Exploiting Locality for Improved Decoding of Binary Cyclic Codes

The conventional parity-check matrix transformation algorithm (PTA) requires matrix inversion to transform matrices of maximum distance separable (MDS) codes. However, such matrix transformation is not always guaranteed for the class of non-MDS codes. Hence, the PTA fails for binary cyclic (BC) codes. To overcome this limitation, we developed a generalized parity-check matrix transformation (GPT) algorithm for binary cyclic codes. The GPT avoids the matrix inversion step of the PTA. It permutes the columns of the parity-check matrix based on the reliability information from the channel. Results show a significant bit error rate (BER) performance gain as compared to the existing PTA. It also presents a reasonable BER performance as compared to the other soft-decision (SD) decoding algorithms. In addition, the decoder functions within a practical decoding time complexity, particularly at the message passing stage.

Evaluation of the effectiveness of the application of innovative technologies in industry should be considered in the context of general principles and methods used in the implementation of information technology (IT). The main factors considered in these models can be taken as a basis for deciding on the appropriate level of investments channeled into IT systems to ensure a given level of reliability. The goal is to summarize the concepts and principles underlying these models and describe their common characteristics. Systematization of general models of the value estimation created due to investments into information technologies (IT). The main factors considered in these models are the basis for deciding on the appropriate level of investments in IT to ensure a given level of reliability. The characteristics of the principal types of models are given, which are proposed to be divided into four groups: investment-oriented; cost-oriented; models reflecting environmental factors; quantitative assessment models. It is offered to allocate material and non-material factors of information value formation. The resulting value of the technology under consideration for the whole life cycle is calculated as the sum of the material and non-material values of the components. Estimations have been made and a methodology for calculating the economic gains from the use of innovative technologies is demonstrated using the example of JSC Concern “Sozvezdie” (Voronezh).

Purpose. To build a graph of states and transitions of the surveying-geodetic network (SGN), which includes 16 points. To study the functioning of constructed discrete-continuous stochastic Markov models of the surveying-geodetic network with full and current recovery. To perform a numerical calculation of reliability, safety and efficiency indicators: readiness ratio, limit probability states, mean time to failure, mean time between failures. Methodology. A model of SGN functioning is built in the form of a graph of states and transitions with current and full recovery. Based on the model in the Mathcad software, the availability factor, mean time to failure, mean time between failures are calculated. The following graphs are built: readiness functions, probabilities of operation until the first failure, and frequency of getting into an emergency situation. Findings. Constructed discrete-continuous stochastic Markov reliability models of the boundary probability states, mean time between failures, mean time to the first failure have been analyzed. The probability of fault-free operation is presented graphically in the form of a transition graph, which describes the logic of the operation of the SGN. Based on the graph of states and transitions (graphical model) according to the Kolmogorov-Chapman algorithm, an analytical model of the reliability behavior of the surveying-geodetic network was built. A system of linear Kolmogorov-Chapman differential equations was compiled and solved. The distribution of probabilities of being in each state of the surveying-geodetic network has been obtained. Originality. For the first time in surveying practice, a reasonable choice of a discrete-continuous stochastic model of the functioning of a surveying-geodetic network based on the application of the state space method has been made. This model most fully describes the process of functioning (behavior) of the dynamic system. Dependencies between reliability indicators and safety indicators are established. It is recommended to use a model with ongoing network recovery, which allows you to maintain a given level of reliability through timely maintenance (recovery). Practical value. The most expedient time for restoration of geodetic points with certain failure intensity parameters has been determined. It has been done in order to maintain the SGN in an operational state with a given level of reliability. Current network recovery makes it possible to maintain reliability at the desired level. In the case of complete restoration of the SGN, the readiness factor will be lower, but such a system will be significantly cheaper.

We compute the covering radius of each binary cyclic code of length < 64 (for both even and odd lengths) and redundancy < 28 .We also compute the covering radii of their punctured codes and shortened codes.Thus we give exact covering radii of over six thousand codes.For each of these codes (except for certain composite codes), we also determine the number of cosets of each weight less than or equal to the covering radius.These results are used to compute the minimum distances of the above cyclic codes.We use the covering radii of shortened codes and other criteria for normality to show that all but eight of the cyclic codes for which we determine the covering radius are normal.For all but seven of these normal codes, we determine the norm using some old results and some new results proved here.We observe that many cyclic codes are among the best covering codes discovered so far, and some of them lead to improvements on the previously published bounds on t[n , k], the smallest covering radius of any binary linear [n , k] code.Among some other applications of our results, we use our table of covering radii and a code augmentation argument to give four improvements on the values of dmax(n , k) .wheredmix{n, k) is the largest minimum distance of any binary [n , k] code.These results show that the covering radius is intimately connected with the other three parameters of a linear code, n, k , and d .We also give a complete classification (up to isomorphism) of cyclic self-dual codes of lengths 42, 56, and 60.The computations were carried out mainly on concurrent machines (hypercubes and Connection Machines); we give a description of our algorithm.

The conventional soft decision decoding (SDD) methods require various hard decision decoders (HDDs) based on different codes or re-manipulate the generator matrix by the complicated Gaussian elimination technique according to the bit reliability. This paper presents a general multi-class neural network (NN)-based decoder for the short linear block codes, where no HDD and Gaussian elimination are required once the NN is constructed. This network architecture performs multi-classification to select the messages with high occurrence probabilities and chooses the best codeword on a maximum likelihood basis. Simulation results show that the developed approach outperforms the existing deep neural network (DNN)-based decoders in terms of decoding time and bit error rate (BER). The error-correcting performance is also superior to the conventional Chase-II algorithm and is close to the ordered statistics decoding (OSD) in most cases. For Bose–Chaudhuri–Hocquenghem (BCH) codes, the SNR is improved by 1dB to 4dB as the BER is 10−4. For the (23, 12) quadratic residue (QR) code, the SNR is improved by 2dB when the BER is 10−3. The developed NN-based decoder is quite general and applicable to various short linear block codes with good BER performance.

