High Coding Research Articles

A New Class of Braided Block Codes Constructed by Convolutional Interleavers

Parallel Concatenated Block (PCB) codes are conventionally represented as high-rate codes with low error correcting capability. To form a reliable and outstanding code, this paper presents a modification on the structure of PCB codes, which is accomplished by encoding some parity bits of one of their component codes. For the newly proposed code, named as the braided code, non-stuff bit-based convolutional interleavers are applied, aiming to minimize the design complexity while ensuring the proper permutations of the original message and selected parity bits. To precisely determine the error correcting capability, a tight bound for the minimum weight of braided code is presented. Additionally, further analyses are provided, which verify iterative decoding performance and the complexity of the constructed code. It is concluded that an outstanding braided code is formed by utilizing a reasonable number of iterations applied at its decoding processes, while maintaining its design complexity at a level similar to other well-known codes. The significant performance of short and long-length-based braided codes is evident in both waterfall and error floor regions.

On the Exploration of Quantum Polar Stabilizer Codes and Quantum Stabilizer Codes with High Coding Rate.

Inspired by classical polar codes, whose coding rate can asymptotically achieve the Shannon capacity, researchers are trying to find their analogs in the quantum information field, which are called quantum polar codes. However, no one has designed a quantum polar coding scheme that applies to quantum computing yet. There are two intuitions in previous research. The first is that directly converting classical polar coding circuits to quantum ones will produce the polarization phenomenon of a pure quantum channel, which has been proved in our previous work. The second is that based on this quantum polarization phenomenon, one can design a quantum polar coding scheme that applies to quantum computing. There are several previous work following the second intuition, none of which has been verified by experiments. In this paper, we follow the second intuition and propose a more reasonable quantum polar stabilizer code construction algorithm than any previous ones by using the theory of stabilizer codes. Unfortunately, simulation experiments show that even the stabilizer codes obtained from this more reasonable construction algorithm do not work, which implies that the second intuition leads to a dead end. Based on the analysis of why the second intuition does not work, we provide a possible future direction for designing quantum stabilizer codes with a high coding rate by borrowing the idea of classical polar codes. Following this direction, we find a class of quantum stabilizer codes with a coding rate of 0.5, which can correct two of the Pauli errors.

Recursive expansion of Tanner graph: A method to construct stabilizer codes with high coding rate

Recursive expansion of Tanner graph: A method to construct stabilizer codes with high coding rate

Methods of countering attacks and organizing the choice of channel protection tools when controlling aviation robotic devices

The purpose of the research is identification of organizational and technical methods of countering attacks on command and telemetry data transmission lines between aviation robotic devices and ground control points, as well as the formation of comprehensive information protection of the communication channels under consideration.Methods. The scientific article substantiates methods for mitigating and countering attacks at the physical level of the ISO/OSI open systems interaction model for organizing communication using the MAVLINK protocol for the purpose of controlling aviation robotic devices (noise-resistant coding with a high code rate (using the example of the most common code - Viterbi), extension method Frequency Hopping Spectrum (FHSS), Direct Sequence Spread Spectrum (DSSS), Multiple Input Multiple Output (MIMO) technology). A method for organizing the selection of protection and countermeasures when controlling aviation robotic devices is outlined, which consists of assessing the risks and consequences of the implementation of vulnerabilities in order to introduce countermeasures there and in such quantities that they have the greatest benefit.Results. The article discusses the main possibilities for intentional interference on the control and data transmission channels of consumer aviation robotic devices, an algorithm for assessing the risk of "leaving the route" is considered; a risk assessment option is provided in relation to the risk of an aircraft going off route, indicating the name of the attack, its likelihood, impact and resulting risk, as well as the acceptability of this risk and recommendations regarding the urgency of mitigating it; recommendations for countermeasures are presented in accordance with the acceptability of likelihood and impact; describes the relationship between risk and countermeasures used to reduce unauthorized exposure, in accordance with weighting coefficients.Conclusion. The scientific article discusses the main methods of countering attacks and unauthorized access when controlling autonomous robotic devices. The risk coefficients of attacks and countermeasures taken are considered.

