Check Codes Research Articles

Secrecy Coding Analysis of Short-Packet Full-Duplex Transmissions with Joint Iterative Channel Estimation and Decoding Processes.

This paper studies the secrecy coding analysis achieved by the self-jamming technique in the presence of an eavesdropper by considering a short-packet Full-Duplex (FD) transmission developed based on iterative blind or semi-blind channel estimation and advanced decoding algorithms. Indeed, the legitimate receiver and eavesdropper can simultaneously receive the intended signal from the transmitter and broadcast a self-jamming or jamming signal to the others. Unlike other conventional techniques without feedback, the blind or semi-blind algorithm applied at the legitimate receiver can simultaneously estimate, firstly, the Self-Interference (SI) channel to cancel the SI component and, secondly, estimate the propagation channel, then decode the intended messages by using 5G Quasi-Cyclic Low-Density Parity Check (QC-LDPC) codes. Taking into account the passive eavesdropper case, the blind channel estimation with a feedback scheme is applied, where the temporary estimation of the intended channel and the decoded message are fed back to improve both the channel estimation and the decoding processes. Only the blind algorithm needs to be implemented in the case of a passive eavesdropper because it achieves sufficient performances and does not require adding pilot symbols as the semi-blind algorithm. In the case of an active eavesdropper, based on its robustness in the low region of the Signal-to-Noise Ratio (SNR), the semi-blind algorithm is considered by trading four pilot symbols and only requiring the feedback for channel estimation processes in order to overcome the increase in noise in the legitimate receiver. The results show that the blind or semi-blind algorithms outperform the conventional algorithm in terms of Mean Square Error (MSE), Bit Error Rate (BER) and security gap (). In addition, it has been shown that the blind or semi-blind algorithms are less sensitive to high SI and self-jamming interference power levels imposed by secured FD transmission than the conventional algorithms without feedback.

Study of Different Types of Error Detection and Correction Code in Wireless Communication

The integrity of received data is a critical consideration in the design of digital communications and storage systems. The technique involved in attaining data reliability while transmission over a wireless channel is to use Channel Coding. These coding methods involve the use of Error Control Codes and there are two basic ways of controlling errors. They are Automatic Repeat Request and Forward Error Correction. This thesis concentrates on Forward error correction that deals with error detection and error correction. There are two types of error control codes: Block Codes and Convolutional Codes. The extent to which the errors are detected is a measure of the success of the code. The main trade-off in the error correction/detection technique lies in the key parameters involved in evaluating a coding system. Various block codes are analyzed using the performance metrics, namely, Improvement ratio and Error Resilience. It is observed that Cyclic Redundancy Check (CRC) codes showed better performance, and hence, they are chosen for further study.

Hardware Designs of Cyclic Redundancy Check Code with Calculation Time Trade-Off Strategy

This paper will discuss the design of cyclic redundancy check code (CRC), a most popular error detecting scheme in intelligent communication. At first, the concepts of CRC are given in detail with mathematical model and software simulation in python scripts. And mainly, with calculation time trade-off strategy, we provide the CRC hardware design with three architecture models serial, parallel, hybrid serial and parallel. Keywords: Error Detection Scheme; Cyclic Redundancy Check; Python; Verilog HDL; Digital System Design

A Novel Channel Coding Scheme by Concatenating LDPC with BCH for NAND Flash Memory

Insuring data reliability on NAND Flash Memory is an important research issue. As adopting a very powerful error-correcting code gradually becomes a strategic demand for the endurance of nowadays NAND Flash memory, Low Density Parity Check (LDPC) codes are recently proposed due to their outstanding error correcting capability. In this paper, a novel Channel Coding Scheme concatenated LDPC with BCH NAND Flash Memory is proposed. Firstly a particular LDPC code with low error floor is constructed and BCH codes are used to generate soft information for LDPC codes. Simulation showed that the proposed Channel Coding Scheme obtains the benefit of both overcoming difficulties of soft information generation and the compatiblity with existing BCH code. With the low error floor of constructed LDPC codes, the proposed Channel Coding Scheme can increase P/E cycles of NAND flash memory more significantly comparing the BCH code.

