communication among multiple parties in a quantum network. The paper outlines a comprehensive framework incorporating quantum state preparation, VQE‐based key generation, error correction, and privacy amplification circuits. Mathematical formulations guide the design of quantum gates, variational parameters, and error correction codes. The protocol utilizes quantum entanglement, VQE optimization, and classical operations for error correction and secure key extraction. The paper's experimental focus involves implementing the proposed protocol on a quantum computer, analyzing security metrics such as mutual information and min‐entropy, and simulating circuit outcomes.

XPM estimation and compensation in the WDM system based on a low-complexity inner FEC.

In this work, we focus on compensation of inter-channel nonlinearity in optical wavelength division multiplexed (WDM) systems. We consider pre-coding with a high-rate forward error correction (FEC) code and a low-complexity and low-latency decoding and equalization scheme at the receiver. The 2 × 2 multiple-input multiple-output (MIMO) recursive least square (RLS) equalizer is applied to reduce the inter-symbol interference (ISI) caused by the inter-channel nonlinearity, while the decoder improves the quality of the data feedback. Decisions based on feedback reliability have been implemented to prevent error propagation. We demonstrate that our system can readily utilize the inner FEC part of a mainstream concatenated optical FEC designs such as the 400ZR standard FEC. We evaluate the proposed algorithm for the dual-polarization 16QAM and 256QAM optical links. Based on our simulation results, the Q-factor has been increased by 0.36 and 0.67 dB for the 16QAM and 256QAM, respectively. The optimum launch power has been increased by 0.4 dB for both cases.

Performance analysis of several common error correction codes

With the rapid development of information technology and advances in science and technology, people are constantly interacting with data and coding. Error correction codes are integral to ensuring the security, robustness, and accuracy of information and systems, used not only in various engineering fields but in our daily lives as well. Systems that incorporate error correction codes have been proven to perform significantly better than those that do not, which makes it essential to understand the principles behind coding, encoding techniques, and their performance in specific domains.This paper focuses on three widely used error correction codes: Hamming code, RS code, and convolutional code. By introducing each code separately and evaluating their performance in different practical areas using proper simulations and relevant research results, this paper provides a comprehensive understanding of the vital role of error correction codes in channel encoding. Each code has its strengths, weaknesses, and specific applications. Hamming code, for example, is suitable for correcting bit errors in computer memories and communication systems. RS code is widely used in digital storage and broadcast systems due to its high level of error correction capability. Convolutional code is ideal for correcting bit-errors in continuous channels, making it an excellent choice for wireless communication systems. Overall, the results demonstrate that these error correction codes are crucial to guaranteeing data transmission integrity and system robustness. Understanding their principles and performance can guide future research and development of coding techniques in advancing technological progress and improving our daily lives.

Linear codes of larger lengths with Galois hulls of arbitrary dimensions and related entanglement-assisted quantum error-correcting codes

Galois hulls are generalizations of Euclidean and Hermitian hulls, which have attracted interest because of their important applications in determining the complexity of some algorithms about linear codes and in constructing entanglement-assisted quantum error-correcting codes (EAQECCs). In this paper, the whole contribution is two-folded. On one hand, we propose explicit methods to construct linear codes of larger lengths with Galois hulls of arbitrary dimensions from given Galois self-orthogonal codes. Conditions required in our approach are proven to be relatively weak. On the other hand, we apply these results to construct EAQECCs. Two bounds for EAQECCs constructed from linear codes with prescribed dimensional Galois hull are given and EAQECCs with rates greater than or equal to 12 and positive net rates can be obtained. We also present many interesting examples to explain visually how these two aspects work.

Performance of Unslotted ALOHA With Capture and Multiple Collisions in LoRaWAN

This paper explores the capacity limits and the tradeoff between the antagonistic means of enabling reliable data delivery in a loaded LoRaWAN cell. In fact, channel attenuation and variability call for robust transmission settings but the associated load increase causes more collisions between frames. In addition to the physical layer parameters of the LoRa modulation, this paper considers the benefits and tuning of inter-packet Error Correction Codes (ECC), which also trades transmission redundancy for reliability. We thus start by proposing a refined Packet Delivery Ratio (PDR) model that improves the ones found in the literature in that, first, it takes into account the dependency between overcoming ambient noise and dominating colliding frames, and second, it considers the sum of interference powers when multiple colliding frames are present, even if the interference preexists. Moreover, the model extends to the case of a gateway with receiver diversity. In a second step, the model allows to set out the level of redundancy at which ECC is the most effective without hindering capacity: a coding rate of one third. When this is fixed, it allows to define the transmission parameters allocation within a cell and thus the size of the cell. We finally develop an ad-hoc Python discrete-event simulator, freely accessible, to complement the model for assessing the effect of inter-SF and near-far interference and to show the benefits of power control in this respect.