LoRaWAN: The dilemma of optimal transmission parameter

Low-Power Wide-Area Network (LPWAN) technologies, particularly LoRaWAN, have gained significant attention for their ability to facilitate long-range communication with low power consumption, making them ideal for Internet of Things (IoT) applications. However, achieving optimal performance in LoRaWAN systems requires careful selection of transmission parameters such as spreading factor, bandwidth, and coding rate. This paper addresses the dilemma faced by network designers and operators in determining the optimal transmission parameters for LoRaWAN deployments. We provide an overview of the key parameters and their impact on network performance, considering factors such as latency, packet delivery rate, and energy efficiency. Furthermore, we discuss the trade-offs involved in parameter selection. Through simulations, we evaluate the performance of different parameter configurations under various network conditions and provide insights into achieving the best balance between coverage, capacity, and energy consumption in LoRaWAN deployments. Findings from the study established that using high coding rate and bandwidth only provides minimal improvement in packet delivery rate particularly at large distances but at the cost energy consumption while spreading factor remains the most important transmission parameter in LoRa networks.

BEP evaluation of 5G LDPC codes in a pre-amplified optical PPM receiver

We present results for the performance of a pre-amplified optical pulse-position modulation (PPM) receiver that utilizes the low-density parity-check (LDPC) correction codes of the 5G standard. The code construction is suitable for correcting burst errors that are introduced by PPM. Simulation results show that the LDPC codes can provide a very significant real gain, provided that the code rate is chosen appropriately. We find that the code rates that minimize the bit-error-probabilities (BEPs) of the system range between 2/3 and 22/26, with higher code rates being required in receivers that operate under increased optical noise. It is also shown that a comparable real gain is obtained for both the sum–product and min-sum decoders, while the power penalty of the latter one is only limited to 0.2 dB, when the aforementioned code rates are utilized.

Graphical structures for design and verification of quantum error correction

We introduce a high-level graphical framework for designing and analysing quantum error correcting codes, centred on what we term the coherent parity check (CPC). The graphical formulation is based on the diagrammatic tools of the ZX-calculus of quantum observables. The resulting framework leads to a construction for stabilizer codes that allows us to design and verify a broad range of quantum codes based on classical ones, and that gives a means of discovering large classes of codes using both analytical and numerical methods. We focus in particular on the smaller codes that will be the first used by near-term devices. We show how CSS codes form a subset of CPC codes and, more generally, how to compute stabilizers for a CPC code. As an explicit example of this framework, we give a method for turning almost any pair of classical codes into a CPC code. Further, we give a simple technique for machine search which yields thousands of potential codes, and demonstrate its operation for distance 3 and 5 codes. Finally, we use the graphical tools to demonstrate how Clifford computation can be performed within CPC codes. As our framework gives a new tool for constructing small- to medium-sized codes with relatively high code rates, it provides a new source for codes that could be suitable for emerging devices, while its ZX-calculus foundations enable natural integration of error correction with graphical compiler toolchains. It also provides a powerful framework for reasoning about all stabilizer quantum error correction codes of any size.

UDP-RT: A UDP-based reliable transmission scheme for power WAPS

It is expected that TCP/IP networks take the place of point-to-point fiber channels for the communications of WAPS. In TCP/IP networks, TCP does not guarantee real-time while UDP does not guarantee reliability. An efficient method is demanded for WAPS to guarantee the real-time and reliability of messages transmitted in TCP/IP networks under congestion states. To address the challenge, we propose a UDP-based reliable transmission (UDP-RT) scheme, which achieves low latency by adopting UDP at the transport layer and high reliability by adding the mechanisms of error correction, error detection, resending and timeout retransmission at the application layer. The error correction mechanism employs TPCs, which has low complexity and good performance at high code rate, to correct errors in a message. A blocking rule for TPCs considering the features of communication channels and messages of WAPS is presented. The error detection mechanism is for detecting whether all errors in the message are corrected by the error correction mechanism. The resending mechanism and the timeout retransmission mechanism (optional) is for ensuring the reliability in the two cases of message loss and not all errors corrected. Additionally, algorithms for UDP-RT are presented, and their correctness are validated through experiment. Our analyses demonstrate that the proposed scheme can meet the real-time requirements of WAPS businesses when network congesting and has higher reliability than the TCP transmission scheme and other UDP transmission schemes.

