Single Parity Research Articles

Errors, error detection and correction efficiency in the container number code

The container number is an 11-digit code that uses a single parity check of modulo 11 to check the authenticity of the container numbers. The world relies on shipment containers to transport goods. Various types of cargos have been erroneously delivered in different places. The modulo 11 container number is divided into four parts. The owner code that consists of three capital letters of the Latin alphabet to indicate the owner or principal operator of the container. Such code needs to be registered at the Bureau International des Conteneurs in Paris to ensure uniqueness worldwide (per ISO 6346). The equipment category identifier consists of one of the following three capital letters of the Latin alphabet U for all freight containers, J for detachable freight container-related equipment, Z for trailers and chassis. The serial number consists of six numeric digits, assigned by the owner or operator, uniquely identifying the container within that owner/operator’s fleet. The check digit consists of one numeric digit providing a means of validating the recording and transmission accuracies of the owner code and serial number. The objective of this study is to determine the efficiency of the current modulo 11 container number in the error detection and correction. While the modulo 11 checksum calculation method is an effective way to detect errors in container numbers, it is not foolproof and errors can still occur. Modulo 11 container number code does not detect some transposition and substitution errors. The container number code and its check digit do not possess inherent error correction capabilities. This study therefore recommends a new modulo 13 container number code with higher error correction and detection capability.

Improved adaptive belief propagation algorithm with reduced complexity for concatenated SPC‐RS codes

AbstractIn this letter, a novel single parity check‐aided minimum sum (SPC‐aided MS) algorithm is proposed. A cascaded compiled code scheme is used to approximate the adaptive belief propagation (ABP) algorithm for Reed–Solomon (RS) codes using the min sum (MS) algorithm. The computational complexity is greatly reduced compared with the previous algorithm. Simulation results show that the SPC‐aided MS algorithm can achieve coding gains of up to 1.1, 0.7, and 0.6 dB for RS (255,239) code compared with the conventional ABP, LRBP, and HD‐P‐ABP algorithms, respectively under the condition of .

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.

Application of the method of equivalent message encoding structures to simplify coding complexity

Formulation of the problem. Modern telecommunication technologies make it possible to transmit data over long distances with limitations in the form of low power consumption and low error rate using error correction codes. The use of such codes plays an important role and is necessary to detect and correct errors caused by signal distortion and noise in the communication channel. According to Shannon's channel coding theorem, the probability of error can be arbitrarily small or close to zero if the encoding rate of transmission R is less than or equal to the bandwidth of channel C. Assuming that the bandwidth C is achievable, we can calculate the minimum signal-to-noise power ratio (SNR) to achieve zero error, or an arbitrarily small error called the Shannon limit, while maintaining R ≤ C. This article discusses a method of applying equivalent message encoding structures to construct low-density parity-checking (LDPC) codes. Low-density parity-checking (LDPC) codes are a class of linear block codes in which the complexity of iterative decoding increases linearly with increasing block length. Standard LDPC codes without modifications are considered to demonstrate the effectiveness of the proposed method, which is expected to provide high encoding speed when transmitting messages with a short block length. The method of obtaining equivalent structures allows: to reduce the computational complexity of encoding and decoding; to provide the possibility of finding a new encoding scheme and evaluating its effectiveness. The validity of the method for obtaining equivalent message encoding structures is evaluated by modeling the bit error rate (BER) of LDPC codes. Purpose. to show the effectiveness of the use of equivalent structures for various methods of compression of transmitted information, to minimize the complexity of encoding, while maintaining energy efficiency, correcting ability and data transfer rate. Results. A method is considered for obtaining equivalent message element encoding structures that can be used to create more LDPC codes for data transmission applications with a short block length. The cascade principle of constructing an equivalent generator and a parity check matrix was analyzed, which also leads to minimizing the computational complexity of the encoder and decoder. An equivalent structure G can be obtained from cascading two (or more) matrices by modifying the second matrix so that it has a unit matrix with the size of the parity check length and a shift to the right by k bits. On the other hand, the equivalent structure H can be obtained by simply cascading directly the second matrix and shifting to the right by k bits. According to the simulation results, the proposed method is adequate, since LDPC codes have the same BER characteristics as codes based on the low density generator matrix (LDGM). During the simulation, it was concluded that the SPC codes (single parity check (single parity check (SPC)) are the most efficient codes (for a given block length), since SPC codes have the smallest interval up to the Shannon limit. Practical significance. The results presented in this article will give a new insight into the development of simple channel coding of LDPC codes of short block length with high encoding speed for future applications with lower power consumption.

