How to obtain division algebras used for fast-decodable space-time block codes

We present families of unital algebras obtained through a doubling process from a cyclic central simple algebra D, employing a K-automorphism tau and an invertible element d in D. These algebras appear in the construction of iterated space-time block codes. We give conditions when these iterated algebras are division which can be used to construct fully diverse iterated codes. We also briefly look at algebras (and codes) obtained from variations of this method

Physical layer security: A paradigm shift in data confidentiality

Physical layer security (PLS) draws on information theory to characterize the fundamental ability of the wireless physical layer to ensure data confidentiality. In the PLS framework it has been established that it is possible to simultaneously achieve reliability in transmitting messages to an intended destination and perfect secrecy of those messages with respect to an eavesdropper by using appropriate encoding schemes that exploit the noise and fading effects ofwireless communication channels. Today, after more than 15 years of research in the area, PLS has the potential to provide novel security solutions that can be integrated into future generations of mobile communication systems. This chapter presents a tutorial on advances in this area. The treatment begins with a review of the fundamental PLS concepts and their corresponding historical background. Subsequently it reviews some of the most significant advances in coding theory and system design that offer a concrete platform for the realization of the promise of this approach in data confidentiality

Fuchsian codes with arbitrarily high code rates

Recently, Fuchsian codes have been proposed in Blanco-Chacon et al. (2014) [2] for communication over channels subject to additive white Gaussian noise (AWGN). The two main advantages of Fuchsian codes are their ability to compress information, i.e., high code rate, and their logarithmic decoding complexity. In this paper, we improve the first property further by constructing Fuchsian codes with arbitrarily high code rates while maintaining logarithmic decoding complexity. Namely, in the case of Fuchsian groups derived from quaternion algebras over totally real fields we obtain a code rate that is proportional to the degree of the base field. In particular, we consider arithmetic Fuchsian groups of signature (1; e) to construct explicit codes having code rate six, meaning that we can transmit six independent integers during one channel use. (C) 2015 Elsevier B.V. All rights reserved.Peer reviewe