Navigating through Noise Comparative Analysis of Using Convolutional Codes vs. Other Coding Methods in GPS Systems

This research highlights the importance of error-correcting codes in ensuring secure and efficient data transmission over noisy channels. This paper aims to address the issue of limited information regarding the factors that contribute to the effectiveness of the implementation of Convolutional Codes in GPS systems. The research problem revolves around the insufficiency of scholarly sources elucidating the rationale behind the utilization of convolutional codes, specifically in GPS systems, rather than others. Through an in-depth analysis of these factors, this study strives to achieve a comprehensive understanding of the application of Convolutional Codes in GPS. To tackle this research problem, a novel methodology involving comparative analysis is employed. The coding techniques commonly used in satellite communication systems (such as BCH, LDPC, and turbo codes) are carefully examined and compared to the advantages and suitability of Convolutional codes and the Viterbi algorithm for GPS systems. Each coding technique is evaluated based on factors such as error detection and correction capabilities, bandwidth efficiency, computational complexity, and resilience to noise. The key findings of this study shed light on the unique advantages offered by Convolutional codes and the Viterbi algorithm for GPS systems. The analysis reveals that these coding techniques exhibit superior error detection and correction capabilities, efficient bandwidth utilization, and the ability to withstand noise in the GPS communication channel. The results also highlight the computational complexity associated with these techniques, providing valuable insights for the implementation of convolutional codes in GPS systems. Overall, this article contributes to the existing knowledge by providing a comprehensive understanding of the reasons behind the suitability of convolutional codes for GPS systems. The findings of this study serve as a resource for researchers, engineers, and practitioners in the field of satellite communication, aiding in the comprehensive understanding, advancement, and optimization of GPS system designs.

Quantum error-correcting codes from the quantum construction X

Quantum error-correcting codes from the quantum construction X

Application of double-error correction codes to protect configuration programmable logic memory against space radiation

Objectives. Programmable logic integrated circuits of the field programmable gate array (FPGA) type based on static configuration memory are widely used in the electronics of onboard spacecraft systems. Under the influence of space radiation, errors may occur in the FPGA configuration memory. The main methods of protection against such errors involve various options for reservation triggers, as well as the use of error-correcting codes in special error detection and correction circuits. The purpose of the present work is to determine which error-correcting codes are best suited to the implementation of internal scrubbing of the FPGA configuration memory taking redundancy into account.Methods. The paper analyses various methods for scrubbing FPGA configuration memory, which are used to correct errors caused by the action of space radiation. It is proposed to increase the efficiency of internal scrubbing of the FPGA configuration memory using codes that correct both single- and double-adjacent SEC-DED-DAEC errors. In this case, the need to perform external scrubbing of the configuration memory is reduced by overwriting it with a reference configuration from non-volatile radiation-resistant memory; in this way, FPGA downtime caused by the external scrubbing procedure is reduced. Due to the known SEC-DED-DAEC codes having a non-zero probability of erroneous detection and subsequent erroneous correction of a double non-adjacent error, as well as various redundancy and implementation complexities, a study was made of the most efficient code for internal scrubbing.Results. The results showed that the Datta, Neale and Hoyoon–Yongsurk codes are optimal from the indicated positions. Recommendations are given for selecting a specific code depending on the specific requirements for a particular planned space mission.Conclusions. The study confirms the effectiveness of protecting the memory of programmable logic by using two-error-correcting codes.

Hybrid feature extraction and LLTSA-based dimension reduction for vein pattern recognition

ABSTRACT In information and security, the personal identification of individuals becomes much more important. For improving security, several biometric recognition techniques are implemented. However, in finger vein recognition, it faces the critical problem of fake finger vein images, security and less accuracy. To conquer this problem, Hybrid Feature Extraction with Linear Local Tangent Space Alignment-based dimension reduction and Support Vector Machine classifier (HFE–LLTSA–SVM) is proposed. In this hybrid, FE is considered as the combination of histogram of oriented gradients (HOG), grey-level co-occurrence matrix (GLCM), stationary wavelet transform (SWT), and local binary pattern (LBP) for extracting the hybrid feature. LLTSA perform dimension reduction in the outputs of HFE from HOG, GLCM, and LBP. Furthermore, SVM is used for classification which gives authentication based on error-correcting code. Finally, the performance parameters were calculated and the proposed method achieved better accuracy of 99.75%, when compared with existing methods.