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A description of the algorithm for optimal symbol-by-symbol reception of signal structures based on block noise-resistant codes in non-binary Galois fields is given. It is shown that the basis of this algorithm is the fast spectral transformation algorithm in the Walsh–Hadamard basis with the dimension of the Galois field. It is shown that the resulting complexity of the analyzed character-by-character reception algorithm is determined by the dimension of the dual code, which determines the prospects of its application for block noise-resistant codes with a high code rate (with low redundancy). The results of modeling a character-by-symbol reception algorithm are presented in order to study noise immunity for a number of frequency-efficient digital signals with quadrature-amplitude and amplitude-phase manipulations (with frequency coefficient efficiencies of 3, 4 and 6 bps/Hz) in combination with a parity check code. It is shown that the use of a symbol-by-symbol reception algorithm provides an energy gain of up to 1.5...3.0 dB in relation to the transmission and reception of the considered series of signals without coding.

Identifying potential biases in code sequences in primary care electronic healthcare records: a retrospective cohort study of the determinants of code frequency

ObjectivesTo determine whether the frequency of diagnostic codes for long-term conditions (LTCs) in primary care electronic healthcare records (EHRs) is associated with (1) disease coding incentives, (2) General Practice (GP),...

Interpolation-based decoding of folded variants of linearized and skew Reed–Solomon codes

The sum-rank metric is a hybrid between the Hamming metric and the rank metric and suitable for error correction in multishot network coding and distributed storage as well as for the design of quantum-resistant cryptosystems. In this work, we consider the construction and decoding of folded linearized Reed–Solomon (FLRS) codes, which are shown to be maximum sum-rank distance (MSRD) for appropriate parameter choices. We derive an efficient interpolation-based decoding algorithm for FLRS codes that can be used as a list decoder or as a probabilistic unique decoder. The proposed decoding scheme can correct sum-rank errors beyond the unique decoding radius with a computational complexity that is quadratic in the length of the unfolded code. We show how the error-correction capability can be optimized for high-rate codes by an alternative choice of interpolation points. We derive a heuristic upper bound on the decoding failure probability of the probabilistic unique decoder and verify its tightness by Monte Carlo simulations. Further, we study the construction and decoding of folded skew Reed-Solomon codes in the skew metric. Up to our knowledge, FLRS codes are the first MSRD codes with different block sizes that come along with an efficient decoding algorithm.

Deriving equivalent structure of elements for low density parity check codes construction

This paper proposes a method to derive equivalent coding structures of elements to construct low density parity check (LDPC) codes. We propose stairs LDPC (SLDPC) codes to demonstrate the effectiveness of the proposed method, which is expected to be beneficial for short block-length transmissions, but providing high coding rate. The equivalent coding structures are both for transmitter and receiver to: (i) reduce the encoding and decoding computational complexity, and (ii) search possibility of finding new coding scheme and observe their performances. We evaluate the validity of the method by confirming the equality in performances of the SLDPC codes in terms of bit-error-rate (BER) followed by investigation on their performance gaps to the Shannon limit via a series of computer simulations. The results show that the SLDPC codes have the same BER performance with that of the low density generator matrix (LDGM) codes confirming the validity of the proposed equivalent matrix derivation. This result indicates that different graphs can provide the same performances, because their equivalent matrices are the same. This result is expected to open new insight for the designing simple channel coding for short block-length LDPC codes having high coding rate for future less power consumption applications.