Anti error and erasure coding for water-to-air visible light communication through wavy water surface with wave height up to 0.6 meters.

Considering large dynamic optical intensity range in a water-to-air (W2A) channel, we propose two promising channel coding schemes, namely the concatenated Reed Solomon-Low Density Parity Check (RS-LDPC) code and Raptor code, for W2A visible light communication (VLC). We establish a W2A-VLC link to verify the performance under different wavy water environments and different water depths with a green light emitting diode (LED). A wave generator is adopted to emulate the wavy water surface with wave height up to 0.6 m. The receiver is fixed 3.2 m above the water, and the transmitter varies from 2.5 m to 4.0 m under the water through a up-down-moveable platform. We test the coding schemes with different code lengths and code rates under 5 MSym/s air-interface symbol rate. Experimental results show that both schemes can reduce the bit error ratio (BER) and frame error rate (FER) of a W2A-VLC system, and thus can improve the reliability. Via comparing the two codes with the same overhead and approximately the same code length, it is demonstrated that Raptor code can generally outperform the concatenated RS-LDPC code. Our research provides promising channel coding methods without feedback for a W2A-VLC system.

A Polygonal Line Min-Sum Decoding Scheme for Low Density Parity Check Codes

Low-density parity-check (LDPC) codes are widely used as error correction codes in new generation digital TV standards, such as the second generation of terrestrial digital video broadcasting standard (DVB-T2), Advanced Television Systems Committee (ATSC) 3.0, etc. The nonlinear belief propagation (BP) algorithm has excellent decoding performance for LDPC codes, but is often simplified in hardware implementations by linear min-sum (MS) algorithm due to its high complexity. This simplification also leads to over-estimation problems, which can be corrected by adding factors in conventional algorithms (e.g., normalized min-sum (NMS), offset min-sum (OMS), and variable scaling normalized min-sum (VMS) algorithms). However, the correction factors of these modified MS algorithms cannot adapt to different channels and modulations, and the performance needs further improvement. In this paper, the concepts of over-estimation value (OEV) and over-estimation rate (OER) are introduced to describe the over-estimation problem of the MS algorithm. Then, under the guidance of OEV and OER, a polygonal line min-sum (PMS) algorithm with correction factors adapted to different channels and modulations is proposed according to LLR distribution. Following the properties of OEV and OER, PMS algorithm is further simplified into Simplified PMS (SPMS) algorithm. LDPC codes from ATSC 3.0 are adopted in this paper to evaluate SPMS algorithm in comparison with the conventional algorithms. Extensive simulation results show that the SPMS algorithm for ATSC 3.0 LDPC decoder has at most 1.61dB, 0.24dB and 0.36dB gain over NMS, OMS and VMS algorithms respectively when frame error rate (FER) is at 10⁻⁴ level over additive white Gaussian noise (AWGN) channel with QPSK modulation. More importantly, the simulation results show that the SPMS algorithm can achieve much better performance than these modified MS algorithms over AWGN and Rayleigh channel with higher-order modulations or under limited maximum iteration number.

Joint Iterative Blind Self-Interference Cancellation, Propagation Channel Estimation and Decoding Processes in Full-Duplex Transmissions

The paper proposes a joint blind iterative Self-Interference (SI) cancellation, propagation channel estimation and decoding algorithm in Full-Duplex (FD) transmissions via feedback of channel estimates and decoded messages combined with the process of Digital Self-Interference Cancellation (DSIC). Different from the conventional algorithm, the proposed blind algorithm simultaneously estimates the self-interference and propagation channels and decodes messages in each decoding iteration of 5G Quasi-Cyclic Low Density Parity Check (QC-LDPC) codes. The temporary propagation channel estimate and decoded message are fed back to improve the self-interference cancellation and also the channel estimation as well as decoding in the next iteration. The results show that the proposed algorithm outperforms the conventional algorithm, especially at high signal to noise ratio (SNR) and small number of symbols, and requires much less processing time and computational complexity while achieving the convergence performance. The results also show that the proposed algorithm is less sensitive to SI level than the conventional algorithm. The paper further proposes a partial feedback scheme, which only use few feedback symbols for channel estimation, to significantly reduce the processing time and computational complexity while maintaining the performance. These good properties seem quite suitable for a use of this proposed blind iterative algorithm for short-length packet FD transmissions in Internet-of-Things (IoT) applications and green communications.