Joint BCH and XOR Decoding for Solid State Drives

At a flash memory, each stored data frame is protected by error correction codes (ECC) such as Bose-Chaudhuri-Hocquenghem (BCH) codes from random errors. Exclusive-OR (XOR) based erasure codes like RAID-5 have also been employed at the flash memory to protect from memory block defects. Conventionally, the ECC and erasure codes are used separately since their target errors are different. Due to recent aggressive technology scaling, additional error correction capability for random errors is required without adding redundancy. We propose an algorithm to improve error correction capability by using XOR parity with a simple counter that counts the number of unreliable bits in the XOR stripe. We also propose to apply Chase decoding to the proposed algorithm. The counter makes it possible to reduce the false correction and execute the efficient Chase decoding. We show that combining the proposed algorithm with Chase decoding can significantly improve the decoding performance.

Analysis of code-based digital signature schemes

<span lang="EN-US">Digital signatures are in high demand because they allow authentication and non-repudiation. Existing digital signature systems, such as digital signature algorithm (DSA), elliptic curve digital signature algorithm (ECDSA), and others, are based on number theory problems such as discrete logarithmic problems and integer factorization problems. These recently used digital signatures are not secure with quantum computers. To protect against quantum computer attacks, many researchers propose digital signature schemes based on error-correcting codes such as linear, Goppa, polar, and so on. We studied 16 distinct papers based on various error-correcting codes and analyzed their various features such as signing and verification efficiency, signature size, public key size, and security against multiple attacks.</span>

Secure key distribution exploiting error rate criticality for radio frequency links.

We propose a method by which two radio frequency (RF) communication terminals exchange encryption keys or other data securely. This method draws on the approach developed for quantum key distribution (QKD) for detecting eavesdroppers but our method does not use any quantum properties at all. Instead, by exploiting the effects an eavesdropper has on channel stability, we explore a line-of-sight link radio in which data transfer rates are so high as to approach the Shannon limit. With very steep rises in bit error rate accompanying a small degradation of signal-to-noise limits for certain forward error correction codes, it becomes possible to infer the existence of an eavesdropper before they are able to obtain a complete key. We describe our method and analyse one possible implementation using low density parity check codes with quadrature phase shift keying modulation. The proposed technique is in principle far easier to implement than quantum-based approaches for RF and optical wireless links since the required hardware is readily available and the basic principles are well known and well understood. Finally, we show our method to have a higher key rate and spectral efficiency than those of QKD.

Transversal diagonal logical operators for stabiliser codes

Storing quantum information in a quantum error correction code can protect it from errors, but the ability to transform the stored quantum information in a fault tolerant way is equally important. Logical Pauli group operators can be implemented on Calderbank-Shor-Steane (CSS) codes, a commonly-studied category of codes, by applying a series of physical Pauli X and Z gates. Logical operators of this form are fault-tolerant because each qubit is acted upon by at most one gate, limiting the spread of errors, and are referred to as transversal logical operators. Identifying transversal logical operators outside the Pauli group is less well understood. Pauli operators are the first level of the Clifford hierarchy which is deeply connected to fault-tolerance and universality. In this work, we study transversal logical operators composed of single- and multi-qubit diagonal Clifford hierarchy gates. We demonstrate algorithms for identifying all transversal diagonal logical operators on a CSS code that are more general or have lower computational complexity than previous methods. We also show a method for constructing CSS codes that have a desired diagonal logical Clifford hierarchy operator implemented using single qubit phase gates. Our methods rely on representing operators composed of diagonal Clifford hierarchy gates as diagonal XP operators and this technique may have broader applications.

Fault Detection and Analysis in SRAM through Self Refreshing Operation

Numerous soft faults in SRAM memory emerge as technological innovations scales down, resulting in single and several cell upsets. The increased use of transistors in space applications has rendered semiconductor devices more vulnerable to soft errors caused by harm from radiation. A single event upset (SEU) is occurring whenever a soft error produces a tiny bit flipped in a storage device. Because SEU faults affect system performance, they must be addressed as soon as possible. Error-correcting codes, like the method known as (7,4) hamming codes, were devised and their decoding and encoding procedures were verified. It also used to detect single errors that can be fixed. It also helps detect double errors, SECDED however repair of double errors is tough. The decoding and encoding techniques of these approaches were investigated, and all computational findings had been verified and executed in a Xilinx NEXYS 4 DDR FPGA board.