Information Theory (cs.IT)

Abstract: In this paper, we describe a correspondence between a fuzzy linear code and a family of nested linear codes. We also describe the arithmetic of fuzzy linear codes. As a special class of nested linear codes, we consider a family of nested self-orthogonal codes. A linear code is self-orthogonal if it is contained in its dual and self-dual if it is equal to its dual. We introduce a definition of fuzzy self-dual or self-orthogonal codes which include classical self-dual or self-orthogonal codes. As examples, we construct several interesting classes of fuzzy linear codes including fuzzy Hamming codes, fuzzy Golay codes, and fuzzy Reed-Muller codes. We also give a general decoding algorithm for fuzzy linear codes.

Abstract: Covert communications assisted by simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) in non-orthogonal multiple access (NOMA) systems have been explored in this paper. In particular, the access point (AP) transmitter adopts NOMA to serve a downlink covert user and a public user. The minimum detection error probability (DEP) at the warden is derived considering the uncertainty of its background noise, which is used as a covertness constraint. We aim at maximizing the covert rate of the system by jointly optimizing APs transmit power and passive beamforming of STAR-RIS, under the covertness and quality of service (QoS) constraints. An iterative algorithm is proposed to effectively solve the non-convex optimization problem. Simulation results show that the proposed scheme significantly outperforms the conventional RIS-based scheme in ensuring system covert performance.

Abstract: The effect of the relative entropy asymmetry is analyzed in the empirical risk minimization with relative entropy regularization (ERM-RER) problem. A novel regularization is introduced, coined Type-II regularization, that allows for solutions to the ERM-RER problem with a support that extends outside the support of the reference measure. The solution to the new ERM-RER Type-II problem is analytically characterized in terms of the Radon-Nikodym derivative of the reference measure with respect to the solution. The analysis of the solution unveils the following properties of relative entropy when it acts as a regularizer in the ERM-RER problem: i) relative entropy forces the support of the Type-II solution to collapse into the support of the reference measure, which introduces a strong inductive bias that dominates the evidence provided by the training data; ii) Type-II regularization is equivalent to classical relative entropy regularization with an appropriate transformation of the empirical risk function. Closed-form expressions of the expected empirical risk as a function of the regularization parameters are provided.