Digital Watermarking Technology Based on LDPC Code and Chaotic Sequence

The number of ways to obtain information has increased by 5th Generation Mobile Communication Technology commercial. But easier access to information also means more security issues. Digital watermarking is an effective method to solve the security problem of information. Aiming at the problems of one-dimensional single chaotic image encryption algorithm, such as simple structure, small key space, and the invisibility and robustness of traditional information hiding technology cannot be well reconciled. The improved encryption algorithm based on Low Density Parity Check Code and double Logistic chaotic system is proposed, which can expand the key space, reduce the bit error rate, and enhance the security and anti-interference ability of the system. The feasibility, reliability and practicability of the algorithm are verified by MATLAB simulation.

DNN‐aided read‐voltage threshold optimization for MLC flash memory with finite block length

The error-correcting performance of multi-level-cell (MLC) NAND flash memory is closely related to the block length of error-correcting codes (ECCs) and log-likelihood-ratios of the read-voltage thresholds. Driven by this issue, this paper optimizes the read-voltage thresholds for MLC flash memory to improve the decoding performance of ECCs with finite block length. First, through the analysis of channel coding rate and decoding error probability under finite block length, the optimization problem of read-voltage thresholds to minimize the maximum decoding error probability is formulated. Second, a cross-iterative search algorithm to optimize read-voltage thresholds under the perfect knowledge of flash memory channel is developed. However, it is challenging to analytically characterize the voltage distribution under the effect of data retention noise. To address this problem, a deep neural network (DNN)-aided optimization strategy to optimize the read-voltage thresholds is developed, where a multi-layer perception network is employed to learn the relationship between voltage distribution and read-voltage thresholds. Simulation results show that, compared with the existing schemes, the proposed DNN-aided read-voltage threshold optimization strategy with a well-designed Low Density Parity Check (LDPC) code can not only improve the program-and-erase endurance but also reduce the read latency.

Maximum-Likelihood Deletion Error Location for Decoding Marker Guess & Check Codes

Guess & check (GC) codes can correct multiple deletions with high probability by guessing all possible deletion patterns at a polynomial complexity. This paper investigates an efficient way of guessing deletion patterns with the aid of markers. The marker are inserted as block identifiers into GC codewords and examined for implementing maximum-likelihood inference of deletion patterns in trellis graph. The resulting number of guesses for decoding marker GC codes can be reduced significantly by an increasing order of magnitude as the code length grows.

Self-Corrected Belief-Propagation Decoder for Source Coding With Unknown Source Statistics

This letter describes a practical Slepian-Wolf source coding scheme based on Low Density Parity Check (LDPC) codes. It considers the realistic setup where the parameters of the statistical model between the source and the side information are unknown. A novel Self-Corrected Belief-Propagation (SC-BP) algorithm is proposed in order to make the coding scheme robust to incorrect model parameters by introducing some memory inside the LDPC decoder. A Two Dimensional Density Evolution (2D-DE) analysis is then developed to predict the theoretical performance of the SC-BP decoder. Both the 2D-DE analysis and Monte-Carlo simulations confirm the robustness of the SC-BP decoder. The proposed solution allows for an important complexity reduction and shows a performance very close to existing methods which jointly estimate the model parameters and the source sequence.

A Survey on Old and New Approximations to the Function ϕ(x) Involved in LDPC Codes Density Evolution Analysis Using a Gaussian Approximation

Low Density Parity Check (LDPC) codes are currently being deeply analyzed through algorithms that require the capability of addressing their iterative decoding convergence performance. Since it has been observed that the probability distribution function of the decoder’s log-likelihood ratio messages is roughly Gaussian, a multiplicity of moderate entanglement strategies to this analysis has been suggested. The first of them was proposed in Chung et al.’s 2001 paper, where the recurrent sequence, characterizing the passage of messages between variable and check nodes, concerns the function ϕ(x), therein specified, and its inverse. In this paper, we review this old approximation to the function ϕ(x), one variant on it obtained in the same period (proposed in Ha et al.’s 2004 paper), and some new ones, recently published in two 2019 papers by Vatta et al. The objective of this review is to analyze the differences among them and their characteristics in terms of accuracy and computational complexity. In particular, the explicitly invertible, not piecewise defined approximation of the function ϕ(x), published in the second of the two abovementioned 2019 papers, is shown to have less relative error in any x than most of the other approximations. Moreover, its use conducts to an important complexity reduction, and allows better Gaussian approximated thresholds to be obtained.

