Check Codes Research Articles

Performance Evaluation of 5G New Radio Low Density Parity Check Codes over Different Scenarios of Lognormal Fading Channel

Performance Evaluation of 5G New Radio Low Density Parity Check Codes over Different Scenarios of Lognormal Fading Channel

ANALYSIS OF DEVELOPMENT TRENDS IN MODERN BUSINESS COMMUNICATIONS

Advanced communication techniques are used to organize fixed-user access to corporate communication network (CCNs) resources, with the ability to quickly change the encoding speed during network overloads. Estimating the probability of a denial of service caused by a lack of free channel resources at Access Network was one of the research's aims. IP based network enable the delivery of different services. Primary determinants of users' subjective quality evaluation of communication: data transmission: fast, without errors or failures; video communication: high-quality images, no delays; audio communication: no voice distortion, no call failures. Important to network operators to make effective use of their own resources while maintaining transmission quality standards. Control over metrics such packet loss ratio, delay variations, and latency is crucial. For certain corporate networks, the implementation of 5G mobile communication equipment holds great potential, especially in terms of enabling remote access for staff members. Simultaneously, concerns over unauthorized access to information and the risk of packet loss during transmission have become increasingly pressing. This paper discusses the effectiveness of Low-Density Parity Check (LDPC) codes and polar codes in variable length packet transmission in a 5G system. The modeling results of 5G communication system operation at a fixed value of packet loss are discussed.

Parity Check Codes for Second Order Diversity

Short block length “block” codes are typically not used in wireless standards as soft decision decoding is computationally intensive and hard decision decoding results in performance loss. However, short block lengths are of interest to massive machine-type communications (mMTC) and ultra-reliable low-latency communications (URLLC). In this paper, we propose a diversity preserving enhanced hard-decision decoding scheme for parity check codes (PCC) over Rayleigh fading channels. The proposed flip decoding scheme has linear complexity in the block length. Theoretical analysis and simulation results verify the correctness of the proposed detection scheme.

Efficient Protection of FPGA Implemented LDPC Decoders Against Single Event Upsets (SEUs) on Configuration Memories

Low Density Parity Check (LDPC) codes are used in 5G systems for traffic channels due to their excellent error correction capability for long sequences, and the Min-Sum algorithm is widely applied in practical implementations of LDPC decoders due to its low complexity. If the decoder is implemented on a SRAM-based field-programmable gate array (SRAM-FPGA), the radiation-induced single-event upsets (SEUs) can affect the operation of the LDPC decoder by corrupting the configuration memory, which can change the circuit functionality and will not be corrected unless the FPGA is reconfigured. Therefore, protection of LDPC decoders with low overhead is an important problem, especially for resource-limited on-board space systems. In this paper, an efficient Duplicate With Comparison (DWC) protection scheme is proposed based on the different distribution of the parity check sum of the LDPC decoder in the error-free case and the faulty case. In particular, the check sum accumulation number and threshold are optimized to achieve high detection probability with short delay. FPGA based implementation and hardware fault injection experiments are conducted to evaluate the performance of the proposed schemes. Experimental results show that, the effect of SEUs on the LDPC decoder can be completely eliminated by the proposed scheme with 2 times computational overhead and 1.69 times power consumption overhead compared to the unprotected decoder.

Concatenated Forward Error Correction With KP4 and Single Parity Check Codes

Concatenated forward error correction is studied using an outer KP4 Reed-Solomon code with hard-decision decoding and inner single parity check (SPC) codes with Chase/Wagner soft-decision decoding. Analytical expressions are derived for the end-to-end frame and bit error rates for transmission over additive white Gaussian noise channels with binary phase-shift keying (BPSK) and quaternary amplitude shift keying (4-ASK), as well as with symbol interleavers and quantized channel outputs. The BPSK error rates are compared to those of two other inner codes: a two-dimensional product code with SPC component codes and an extended Hamming code. Simulation results for unit-memory inter-symbol interference channels and 4-ASK are also presented. The results show that the coding schemes achieve similar error rates, but SPC codes have the lowest complexity and permit flexible rate adaptation.

