On efficient designing of protograph LDPC codes

This paper designs two protograph LDPC codes with code-rate $R > 1/2$. A simple method using the protograph extrinsic information transfer (PEXIT) to design the codes with a low decoding threshold and the asymptotic weight enumerator (AWE) to evaluate the error floor of the codes is deployed. Simulation results show that the proposed codes have a better error floor than prior art protograph codes and offer higher rate protographs.

MindLink-Eumpy: An Open-Source Python Toolbox for Multimodal Emotion Recognition

Emotion recognition plays an important role in intelligent human–computer interaction, but the related research still faces the problems of low accuracy and subject dependence. In this paper, an open-source software toolbox called MindLink-Eumpy is developed to recognize emotions by integrating electroencephalogram (EEG) and facial expression information. MindLink-Eumpy first applies a series of tools to automatically obtain physiological data from subjects and then analyzes the obtained facial expression data and EEG data, respectively, and finally fuses the two different signals at a decision level. In the detection of facial expressions, the algorithm used by MindLink-Eumpy is a multitask convolutional neural network (CNN) based on transfer learning technique. In the detection of EEG, MindLink-Eumpy provides two algorithms, including a subject-dependent model based on support vector machine (SVM) and a subject-independent model based on long short-term memory network (LSTM). In the decision-level fusion, weight enumerator and AdaBoost technique are applied to combine the predictions of SVM and CNN. We conducted two offline experiments on the Database for Emotion Analysis Using Physiological Signals (DEAP) dataset and the Multimodal Database for Affect Recognition and Implicit Tagging (MAHNOB-HCI) dataset, respectively, and conducted an online experiment on 15 healthy subjects. The results show that multimodal methods outperform single-modal methods in both offline and online experiments. In the subject-dependent condition, the multimodal method achieved an accuracy of 71.00% in the valence dimension and an accuracy of 72.14% in the arousal dimension. In the subject-independent condition, the LSTM-based method achieved an accuracy of 78.56% in the valence dimension and an accuracy of 77.22% in the arousal dimension. The feasibility and efficiency of MindLink-Eumpy for emotion recognition is thus demonstrated.

The Weight Enumerator of GRM codes

The distribution of weight enumerator gives the new idea to contract the information about the code for finding the error probability of a code. In this paper, we have extended the result of the weight enumerator of GRM codes [3]. The weight enumerator of GRM codes for order (m - 3) , m ³ 3,r ³ 0 has been developed and analyzed.

On one-lee weight and two-lee weight $ \mathbb{Z}_2\mathbb{Z}_4[u] $ additive codes and their constructions

<p style='text-indent:20px;'>This paper mainly study <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{Z}_{2}\mathbb{Z}_{4}[u] $\end{document}</tex-math></inline-formula>-additive codes. A Gray map from <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{Z}_{2}^{\alpha}\times\mathbb{Z}_{4}^{\beta}[u] $\end{document}</tex-math></inline-formula> to <inline-formula><tex-math id="M4">\begin{document}$ \mathbb{Z}_{4}^{\alpha+2\beta} $\end{document}</tex-math></inline-formula> is defined, and we prove that is a weight preserving and distance preserving map. A MacWilliams-type identity between the Lee weight enumerator of a <inline-formula><tex-math id="M5">\begin{document}$ \mathbb{Z}_{2}\mathbb{Z}_{4}[u] $\end{document}</tex-math></inline-formula>-additive code and its dual is proved. Some properties of one-weight <inline-formula><tex-math id="M6">\begin{document}$ \mathbb{Z}_{2}\mathbb{Z}_{4}[u] $\end{document}</tex-math></inline-formula>-additive codes and two-weight projective <inline-formula><tex-math id="M7">\begin{document}$ \mathbb{Z}_{2}\mathbb{Z}_{4}[u] $\end{document}</tex-math></inline-formula>-additive codes are discussed. As main results, some construction methods for one-weight and two-weight <inline-formula><tex-math id="M8">\begin{document}$ \mathbb{Z}_{2}\mathbb{Z}_{4}[u] $\end{document}</tex-math></inline-formula>-additive codes are studied, meanwhile several examples are presented to illustrate the methods.</p>

Linear codes from vectorial Boolean functions in the context of algebraic attacks

In this paper, we study the relationship between vectorial (Boolean) functions and cyclic codes in the context of algebraic attacks. We first derive a direct link between the annihilators of a vectorial function (in univariate form) and certain [Formula: see text]-ary cyclic codes (which we show that they are LCD codes). We also present some properties of those cyclic codes as well as their weight enumerator. In addition, we generalize the so-called algebraic complement and study its properties.

Theta series and weight enumerator over an imaginary quadratic field

In this paper, we consider an imaginary quadratic field [Formula: see text] with [Formula: see text] (mod 4). In particular, we study the ring of integers corresponding to the field [Formula: see text] and visualize the form of [Formula: see text]. We also consider lattices over the ring of integers [Formula: see text] and discuss the theta series to see its relation with the weight enumerator. As a consequence, we will see how the theta series differs for different [Formula: see text] and [Formula: see text].

Extended maximal self-orthogonal codes

Self-dual and maximal self-orthogonal codes over [Formula: see text], where [Formula: see text] is even or [Formula: see text](mod 4), are extensively studied in this paper. We prove that every maximal self-orthogonal code can be extended to a self-dual code as in the case of binary Golay code. Using these results, we show that a self-dual code can also be constructed by gluing theory even if the sum of the lengths of the gluing components is odd. Furthermore, the (Hamming) weight enumerator [Formula: see text] of a self-dual code [Formula: see text] is given in terms of a maximal self-orthogonal code [Formula: see text], where [Formula: see text] is obtained by the extension of [Formula: see text].