Recursive Decoding of Reed-Muller Codes Starting With the Higher-Rate Constituent Code

Recursive list decoding of Reed-Muller (RM) codes, with moderate list size, is known to approach maximum-likelihood (ML) performance of short length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\leq 256)$ </tex-math></inline-formula> RM codes. Recursive decoding employs the Plotkin construction to split the original code into two shorter RM codes with different rates. In contrast to the standard approach which decodes the lower-rate code first, the method in this paper decodes the higher-rate code first. This modification enables an efficient permutation-based decoding technique, with permutations being selected on the fly from the automorphism group of the code using soft information from a channel. Simulation results show that the error-rate performance of the proposed algorithms, enhanced by a permutation selection technique, is close to that of the automorphism-based recursive decoding algorithm with similar complexity for short RM codes, while our decoders perform better for longer RM codes. In particular, it is demonstrated that the proposed algorithms achieve near-ML performance for short RM codes and for RM codes of length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{m}$ </tex-math></inline-formula> and order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m-3$ </tex-math></inline-formula> with reasonable complexity.

Neural decoders with permutation invariant structure

Neural decoders were introduced as a generalization of the classic Belief Propagation (BP) decoding algorithms. In this work, we propose several neural decoders with different permutation invariant structures for BCH codes and punctured RM codes. Firstly, we propose the cyclically equivariant neural decoder which makes use of the cyclically invariant structure of these two codes. Next, we propose an affine equivariant neural decoder utilizing the affine invariant structure of those two codes. Both these two decoders outperform previous neural decoders when decoding cyclic codes. The affine decoder achieves a smaller decoding error probability than the cyclic decoder, but it usually requires a longer running time. Similar to using the property of the affine invariant property of extended BCH codes and RM codes, we propose the list decoding version of the cyclic decoder that can significantly reduce the frame error rate(FER) for these two codes. For certain high-rate codes, the gap between the list decoder and the Maximum Likelihood decoder is less than 0.1 dB when measured by FER.

Performance analysis of Polar Codes in a Visible Light Communication System

One of the vital entity of any communication systems is Channel coding, which leads to the design of high performance codes for future wireless systems having low complexity encoder and decoder design. These systems will have a requirement of operating in highly reliable conditions, maximum throughput, and low and high code rates and to work with short and long information messages. Polar codes are one of the promising error correcting channel codes that can be used in these situations to obtain maximum throughput and coding gain in a communication systems because of their capacity approaching performance and finds interests in Satellite communication and 4G/5G services. These codes uses the concept of channel polarization to be constructed. The work proposed in this paper focusses on the Bit Error Rate evaluation and analysis of the Polar codes using traditional approach and Deep learning approach. The feedforward deep learning networks using different activation functions were used for the Deep learning approach. The Successive Cancellation algorithm and its variant using List decoding were used as traditional decoding methodology. The results obtained using Deep learning approach were satisfactory and was matching as per the traditional decoding.

Differential properties of polar codes

This paper discusses the features of polar coding as a differential encoder for a binary erasure channel. One of the modern methods of error-correcting coding is polar codes, which has great prospects in the development of current and future wireless communication systems. At the moment, polar coding is used only in fifth-generation systems. In this paper, a description of polar coding is presented, a description of a polar decoding algorithm capable of restoring messages with an error probability close to 1 is presented, and a general model of a binary channel with erasures is described. The channel model represents a fixed number of introduced errors, depending on the size of the transmitted message. The result of the study is the dependence of the bit-error ratio (BER) on the error probability for low, medium and high code rates, which illustrate the possibility of the polar coding algorithm to restore a message with a partially or completely inverse data stream.

High-Rate Storage Codes on Triangle-Free Graphs

Consider an assignment of bits to the vertices of a connected graph <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$G(V,E)$ </tex-math></inline-formula> with the property that the value of each vertex is a function of the values of its neighbors. A collection of such assignments is called a storage code of length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$|V|$ </tex-math></inline-formula> on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> . The storage code problem can be equivalently formulated as maximizing the probability of success in a guessing game on graphs, or constructing index codes of small rate. If <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> contains many cliques, it is easy to construct codes of rate close to 1, so a natural problem is to construct high-rate codes on triangle-free graphs, where constructing codes of rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$&gt; 1/2$ </tex-math></inline-formula> is a nontrivial task, with few known results. In this work we construct infinite families of linear storage codes with high rate relying on coset graphs of binary linear codes. We also derive necessary conditions for such codes to have high rate, and even rate potentially close to one. We also address correction of multiple erasures in the codeword, deriving recovery guarantees based on expansion properties of the graph. Finally, we point out connections between linear storage codes and quantum CSS codes, a link to bootstrap percolation and contagion spread in graphs, and formulate a number of open problems.