Analysis of MMSE Multiuser Detector in a Low-density Parity Check Coded Large Scale MIMO OFDM

Background: Large-scale MIMO OFDM technique satisfies the demands on performance and the service quality preferred in wireless communication systems. Since numerous antenna terminals have been incorporated in the base station, multiuser detection is crucial for retrieving the data appropriately. Thus, the complexities of the detectors increase rapidly in large-scale MIMO OFDM schemes. Objective: This work is a solution to achieve an extensively high rate of data transmission, which will help improve the capacity of the LS MIMO OFDM system. Methods: A unique detection approach of multiuser detection in LS MIMO OFDM model with channel coding, like Low Density Parity Check Codes (LDPC), is suggested in this paper. The LDPCcoded large-scale MIMO OFDM system has also been analysed in the study with users of around ten at the transmitter and several antennas in the base station. Results: BER of the LDPC-coded LS MIMO OFDM exhibited a waterfall region for SNR greater than 6dB as the study has been done with different decoding iterations. The BER performance worsened with the increase in modulation symbols. The study has shown how the BER performance has improved with respect to the increasing fading channels and subcarriers. Conclusion: The proposed system exhibited performance closer to the MIMO capacity with low complexity MMSE detection. The multiuser detector of LDPC-coded LS MIMO OFDM has been analysed by error rate in received bits (BER) with respect to different parameters, such as modulation orders, iteration values, receiving antennas, and OFDM subcarriers.

Multimedia Authentication Through Digital Tattooing Scheme at IoT Perception Layer for Smart City

The move to a digital environment, where consumers may utilise, process, store, and transfer their data, has occurred in recent years. Furthermore, the quick and ongoing evolution of the Internet of Things (IoT) has resulted in a massive increase in the utilisation of digital signals and images. The Internet of Things (IoT) is a huge and varied network of connected devices, everyday objects, and gadgets that can communicate with one another over the Internet. The Internet of Things has a lot of potential to become a part of everyday life and improve people’s lives. In recent decades, digital tattooing has been offered as a great way to handle numerous elements of IoT security. This technology works by embedding a digital signal called a digital tattoo into another digital signal called a host signal, which can be text, image, audio, or video. The principle of this approach is to detect changed pixels using the Cyclic Redundancy Check (CRC) code. The CRC is a data integrity check that is both powerful and simple to use. It is the most used method of mistake detection in telecommunications. For these reasons, it has been used in the context of the fragile tattoo to determine whether or not the picture has been altered. The experimental results show that the proposed schemes perform well in contrast to the existing scheme and use traditional evaluation criteria, proving that the new scheme is distinctive.

Reduced complexity XOR trees for LDPC codes and BS-LFSR techniques to High-Speed memory applications

Low-Density Parity Check (LDPC) Codes exhibit dominant role which deal with limitation of storage capacity. Hardware realization of Parity Check Codes is slow and consumes more power which makes it vulnerable for the light weight applications. Hence, to improve the throughput, area and power dissipation, parity check architectures must be constrained. This article proposes architecture of LDPC codes for high-speed memory applications with comparable XOR-gate tree-based VLSI design. The designed extension module includes Bit Swapping Linear Feedback Shift Register (BS-LFSR) technique that can illustrate and gauge expansion of faults in both the versions of faulty and fault-free. Furthermore, the power dissipation has been reduced by 8% and area by 83% with its extension module. This work has been designed using Vivado HLS and the hardware implementation of BS-LFSR has been verified on Zync 7000 series FPGA board for faulty and fault-free test patterns.