A Modified 2D-Checksum Error Detecting Method for Data Transmission in Noisy Media

In data transmission a change in single bit in the received data may lead to miss understanding or a disaster. Each bit in the sent information has high priority especially with information such as the address of the receiver. The importance of error detection with each single change is a key issue in data transmission field.The ordinary single parity detection method can detect odd number of errors efficiently, but fails with even number of errors. Other detection methods such as two-dimensional and checksum showed better results and failed to cope with the increasing number of errors.Two novel methods were suggested to detect the binary bit change errors when transmitting data in a noisy media.Those methods were: 2D-Checksum method and Modified 2D-Checksum. In 2D-checksum method, summing process was done for 7×7 patterns in row direction and then in column direction to result 8×8 patterns. While in modified method, an additional parity diagonal vector was added to the pattern to be 8×9. By combining the benefits of using single parity (detecting odd number of error bits) and the benefits of checksum (reducing the effect of 4-bit errors) and combining them in 2D shape, the detection process was improved. By contaminating any sample of data with up to 33% of noise (change 0 to 1 and vice versa), the detecting process in first method was improved by approximately 50% compared to the ordinary traditional two dimensional-parity method and gives best detection results in second novel method

High-Performance Soft Decision Decoding for Compound Channel Using RS-SPC Concatenated Codes

A novel single parity check-assisted ordered statistic decoding (SPC-OSD) algorithm for the compound channel is proposed for Reed-Solomon (RS) codes. The algorithm can effectively use the channel soft information to accurately determine the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N - K</i> unreliable symbol positions to be erased by using single parity checking and threshold comparison. Besides that, the second-burst error symbol is also proposed as a supplement to unreliable symbols. Based on these predetermined errors, the algorithm can be dynamically adjusted according to the channel environment to achieve the best decoding performance. Compared with burst-error correcting algorithm-based ordered-statistics decoding (BC-OSD) and burst error correcting hard-decision decoding-based low-complexity chase algorithm (BCHDD-LCC), simulation results show that the proposed algorithm can give a coding gain reaching up to 2.0dB and 2.1dB respectively, when symbol error rate (SER) is 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> .

Single parity check node adapted to polar codes with dynamic frozen bit equivalent to binary linear block codes

&lt;span lang="EN-US"&gt;In the context of decoding binary linear block codes by polar code decoding techniques, we propose in this paper a new optimization of the serial nature of decoding the polar codes equivalent to binary linear block codes. In addition to the special nodes proposed by the simplified successive-cancellation list technique, we propose a new special node allowing to estimate in parallel the bits of its sub-code. The simulation is done in an additive white gaussian noise channel (AWGN) channel for several linear block codes, namely bose–chaudhuri–hocquenghem codes (BCH) codes, quadratic-residue (QR) codes, and linear block codes recently designed in the literature. The performance of the proposed technique offers the same performance in terms of frame error rate (FER) as the ordered statistics decoding (OSD) algorithm, which achieves that of maximum likelihood decoder (MLD), but with high memory requirements and computational complexity.&lt;/span&gt;

A Low-Complexity Sorting Network for a Fast List Polar Decoder

Fast list decoding algorithms for polar codes have been proposed to achieve low latency and high error correction performance. In the Rate-1 and SPC nodes of fast list decoding, a high-complexity sorter is required if multiple bits are to be decoded simultaneously in a single clock cycle. This paper proposes a partitioned sorting network (PSN) that reduces the complexity of metric sorter in Rate-1 and single parity check (SPC) decoders for fast list decoding. The proposed PSN consists of two sorting networks. For the first sorting network, we analyze the order of the path metrics (PMs) and reduce the number of input candidate paths. Furthermore, for the second sorting network, we analyze the cumulative results of path selection and identify relatively frequently selected paths. The proposed PSN has up to 90% fewer compare-and-swap units (CASUs) and up to 137% higher operating frequencies than existing sorting networks for Rate-1 and SPC decoders with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L=8$ </tex-math></inline-formula> .