중학교 교과 교육목표 분석

Objectives The purpose of this study is to understand the relationship between detailed goals by period and subject and scientific inquiry ability.&#x0D; Methods From the 1st curriculum to the 2015 curriculum, a total of 10 curriculums, 132 subjects, and 599 detailed goals were used as a coding frame to open coding using the six sub-elements of scientific inquiry ability defined by KSES. Coding was conducted in consultation with science education graduate students and was reviewed by science education experts to ensure the validity of the research.&#x0D; Results As a result of coding, 490 (81.8%) of the total 599 detailed goals were coded, the curriculum with the highest coding rate was the 7th (94.5%), and the lowest curriculum was the 1st (69.6%). Confirmed. At least one specific goal of all subjects was related to scientific inquiry ability, and there was a difference in the scientific inquiry ability emphasized by subject, and there was also a difference according to the times. Among the sub-elements of scientific inquiry ability, the most coded ability through subjects was ‘data interpretation and data transformation (38.6%)’, and the least coded ability was ‘modeling (1.0%)’.&#x0D; Conclusions All subjects' goals were related to scientific inquiry ability in common, and they did not change with the times. There were differences in the scientific inquiry ability emphasized according to the subject and the times. In addition, it has significance in supporting ‘education as inquiry’, ‘a wide range of scientific inquiry’, and ‘education through science’.

Novel construction of quasi‐cyclic low‐density parity‐check codes with variable code rates for cloud data storage systems

AbstractThis paper proposed a novel method for constructing quasi‐cyclic low‐density parity‐check (QC‐LDPC) codes of medium to high code rates that can be applied in cloud data storage systems, requiring better error correction capabilities. The novelty of this method lies in the construction of sparse base matrices, using a girth greater than 4 that can then be expanded with a lift factor to produce high code rate QC‐LDPC codes. Investigations revealed that the proposed large‐sized QC‐LDPC codes with high code rates displayed low encoding complexities and provided a low bit error rate (BER) of 10−10 at 3.5 dB Eb/N0 than conventional LDPC codes, which showed a BER of 10−7 at 3 dB Eb/N0. Subsequently, implementation of the proposed QC‐LDPC code in a software‐defined radio, using the NI USRP 2920 hardware platform, was conducted. As a result, a BER of 10−6 at 4.2 dB Eb/N0 was achieved. Then, the performance of the proposed codes based on their encoding–decoding speeds and storage overhead was investigated when applied to a cloud data storage (GCP). Our results revealed that the proposed codes required much less time for encoding and decoding (of data files having a 10 MB size) and produced less storage overhead than the conventional LDPC and Reed–Solomon codes.

Linear-Equation Ordered-Statistics Decoding

In this paper, we propose a new linear-equation ordered-statistics decoding (LE-OSD). Unlike the OSD, LE-OSD uses high reliable parity bits rather than information bits to recover the codeword estimates, which is equivalent to solving a system of linear equations (SLE). Only test error patterns (TEPs) that create feasible SLEs, referred to as the valid TEPs, are used to obtain different codeword estimates. We introduce several constraints on the Hamming weight of TEPs to limit the overall decoding complexity. Furthermore, we analyze the block error rate (BLER) and the computational complexity of the proposed approach. It is shown that LE-OSD has a similar performance as OSD in terms of BLER, which can asymptotically approach Maximum-likelihood (ML) performance with proper parameter selections. Simulation results demonstrate that the LE-OSD has a significantly reduced complexity compared to OSD, especially for low-rate codes, that usually require high decoding order in OSD. Nevertheless, the complexity reduction can also be observed for high-rate codes. In addition, we further improve LE-OSD by applying the decoding stopping condition and the TEP discarding condition. As shown by simulations, the improved LE-OSD has a considerably reduced complexity while maintaining the BLER performance, compared to the latest OSD approach from literature.