Fast Adaptive Low-density Parity Check Coding Based on Confidence Criteria

Fast Adaptive Low-density Parity Check Coding Based on Confidence Criteria

Machine Learning of Physical Unclonable Functions using Helper Data

Physical Unclonable Functions (PUFs) are used in various key-generation schemes and protocols. Such schemes are deemed to be secure even for PUFs with challenge-response behavior, as long as no responses and no reliability information about the PUF are exposed. This work, however, reveals a pitfall in these constructions: When using state-of-the-art helper data algorithms to correct noisy PUF responses, an attacker can exploit the publicly accessible helper data and challenges. We show that with this public information and the knowledge of the underlying error correcting code, an attacker can break the security of the system: The redundancy in the error correcting code reveals machine learnable features and labels. Learning these features and labels results in a predictive model for the dependencies between different challenge-response pairs (CRPs) without direct access to the actual PUF response. We provide results based on simulated data of a k-SUM PUF model and an Arbiter PUF model. We also demonstrate the attack for a k-SUM PUF model generated from real data and discuss the impact on more recent PUF constructions such as the Multiplexer PUF and the Interpose PUF. The analysis reveals that especially the frequently used repetition code is vulnerable: For a SUM-PUF in combination with a repetition code, e.g., already the observation of 800 challenges and helper data bits suffices to reduce the entropy of the key down to one bit. The analysis also shows that even other linear block codes like the BCH, the Reed-Muller, or the Single Parity Check code are affected by the problem. The code-dependent insights we gain from the analysis allow us to suggest mitigation strategies for the identified attack. While the shown vulnerability advances Machine Learning (ML) towards realistic attacks on key-storage systems with PUFs, our analysis also facilitates a better understanding and evaluation of existing approaches and protocols with PUFs. Therefore, it brings the community one step closer to a more complete leakage assessment of PUFs.

Codes for Correcting Localized Deletions

We consider the problem of constructing binary codes for correcting deletions that are localized within certain parts of the codeword that are unknown a priori. The model that we study is when δ ≤ w deletions are localized in a window of size w bits. These δ deletions do not necessarily occur in consecutive positions, but are restricted to the window of size w. The localized deletions model is a generalization of the bursty model, in which all the deleted bits are consecutive. In this paper, we construct new explicit codes for the localized model, based on the family of Guess & Check codes which was previously introduced by the authors. The codes that we construct can correct, with high probability, δ ≤ w deletions that are localized in a single window of size w, where w grows with the block length. Moreover, these codes are systematic; have low redundancy; and have efficient deterministic encoding and decoding algorithms. We also generalize these codes to deletions that are localized within multiple windows in the codeword.

A comprehensive review of parallel concatenation of LDPC code techniques

Objective: In the code theory, parallel concatenation of codes becomes more popular after the introduction of turbo codes. In recent years, the Low Density Parity Check (LDPC) code has found remarkable advancement and has seen them outshine turbo codes in terms of performance especially in the error floor and higher code rate. The main objective of this paper is to address the various techniques of a parallel concatenation of LDPC code in code theory. Method/Finding: To reduce the complexity of encoding and decoding for longer codes various parallel concatenation of LDPC coding methods were introduced and the performance was compared with other work. Novelty: When a longer block length is used, the parallel LDPC decoder is suffered from the complexity of prohibitive implementation. To overcome this issue and to achieve the best performance for longer codes, the different methods for parallel concatenation of LDPC codes were introduced with reduced complexity. This will helps to break the long and complex LDPC code into less complex and smaller LDPC to distribute the decoding and encoding load. Also, this will provides scalability and scope for improving the performance of LDPC codes in practical delay-sensitive and energy-aware applications. Keywords: Parallel concatenation; LowDensity ParityCheck (LDPC); turbo codes; Parallel Concatenated Gallager Codes (PCGC)