A double serial concatenated code using CRC-aided error correction for highly reliable communication

Highly Reliable Communication (HRC) is an emerging paradigm for meeting the quality of service requirements of new applications such as intelligent vehicle networking and industrial Internet. HRC brings challenges to channel coding and multiple access. Various channel coding techniques have been proposed to improve reliability, but often suffer from limited reliability and high decoding complexity. This work presents a double serial concatenated code using CRC-aided error correction, abbreviated as DSC 3 EC , to improve reliability and reduce complexity. The encoding scheme is a double serial concatenated code, with the cascade of a set of CRC encoders, a linear block encoder, a series of interleavers , and a set of convolutional encoders . The decoding scheme consists of two modules: (i) decoding of serial concatenated codes, which includes the decoding of single parity check convolutional code (SPC-CC) and the decoding of Reed–Solomon convolutional code (RS-CC) for intra-block error correction at the physical layer to control BER; (ii) decoding of CRC-aided linear error correction, which can effectively identify, locate and correct error bits at the inter-block level to solve the problem of block loss caused by residual errors at the physical layer. Simulation results show that the joint scheme can effectively improve communication reliability while reducing complexity.

Impact of childbirth history on dense breast in mammographic screening: a cross-sectional study

BackgroundThe evaluation of breast density is important, because dense breast has been shown to be associated with increased risk of breast cancer and a greater risk of a false-negative diagnostic performance due to masking a tumor. Although the relationship between parity and dense breast is under investigation, conclusive evidence is lacking. We aimed to investigate whether parity affects breast density.MethodsThe study design is a cross-sectional study. The subjects are healthy Japanese women who underwent opportunistic mammographic screening at the center for preventive medicine at a single institution from January 2016 to December 2018. Clinical characteristics and lifestyle factors were obtained from questionnaires. Breast density was categorized into 4 groups, namely, almost entirely fatty dense, scattered fibroglandular dense, heterogeneously dense, and extremely dense, according to the Breast Imaging Reporting and Data System. Heterogeneously and extremely dense were considered collectively as dense breast. Multivariate logistic regression analysis was conducted to investigate the relationship between parity and dense breast among premenopausal and postmenopausal women separately.Results7612 premenopausal and 9252 postmenopausal women were investigated. Dense breast was shown in 62.6% of nulliparity, 57.3% of single parity, 47.3% of two parity, 37.6% of more than two parity among premenopausal women, and in 41.6% of nulliparity, 31.1% of single parity, 19.3% of two parity, 10.1% of more than two parity among postmenopausal women. For premenopausal women, two parity, single parity and nulliparity showed a higher risk for dense breast with statistically significance (Odds Ratio (OR) adjusted for potential confounding factors: 1.458 (95% Confidence interval (CI); 1.123–1.894), 2.349 (95%CI; 1.801–3.064), 3.222 (95%CI; 2.500–4.151), respectively), compared with more than two parity. For postmenopausal women, two parity, single parity and nulliparity had a higher risk (OR: 1.849 (95%CI; 1.479–2.312), 3.023 (95%CI; 2.385–3.830), 4.954 (95%CI; 3.975–6.174), respectively) with statistically significance, compared with more than two parity.ConclusionsParity showed an inverse trend of having dense breast among both premenopausal and postmenopausal women. In particular, nulliparous women need to recognize their higher risk of dense breast. In the future, the declining fertility rate may affect the prevalence of dense breast in the world.

On the Decoding of Lattices Constructed via a Single Parity Check

This paper investigates the decoding of a remarkable set of lattices: We treat in a unified framework the Leech lattice in dimension 24, the Nebe lattice in dimension 72, and the Barnes-Wall lattices. A new interesting lattice, named <inline-formula> <tex-math notation="LaTeX">$L_{3\cdot 24}$ </tex-math></inline-formula>, is constructed as a simple application of the single parity check on the Leech lattice. The common aspect of these lattices is that they can be obtained via a single parity check or via the <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-ing construction. We exploit these constructions to introduce a new efficient paradigm for decoding. This leads to efficient list decoders and quasi-optimal decoders on the Gaussian channel. Both theoretical and practical performance (point error probability and complexity) of the new decoders are provided.

Oviparity, viviparity or plasticity in reproductive mode of the olm Proteus anguinus: an epic misunderstanding caused by prey regurgitation?

