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Error correction coding for optical communication and storage requires high rate codes that enable high data throughput and low residual errors. Recently, different concatenated coding schemes were proposed that are based on binary BCH codes with low error correcting capabilities. In this work, low-complexity hard- and soft-input decoding methods for such codes are investigated. We propose three concepts to reduce the complexity of the decoder. For the algebraic decoding we demonstrate that Peterson's algorithm can be more efficient than the Berlekamp-Massey algorithm for single, double, and triple error correcting BCH codes. We propose an inversion-less version of Peterson's algorithm and a corresponding decoding architecture. Furthermore, we propose a decoding approach that combines algebraic hard-input decoding with soft-input bit-flipping decoding. An acceptance criterion is utilized to determine the reliability of the estimated codewords. For many received codewords the stopping criterion indicates that the hard-decoding result is sufficiently reliable, and the costly soft-input decoding can be omitted. To reduce the memory size for the soft-values, we propose a bit-flipping decoder that stores only the positions and soft-values of a small number of code symbols. This method significantly reduces the memory requirements and has little adverse effect on the decoding performance.
The performance and reliability of non-volatile NAND flash memories deteriorate as the number of program/erase cycles grows. The reliability also suffers from cell to cell interference, long data retention time, and read disturb. These processes effect the read threshold voltages. The aging of the cells causes voltage shifts which lead to high bit error rates (BER) with fixed pre-defined read thresholds. This work proposes two methods that aim on minimizing the BER by adjusting the read thresholds. Both methods utilize the number of errors detected in the codeword of an error correction code. It is demonstrated that the observed number of errors is a good measure for the voltage shifts and is utilized for the initial calibration of the read thresholds. The second approach is a gradual channel estimation method that utilizes the asymmetrical error probabilities for the one-to-zero and zero-to-one errors that are caused by threshold calibration errors. Both methods are investigated utilizing the mutual information between the optimal read voltage and the measured error values.
Numerical results obtained from flash measurements show that these methods reduce the BER of NAND flash memories significantly.
The McEliece cryptosystem is a promising candidate for post-quantum public-key encryption. In this work, we propose q-ary codes over Gaussian integers for the McEliece system and a new channel model. With this one Mannheim error channel, errors are limited to weight one. We investigate the channel capacity of this channel and discuss its relation to the McEliece system. The proposed codes are based on a simple product code construction and have a low complexity decoding algorithm. For the one Mannheim error channel, these codes achieve a higher error correction capability than maximum distance separable codes with bounded minimum distance decoding. This improves the work factor regarding decoding attacks based on information-set decoding.
Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography
(2021)
The code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem together with the one-Mannheim error channel, where the error values are limited to Mannheim weight one. Due to the limited error values, the codes over Gaussian integers achieve a higher error correction capability than maximum distance separable (MDS) codes with bounded minimum distance decoding. This higher error correction capability improves the work factor regarding decoding attacks based on information-set decoding. The codes also enable a low complexity decoding algorithm for decoding beyond the guaranteed error correction capability. In this work, we extend this coding scheme to codes over Eisenstein integers. These codes have advantages for the Niederreiter system. Additionally, we propose an improved code construction based on generalized concatenated codes. These codes extent the rate region where the work factor is beneficial compared to MDS codes. Moreover, generalized concatenated codes are more robust against structural attacks than ordinary concatenated codes.
Interpretability and uncertainty modeling are important key factors for medical applications. Moreover, data in medicine are often available as a combination of unstructured data like images and structured predictors like patient’s metadata. While deep learning models are state-of-the-art for image classification, the models are often referred to as ’black-box’, caused by the lack of interpretability. Moreover, DL models are often yielding point predictions and are too confident about the parameter estimation and outcome predictions.
On the other side with statistical regression models, it is possible to obtain interpretable predictor effects and capture parameter and model uncertainty based on the Bayesian approach. In this thesis, a publicly available melanoma dataset, consisting of skin lesions and patient’s age, is used to predict the melanoma types by using a semi-structured model, while interpretable components and model uncertainty is quantified. For Bayesian models, transformation model-based variational inference (TM-VI) method is used to determine the posterior distribution of the parameter. Several model constellations consisting of patient’s age and/or skin lesion were implemented and evaluated. Predictive performance was shown to be best by using a combined model of image and patient’s age, while providing the interpretable posterior distribution of the regression coefficient is possible. In addition, integrating uncertainty in image and tabular parts results in larger variability of the outputs corresponding to high uncertainty of the single model components.
The main objective of this paper is to revisit the Euro method in a critical and constructive way.Wehave analysed some arguments against the Euro method published recently in the literature as well as some other relevant aspects of the SUT-Euro and SUT-RAS methods not covered before. Although not being the Euro method perfect, we believe that there is still space for the use of the Euro method in updating/regionalizing Supply and Use tables.
For decades now, exports and import have grown more rapidly than domestic production. This is a strong indication that, besides the rapid growth of foreign trade in final goods, trade in intermediates is becoming increasingly important. For this reason, an input-output ap-proach is more appropriate for any analysis of diversification than a traditional approach based purely on macroeconomic data.
This article analyses economic diversification in Gulf Cooperation Council (GCC) countries using data from input-output tables which are an integral part of the national accounts. We compare the performance of the GCC economies with that of a reference case, Norway, which is considered to have successfully diversified its economy despite having a large oil resource base. It also assesses these countries’ relative progress on sustainable development using a measure of the World Bank, adjusted net savings, which evaluates the true rate of savings in an economy after accounting for investments in physical and human capital, de-pletion of natural resources, and damage from environmental pollution.
The article concludes that GCC countries have, contrary to expectation, collectively per-formed relatively well on diversification, but their performance on sustainable development varies.
This paper examines the interdependencies of tourism, Buddhism and sustainability combining in-depth-interviews with Buddhism experts and non-participant observation in a mixed-method approach. The area under investigation is the Alpine region of Austria, Germany and Switzerland, since it is home to Asian and Western forms of Buddhism tourism alike. Results show that Buddhism tourism as a value-based activity on the one hand is not commercial, but since demand is rising, on the other hand tendencies towards more commercial forms can be observed. As a modest form of activity Buddhism tourism does not shape the landscape of the Alpine area and by its nature it incorporates sustainability.
In this article, the collection of classes of matrices presented in [J. Garloff, M. Adm, ad J. Titi, A survey of classes of matrices possessing the interval property and related properties, Reliab. Comput. 22:1-14, 2016] is continued. That is, given an interval of matrices with respect to a certain partial order, it is desired to know whether a special property of the entire matrix interval can be inferred from some of its element matrices lying on the vertices of the matrix interval. The interval property of some matrix classes found in the literature is presented, and the interval property of further matrix classes including the ultrametric, the conditionally positive semidefinite, and the infinitely divisible matrices is given for the first time. For the inverse M-matrices the cardinality of the required set of vertex matrices known so far is significantly reduced.
Positive systems play an important role in systems and control theory and have found applications in multiagent systems, neural networks, systems biology, and more. Positive systems map the nonnegative orthant to itself (and also the non-positive orthant to itself). In other words, they map the set of vectors with zero sign variation to itself. In this article, discrete-time linear systems that map the set of vectors with up to k-1 sign variations to itself are introduced. For the special case k = 1 these reduce to discrete-time positive linear systems. Properties of these systems are analyzed using tools from the theory of sign-regular matrices. In particular, it is shown that almost every solution of such systems converges to the set of vectors with up to k-1 sign variations. It is also shown that these systems induce a positive dynamics of k-dimensional parallelotopes.