Application Analysis of Low Density Parity Check Code for Wireless Network

The Low Density Parity Check (LDPC) codes use an iterative decoding algorithm. The advantages of this algorithm are: the algorithm is completely parallel, so the decoding speed is extremely high; the complexity of the decoding algorithm is low, and the amount of calculation will not increase sharply due to the increase of the code length. It is incomparable with convolutional code and other group codes. A good compromise can be obtained in complexity and performance. Even for the same decoding algorithm, different iteration times can be selected according to channel conditions and system requirements, which is very flexible. In this paper, we review the construction and decoding of LDPC, analyze their advantages and provide their direction of future works.

Two Low-complexity Symbol Flipping Decoding Algorithms for Non-binary LDPC Codes

Two low-complexity symbol flipping decoding algorithms, the Improved weighted-Algorithm B algorithm (Iwtd-AlgB) and the Truncation-based Distance-Symbol-Flipping-Decoding with Prediction (TD-SFDP) algorithm, are presented for non-binary Low Density Parity Check (LDPC) codes. For the Iwtd-AlgB algorithm, the scaling factor of the flipping metric can be replaced by the simple sums of the extrinsic information and the distance-based parameter, which can avoid the multiplication operations in the iterations and thus can reduce the decoding complexity. For the presented TD-SFDP algorithm, the variable nodes and the finite field symbols are truncated and classified based on the extrinsic information frequency and the flipping function. Only those nodes/symbols that satisfy the designed conditions can be involved in the message updating process. Simulations and numeric results show that, the presented two decoding algorithms can reduce the computational complexity at each iteration with a controllable performance degradation, thus can make efficient trade-offs between performance and complexity.

Mitigating the Interference Caused by Pilot Contamination in Multi-cell Massive Multiple Input Multiple Output Systems Using Low Density Parity Check Codes in Uplink Scenario

The effects of pilot contamination (PC) on the performance of multi-cell multi-user massive multiple input multiple output (MC-MU-m-MIMO) system in uplink has been analyzed in this article. In a multi-cell scenario, the channel estimation (CE) at the desired cell using pilot reuse to avoid significant overhead results in poor CE due to PC. The improvement in degraded performance due to the effect of PC has been shown using low Density Parity Check (LDPC) codes. The comparative analysis of performance in terms of variation in bit error rate (BER) with the signal to noise ratio (SNR) for LDPC coded and uncoded information blocks of users has been shown when the number of cells sharing the same frequency band is varied. Further, the expression for sum-rate has been derived and its variation with the number of base station (BS) antennas has also been shown. The simulated results have shown that the LDPC coded scheme performs better than the uncoded counterpart and the sum-rate capacity increases when the strength of channel coefficients between the BS antennas of the desired cell and the users of remaining cells is less.

An Empirical Comparison of Encoding Algorithms of the Low Density Parity Check Code for Decode and Forward Protocol Relay System

Decode and a forward (DF) protocol relay technique in cooperative communication is becoming a more attractive method to achieve a higher throughput requirement for wireless communication these days. But the high complexity operation is a major issue in the DF protocol relay processing system. The encoding operation which is a pre-processing stage of the decoding process consumes high complexity in the DF protocol relay system. Thus, it is important to tackle the encoding operation to ensure low complexity and good performance of the subsequent decoding operation in the DF protocol relay system. Thus far, very limited works have been reported on identifying a suitable encoding algorithm of encoding operation for the DF protocol relay system using the Low Density Parity Check (LDPC) code. In this paper, we present a suitable encoding algorithm for the DF protocol relay system using the LDPC code. To find out the most suitable encoding algorithm for the DF protocol relay system using LDPC code, we introduce the LDPC code encoding model. Eight different encoding algorithms based on Lower Upper and Orthogonal Upper algorithms presented in the LDPC code encoding model. The encoding execution time, the number of nonzero, and the pattern of nonzero was used to evaluate the computational complexity performance of the designed LDPC code encoding model. The most suitable encoding algorithm for the required criteria of the DF protocol relay system using the LDPC code is identified.