Joint Optimization of OFDM and Channel Coding for URLLC in Industrial Channels

Industrial communications have very tight requirements of reliability and latency, which are challenging to achieve at highly dynamic industrial radio channels. Redundancy in the modulation and coding can improve reliability but incurs excess latency. Minimizing latency subject to reliability constraint for a given channel state opens up the scope for static and runtime optimization. In this paper we explore joint optimal configuration of Orthogonal Frequency Division Multiplexing (OFDM) and channel coding, using polar, Low Density Parity Check (LDPC) and convolutional codes to minimize the transmission time subject to a maximum acceptable packet error rate, for three realistic channels reported by National Institute of Standards and Technology, using channel impulse response measurements, as well as perfect and imperfect channel estimation. The results show that the use of strong channel codes can significantly reduce transmission time, by up to 24% compared to convolutional codes, with LDPC achieving fastest transmission. For transmission times of 10-20 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> s the contribution of the Cyclic Prefix (CP) is significant, up to 30% for convolutional codes. Stronger channel codes allow reduced CP, even considering the added redundancy such as Cyclic Redundancy Check (CRC), resulting in overall lower transmission time. The decoding time also introduces significant overheads, up to 50% of transmission time for polar codes. The paper also investigates the impact of channel estimation errors, which adversely impact Ultra-Reliable Low-Latency performance: lower bound errors violate the reliability constraint and higher bound errors introduce excess transmission times.

A Cascade Network for Blind Recognition of LDPC Codes

Coding blind recognition plays a vital role in non-cooperative communication. Most of the algorithm for coding blind recognition of Low Density Parity Check (LDPC) codes is difficult to apply and the problem of high time complexity and high space complexity cannot be solved. Inspired by deep learning, we propose an architecture for coding blind recognition of LDPC codes. This architecture concatenates a Transformer-based network with a convolution neural network (CNN). The CNN is used to suppress the noise in real time, followed by a Transformer-based neural network aimed to identify the rate and length of the LDPC codes. In order to train denoise networks and recognition networks with high performance, we build our own datasets and define loss functions for the denoise networks. Simulation results show that this architecture is able to achieve better performance than the traditional method at a lower signal-noise ratio (SNR). Compared with the existing methods, this approach is more flexible and can therefore be quickly deployed.

Block-Wise Computation of Cyclic Redundancy Code Using Factored Toeplitz Matricesin Lieu of Look-Up Table

Cyclic Redundancy Check (CRC) or Cyclic Redundancy Code is a Cyclic Error Detection Code used to preserve the integrity of data in storage and transmission applications. CRC of a stream of message bits is usually calculated block-wise in parallel with the help of a Look-Up Table (LUT) in software or State Space transformation matrix in hardware. Presented here is a novel method and architecture of parallel computation of Cyclic Redundancy Codes without any Look-Up Table for an arbitrary generating polynomial which is programmable at runtime. The method reduces computational complexity and storage requirements by implicitly factorizing the transformation matrix needed to compute the remainder into two simpler Toeplitz matrices. The resulting hardware architecture is suitable for embedded applications.

Comparison between dicode PPM and offset PPM enhancement with different error correction codes

AbstractOffset pulse position modulation (OPPM) and Dicode pulse position modulation (DiPPM) have been introduced as new attractive modulation techniques, however, they are suffering from erasure, wrong slot, and false alarm errors. in this paper, two types of error correction (EC) codes, Low‐Density Parity Check (LDPC) code and Reed Solomon (RS) code, where paired the OPPM and DiPPM systems to reduce bugs, analyze the best EC parameters, and choose the superlative EC system. In other words, the performance of OPPM engaging LDPC codes and DiPPM employing LDPC codes will be compared against the OPPM engaging RS codes and DiPPM employing RS codes. To systematically carry out this comparison, numbers of photons, transmission efficiency, and the code rate are computed. The evaluation has stated that the data transmission rate at the start has indicated that OPPM with LDPC requires only 1.2 × 103 photons/pulse compared to the necessity of 1.821 × 103 photons/pulse when the DiPPM used LDPC. Accordingly, the transmission efficiency has been increased due to a reduction of number of photons. Also, the coded OPPM with LDPC codes is better than the coded DiPPM with LDPC codes when operating at a code rate that is approximately 0.7.