Abstract Cave animals are biological models of fast evolutionary change induced by transition to extreme subterranean environments. But their concealed lifestyle makes it inherently difficult to study life-history changes. Therefore, currently very little is known on the reproduction of cave species, and even less is known on general patterns and potentially shared reproductive strategies. Theory predicts that the cave environment favours the production of a few well-developed offspring and live birth. For one of the most enigmatic cave animals, the olm (Proteus anguinus), it has been debated fiercely whether they reproduce by live birth (viviparity), egg-laying (oviparity) or facultatively. While successes in captive breeding after the 1950s report oviparity as the single parity mode, some historically older observations claimed viviparity. The controversial neo-Lamarckist Paul Kammerer even claimed to have induced changes in parity mode by altering environmental conditions. Here, we report on the feeding and regurgitation of fire salamander (Salamandra salamandra) larvae by olms. The salamander larvae showed clear teeth marks and other injuries on the head caused by the olm, yet one larva was still alive after regurgitation. We suggest that historical reports of olm viviparity could have been misled by regurgitated salamander larvae. Our data bring additional indications that at least some of Kammerer’s experiments were fraudulent.

Ta2NiSe5 : A candidate topological excitonic insulator with multiple band inversions

The electronic structures and topological properties of the orthorhombic and monoclinic phases of the quasi-one-dimensional excitonic insulator Ta2NiSe5 are investigated based on density functional theory. In contrast to a single parity or band inversion across the Fermi level in many topological insulators studied previously, there are multiple parity and band inversions with or without spin-orbit coupling in both phases of Ta2NiSe5, resulting in more complex and topologically nontrivial electronic structures. The Dirac cone type surface states of the low-temperature monoclinic phase are also obtained. In this paper, we demonstrate that Ta2NiSe5 is a promising candidate as a three-dimensional topological excitonic insulator.

A Rare Case of Diprosopus Buffalo Calf in a Non-Descript Buffalo

A case of diprosopus monauchenos is described in a non-descript buffalo. A 6 year old buffalo with single parity was presented along with a live defective male calf was presented to the clinic. The congenital defective male calf was delivered normally by the dam. The major gross anatomical malformations were restricted to the head only. Physical examination revealed two oral cavities and both of them fused medially forming a single epiglottis and oesophagus. The male calf survived only for a week on hand-feeding of milk. This is the first diprosopus case report in buffalo calf from Jammu and Kashmir, India

Detection of Limited Magnitude Errors in Emerging Multilevel Cell Memories by One-Bit Parity (OBP) or Two-Bit Parity (TBP)

Emerging memory technologies rely on Multilevel Cells (MLC) to achieve high density; the use of multiple levels per cell allows storage of multiple bits, but it also reduces the margins and makes it error prone. Error control codes (including error correction and detection codes) can be used to protect MLC memories from errors; however, most existing coding schemes have been designed for traditional binary memories (so storing a single bit). In MLC memories, errors cause a change from a level to an adjacent level or to the next one (depending on the employed technology), so they are often referred to as limited magnitude errors. For a binary coding of levels to bits, these limited magnitude errors can corrupt several bits making traditional coding schemes inefficient. In this paper, error detection of MLC memories is considered when a binary encoding of levels to bits is used and two new schemes are proposed: One-Bit Parity (OBP) and Two-Bit Parity (TBP). The first scheme targets errors of magnitude-1 for detection using a single parity bit that checks only one bit per cell. The second scheme detects both magnitude-1 and -2 errors using only two parity bits. Both schemes are compared to existing alternatives, namely Gray coding combined with a single parity bit (GP) for OBP and Interleaved Parity (IP) for TBP. The results show that OBP reduces the encoding and error detection circuitry complexity and delay, while TBP additionally reduces the number of parity bits for some configurations. Therefore, OBP and TBP can be efficient alternatives for detection of limited magnitude errors in MLC memories that use a binary encoding of levels to bits.

High-Performance Concatenation Decoding of Reed–Solomon Codes With SPC Codes

A novel single parity check-multiplicity assignment decoding algorithm based on voltage magnitude (VM_SPC-MA) is proposed, which is applied to the concatenated scheme of single parity check (SPC) inner code and Reed-Solomon (RS) outer code, following the Consultative Committee for Space Data Systems (CCSDS) standard. The algorithm determines whether the SPC code is in error by SPC, then obtains the reliability information of the inner code bits for error correction based on the characteristics of the received bit-level voltage, and decodes the outer code based on the reliability information of the inner codewords and the channel information. The decoding performance is greatly improved by connecting the inner and outer codes through the multiplicity assignment (MA) module, which makes full use of the channel information. Compared with the low-complexity Chase decoding based on the hard-decision decoding (HDD-LCC) and SPC_Kaneko-RS_Chase decoding, simulation results show that the SPC-RS concatenated decoding scheme based on VM_SPC-MA algorithm can provide up to 1.78 and 1.05 dB of coding gain when the bit error rate is (BER) = 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> . Besides, the hardware design of the SPC-MA module is provided and applied to the serial LCC decoder based on syndrome calculation-polynomial selection (PS)-Chien search and Forney algorithm (SPCF). The implementation results in ASIC show that the area efficiency of the complete concatenated decoder increases by 27.38% compared to the unified syndrome computation (USC)-based LCC decoder in a 0.13- μm process.