In this work, we present an improvement on low complexity serial concatenation of belief propagation (BP) - order statistic decoding (OSD) algorithm for low-density parity-check (LDPC) codes. We introduce a more reliable method to reconstruct ordered information sequence in terms of the accumulated log-likelihood ratio (LLR) transitions of variable nodes. We give a general expression for both the existing BP-OSD algorithm and our proposed new method according to a structure similar to an infinite impulse response (IIR) filter. This improved algorithm achieves noticeable performance gains with only modest increase in computation complexity.

The known construction of cyclic concatenated codes is based on the fact that the inner is a cyclic minimal code, the outer code is cyclic, and the lengths of the inner and outer codes are relatively prime. It is shown that if the outer code is a suitably chosen constacyclic code the overall concatenated code is always cyclic regardless of the length of the outer code. Moreover, it follows that any cyclic code of composite length is a direct sum of cyclic concatenated codes with inner cyclic minimal codes and outer constacyclic codes. This description of cyclic codes of composite length leads to the introduction of the concept of a poor-code length (PCL). All but low-rate codes of this length have a poor minimum distance. A PCL is directly related to the existence of irreducible binomials. In the binary case, the first few PCLs are 9, 25, 27, 45, 49, 75, 81 and 99. Arbitrarily long binary cyclic codes that are better than binary BCH codes of primitive length are constructed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper, we investigate the structure and properties of cyclic codes over the ring <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> + <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vF</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . We first study the relationship between cyclic codes over <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> + <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vF</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and binary cyclic codes. Then we prove that cyclic codes over the ring are principally generated, and give the generator polynomial of cyclic codes over the ring. Finally, we obtain the unique idempotent generators for cyclic codes of odd length and determine the number of cyclic codes for a given length <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> over <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> + <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vF</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> .

This letter is concerned with a generalized ordered statistic decoding (OSD) algorithm, called locally constrained OSD (LC-OSD). Instead of order- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> reprocessing on the most reliable independent bits, the LC-OSD searches for test error patterns using the serial list Viterbi algorithm (SLVA) over a trellis specified by a local parity-check matrix. We derive several early stopping criteria that can be used to reduce the number of searches. Numerical results show that the LC-OSD algorithm with the proposed stopping criteria has much lower time complexity than the original OSD but incurs negligible performance loss.

In this paper, we present the error probability expressions for a wideband coherent spatially correlated Multiple Input Multiple Output (MIMO) channel in low signal to noise ratio (SNR) regimes. Prior works have depicted a decrease in performance due to spatial correlation in high SNR regimes. This work proves that in a power limited broadband MIMO system, spatial correlation across the channel fading matrix elements improves the probability of error performance. In other words, spatial correlation impacts the MIMO performance differently in high SNR compared to low SNR (wideband) regimes.

This paper considers the optimal generator matrices of a given binary cyclic code over a binary symmetric channel with crossover probability p → 0 when the goal is to minimize the probability of an information bit error. A given code has many encoder realizations and the information bit error probability is a function of this realization. Our goal here is to seek the optimal realization of encoding functions by taking advantage of the structure of the codes, and to derive the probability of information bit error when possible. We derive some sufficient conditions for a binary cyclic code to have systematic optimal generator matrices under bounded distance decoding and determine many cyclic codes with such properties. We also present some binary cyclic codes whose optimal generator matrices are non-systematic under complete decoding.

We address a decoding problem for symmetric binary-input memoryless channels when data are transmitted using a cyclic binary code and show that some algebraic methods, like Berlekamp-Massey algorithm, developed for cyclic codes and binary symmetric channels can be effectively used to solve the problem.

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The levelized cost of energy (LCOE) from PV systems can be reduced by maximizing the energy production of existing/future PV plants through increased availability. This can be achieved by detailed study of root cause and failure analysis of component failures leading to a systematic progress towards improving the reliability of various sub-systems. SunEdison owns/operates ~500 sites across the world and systematically collects field failure data in addition to power output and weather data. Analysis of this information allows following-up on corrective actions to eliminate/minimize the re-occurrence of failures and leads to continuous improvements. This paper will analyze some of the key findings from the system failures as follows: - Inverter failures not only cause most of the system outages, but also result in substantial energy losses. Component failures in PCBs and inverter software/firmware bugs are the most common root cause of system outages - From a systemic root cause perspective, lack of robust quality systems at multiple levels of the supply chain is quite evident, which points toward the need for collectively inculcating the quality culture at every stage of the supply chain - This paper will try to establish the need for "Continuous Improvement Process" (CIP) where systemic issues are confronted and solutions are internalized in the operating procedures as the only path to improving component reliability - For a given level of reliability, cost associated with servicing the plant becomes critical. This paper highlights the importance of using "cost of ownership" metrics for making procurement decisions

The duration of restoration of the operation of emergency overhead power lines is the main indicator that determines the loss and damage in the practice of power supply. The use of special mobile supports, urgently delivered to the accident site of 35–500 kV lines, significantly reduces the duration of emergency downtime. On the basis of the theory of reliability of technical systems, a design technique has been developed in which the structural model of an overhead power transmission line is considered as a system of sequentially connected elements with a mobile emergency reserve of single and multiple actions. The method involves determining the number of mobile supports for planned or existing power transmission lines at a given level of reliability. The author’s patents and technological solutions have been effectively used at the enterprises of the Unified Energy System of Russia since the 1990s and at the present time.KeywordsMobile supportsOverhead power lineX-shaped supportRestorationDropping foundation