Construction of Cyclic Redundancy Check Codes for SDDC Decoding in DRAM Systems

Single device data correction (SDDC) is a main reliability, availability, and serviceability feature of DRAM systems in servers due to the significant hard-failure rate associated with DRAM devices. To correct errors in one DRAM device, error pattern is determined by even parity bits and error location is determined by the error pattern and cyclic redundancy check (CRC) bits in SDDC decoding. In this brief, a SDDC decoding scheme is proposed, which improves the error-correction performance by uniquely determining the error location. For that purpose, requirements for binary CRC generator polynomials to uniquely determine the error location are derived. Based on these requirements, a systematic method for constructing CRC generator polynomials is proposed, which guarantees 100% error-correction rate. Finally, it is confirmed that the proposed SDDC decoding scheme has lower decoding complexity compared with various ECC schemes and also shows 100% SDDC decoding success through simulation.

Adding RLL Properties to Four CCSDS LDPC Codes without Increasing Their Redundancy

This paper presents the construction of Run Length Limited (RLL) Error Control Codes (ECCs) from four Low Density Parity Check (LDPC) Codes specified by Consultative Committee for Space Data Systems (CCSDS). The obtained RLL-ECCs present a practical alternative to the CCSDS codes with pseudo-randomizers. Their advantage is that the maximal runlengths of equal symbols in their codeword sequences are guaranteed, which is not the case if the common approach with pseudo-randomizers is used. The other advantages are that no additional redundancy is introduced into encoded codewords and that the encoding and decoding procedures of the original error control CCSDS codes do not have to be modified in the following cases. In the first case if hard decoding is used and the transmission channel can be modeled as a Binary Symmetric Channel (BSC) or in the second case if soft decoding and coherent Binary Phase Shift Keying (BPSK) modulation is used and the appropriate transmission channel model is an Additive White Gaussian Noise (AWGN) channel.

Transmission Performance of Probabilistic Shaping Orthogonal Frequency Division Multiplexing Radio-over-Fiber Communication System Based on Low Density Parity Check Code

Transmission Performance of Probabilistic Shaping Orthogonal Frequency Division Multiplexing Radio-over-Fiber Communication System Based on Low Density Parity Check Code

Minimum-Rate Spectrum-Blind Sampling Based on Sparse-Graph Codes

We study the problem of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">spectrum-blind</i> sampling, that is, sampling signals with sparse spectra whose frequency support is unknown. The minimum sampling rate for this class of signals has been established as twice the measure of its frequency support; however, constructive sampling schemes that achieve this minimum rate are not known to exist, to the best of our knowledge. We propose a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">constructive</i> sampling framework by leveraging a mix of tools from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">modern coding theory</i> , which has been largely untapped in the field of sampling. We make interesting connections between the fundamental problem of spectrum-blind sampling, and that of designing erasure-correcting codes based on sparse graphs, which have both theoretically and practically revolutionized the design of modern communication systems. Our key idea is to cleverly exploit, rather than avoid, the resulting aliasing artifacts induced by subsampling, which introduce linear mixing of spectral components in the form of parity constraints for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sparse-graph codes</i> . We achieve this by subsampling the input signal after filtering it using a carefully designed ‘sparse-graph coded filter-bank’ structure, where the pass-band on/off patterns of the filters are designed to match the parity-check constraints of a sparse-graph code. We show that the signal reconstruction under this sampling scheme is equivalent to the fast message-passing based “peeling” decoding of sparse-graph codes for reliable transmission over erasure channels. Most importantly, we further show that the achievable sampling rate is determined by the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rate</i> of the sparse-graph codes used in the filter bank. As a result, based on insights derived from the design of capacity-achieving sparse-graph codes (such as Low Density Parity Check codes), we can <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">simultaneously</i> approach the minimum sampling rate for spectrum-blind sampling and low computational complexity based on fast peeling-based decoding with operations per unit of time scaling <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">linearly</i> with the sampling rate.

Study of Different Coding Methods of Polar code in 5G Communication system

Sure, most of you are aware that right now everyone is thinking or at least the industry and researchers are thinking about the next generation, the first generation of what will 5G be, and that a significant part of the 5G telecommunication standard has been finalised, in particular the error control codes that will be used in 5G telecommunication. One of the codes that will be used is called a Low-Density Parity Check code (or LDPC code for short), and the other is called Polar Code. These two famous and celebrated codes have distinct and fascinating histories. Both technologies are now capable of providing near-capacity results, making them formidable competitors in the race to become the 5G communication system's ultimate provider. In this paper, we zeroed in on the 5G Polar codes and their encoding methods.