Design of LDBCH Codes for Ultra Reliable Low Latency Communications

In ultra reliable low latency communications, the demanding requirements on high reliability and low latency make it a challenge to design capable channel codes. In this work, a candidate named low-density BCH-constraint (LDBCH) code is introduced, which generalizes low-density parity-check codes by replacing the single parity check code constraints with the BCH code constraints. Specifically, a design methodology is introduced to construct efficient LDBCH codes of short information lengths and low coding rates. Moreover, the message passing decoding of LDBCH is enhanced by max-log approximation and weighted scaling when updating the BCH check nodes. Numerical results show that, with tolerable increase of decoding complexity, LDBCH codes with the proposed decoding enhancement outperforms CA-Polar and 5G LDPC by about 0.3 dB and 0.5 dB in SNR, respectively, for the information length of 104 and the block error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">- 6</sup> over an AWGN channel with QPSK modulation.

Low Maternal Immunoglobulin G Avidity and Single Parity as Adverse Implications of Human Cytomegalovirus Vertical Transmission in Pregnant Women with Immunoglobulin M Positivity.

Human cytomegalovirus (CMV) is the leading cause of neurological sequelae in infants. Understanding the risk factors of primary CMV infection is crucial in establishing preventive strategies. Thus, we conducted a retrospective cohort study to identify risk factors of vertical transmission among pregnant women with immunoglobulin (Ig) M positivity. The study included 456 pregnant women with IgM positivity. Information on age, parity, occupation, clinical signs, IgM levels, and IgG avidity index (AI) was collected. The women were divided into infected and non-infected groups. The two groups showed significant differences in IgM level, IgG AI, number of women with low IgG AI, clinical signs, and number of pregnant women with single parity. In the multiple logistic regression analysis, pregnant women with single parity and low IgG AI were independent predictors. Among 40 women who tested negative for IgG antibody in their previous pregnancy, 20 showed low IgG AI in their current pregnancy. Among the 20 women, 4 had vertical transmission. These results provide better understanding of the risk factors of vertical transmission in pregnant women with IgM positivity.

Miscorrection Mitigation for Generalized Integrated Interleaved BCH Codes

The generalized integrated interleaved (GII) codes nest BCH sub-codewords to form codewords of more powerful BCH codes. They can achieve hyper-throughput decoding with excellent error-correcting performance and are among the most suitable codes for next-generation memories. However, the new storage class memories require high code rate and short codeword length. In this case, the sub-codewords have small correction capability. The miscorrections of the sub-codewords lead to much more severe degradation on the GII error-correcting performance compared to the miscorrections of classic BCH codes. This letter investigates the miscorrections in GII decoding. Three low-complexity methods are developed to identify and mitigate the miscorrections by utilizing the nested syndromes, adding one single parity to each sub-codeword, and keeping track of the error locator polynomial degree. Besides, formulas for estimating the miscorrection rates are given. Using the proposed mitigation methods, the actual GII decoding performance becomes very close to that of the case without any miscorrections.

Spatially Coupled Generalized LDPC Codes: Asymptotic Analysis and Finite Length Scaling

Generalized low-density parity-check (GLDPC) codes are a class of LDPC codes in which the standard single parity check (SPC) constraints are replaced by constraints defined by a linear block code. These stronger constraints typically result in improved error floor performance, due to better minimum distance and trapping set properties, at a cost of some increased decoding complexity. In this paper, we study spatially coupled generalized low-density parity-check (SC-GLDPC) codes and present a comprehensive analysis of these codes, including: (1) an iterative decoding threshold analysis of SC-GLDPC code ensembles demonstrating capacity approaching thresholds via the threshold saturation effect; (2) an asymptotic analysis of the minimum distance and free distance properties of SC-GLDPC code ensembles, demonstrating that the ensembles are asymptotically good; and (3) an analysis of the finite-length scaling behavior of both GLDPC block codes and SC-GLDPC codes based on a peeling decoder (PD) operating on a binary erasure channel (BEC). Results are compared to GLDPC block codes, and the advantages and disadvantages of SC-GLDPC codes are discussed.