Minimum-Integer Computation Finite Alphabet Message Passing Decoder: From Theory to Decoder Implementations towards 1 Tb/s

In Message Passing (MP) decoding of Low-Density Parity Check (LDPC) codes, extrinsic information is exchanged between Check Nodes (CNs) and Variable Nodes (VNs). In a practical implementation, this information exchange is limited by quantization using only a small number of bits. In recent investigations, a novel class of Finite Alphabet Message Passing (FA-MP) decoders are designed to maximize the Mutual Information (MI) using only a small number of bits per message (e.g., 3 or 4 bits) with a communication performance close to high-precision Belief Propagation (BP) decoding. In contrast to the conventional BP decoder, operations are given as discrete-input discrete-output mappings which can be described by multidimensional LUTs (mLUTs). A common approach to avoid exponential increases in the size of mLUTs with the node degree is given by the sequential LUT (sLUT) design approach, i.e., by using a sequence of two-dimensional Lookup-Tables (LUTs) for the design, leading to a slight performance degradation. Recently, approaches such as Reconstruction-Computation-Quantization (RCQ) and Mutual Information-Maximizing Quantized Belief Propagation (MIM-QBP) have been proposed to avoid the complexity drawback of using mLUTs by using pre-designed functions that require calculations over a computational domain. It has been shown that these calculations are able to represent the mLUT mapping exactly by executing computations with infinite precision over real numbers. Based on the framework of MIM-QBP and RCQ, the Minimum-Integer Computation (MIC) decoder design generates low-bit integer computations that are derived from the Log-Likelihood Ratio (LLR) separation property of the information maximizing quantizer to replace the mLUT mappings either exactly or approximately. We derive a novel criterion for the bit resolution that is required to represent the mLUT mappings exactly. Furthermore, we show that our MIC decoder has exactly the communication performance of the corresponding mLUT decoder, but with much lower implementation complexity. We also perform an objective comparison between the state-of-the-art Min-Sum (MS) and the FA-MP decoder implementations for throughput towards 1 Tb/s in a state-of-the-art 28 nm Fully-Depleted Silicon-on-Insulator (FD-SOI) technology. Furthermore, we demonstrate that our new MIC decoder implementation outperforms previous FA-MP decoders and MS decoders in terms of reduced routing complexity, area efficiency and energy efficiency.

Adaptive Gradient Descent Bit-Flipping Diversity Decoding

In this letter we propose a novel framework for designing decoders, for Low-Density Parity Check (LDPC) codes, that surpasses the frame error rate performance of Belief-Propagation (BP) decoding on binary symmetric channels. Its key component is the adaptation method, based on the genetic optimization algorithm, that is incorporated into the recently proposed Gradient Descent Bit-Flipping Decoding with Momentum (GDBF-w/M). We show that the resulting decoder outperforms all state-of-the-art probabilistic bit-flipping decoders and, additionally, it can be trained to perform beyond BP decoding, which is verified by numerical examples that include codes used in IEEE 802.3an and 5GNR standards. The proposed framework provides a systematic method for decoder optimization without requiring knowledge of trapping sets. Moreover, it is applicable to both regular and irregular LDPC codes.

Improved Layered Normalized Min-Sum Algorithm for 5G NR LDPC

Layered Normalised Min-Sum algorithm is a widely used message passing algorithm for decoding Low Density Parity Check codes. The decoding performance heavily depends on the normalisation factor. Firstly, we leverage the bit structure present in 5G transport blocks to develop an improved decoding algorithm for 5G. Secondly, we determine the optimal normalisation factors of the proposed algorithm using a Deep Neural Network. Performance evaluations show an improvement of 0.3-1.9 dB, with no extra cost on multiplier resources on hardware. Hence, the proposed method is highly attractive for practical 5G decoder implementations.