The DMT classification of real and quaternionic lattice codes

In this paper we consider space-time codes where the code-words are restricted to either real or quaternion matrices. We prove two separate diversity-multiplexing gain trade-off (DMT) upper bounds for such codes and provide a criterion for a lattice code to achieve these upper bounds. We also point out that lattice codes based on Q-central division algebras satisfy this optimality criterion. As a corollary this result provides a DMT classification for all Q-central division algebra codes that are based on standard embeddings.Comment: 6 pages, 1 figure. Conference paper submitted to the International Symposium on Information Theory 201

Decoding by Embedding: Correct Decoding Radius and DMT Optimality

The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP) are the core algorithmic problems on Euclidean lattices. They are central to the applications of lattices in many problems of communications and cryptography. Kannan's \emph{embedding technique} is a powerful technique for solving the approximate CVP, yet its remarkable practical performance is not well understood. In this paper, the embedding technique is analyzed from a \emph{bounded distance decoding} (BDD) viewpoint. We present two complementary analyses of the embedding technique: We establish a reduction from BDD to Hermite SVP (via unique SVP), which can be used along with any Hermite SVP solver (including, among others, the Lenstra, Lenstra and Lov\'asz (LLL) algorithm), and show that, in the special case of LLL, it performs at least as well as Babai's nearest plane algorithm (LLL-aided SIC). The former analysis helps to explain the folklore practical observation that unique SVP is easier than standard approximate SVP. It is proven that when the LLL algorithm is employed, the embedding technique can solve the CVP provided that the noise norm is smaller than a decoding radius $\lambda_1/(2\gamma)$, where $\lambda_1$ is the minimum distance of the lattice, and $\gamma \approx O(2^{n/4})$. This substantially improves the previously best known correct decoding bound $\gamma \approx {O}(2^{n})$. Focusing on the applications of BDD to decoding of multiple-input multiple-output (MIMO) systems, we also prove that BDD of the regularized lattice is optimal in terms of the diversity-multiplexing gain tradeoff (DMT), and propose practical variants of embedding decoding which require no knowledge of the minimum distance of the lattice and/or further improve the error performance.Comment: To appear in IEEE Transactions on Information Theor

Almost universal codes for fading wiretap channels

We consider a fading wiretap channel model where the transmitter has only statistical channel state information, and the legitimate receiver and eavesdropper have perfect channel state information. We propose a sequence of non-random lattice codes which achieve strong secrecy and semantic security over ergodic fading channels. The construction is almost universal in the sense that it achieves the same constant gap to secrecy capacity over Gaussian and ergodic fading models.Comment: 5 pages, to be submitted to IEEE International Symposium on Information Theory (ISIT) 201

Natural radiation sources: a study on NORM in industrial sectors

In Italy some industrial processes involving Naturally Occurring Radioactive Materials (NORM in the following) are regulated by the Legislative Decree of 31 July 2020 n. 101 [1] which transposes the Council Directive 2013/59/Euratom[2]. For several sectors, the entry into radiation protection system is entirely new. The topic of NORM is quite recent in radiation protection system; in fact, it is only in the last few decades that more attention has been paid to this issue. Therefore, the information available is far less than for other topics in the radiation protection field and some aspects, such as sampling protocols, are still being defined. For these reasons, this thesis aims to provide an overview of natural radioactivity content in some NORM-involving industries, selected from the Italian legislative decree 101/2020. The study carried out in this research project can help to understand which kind of material is more critical from the radiation protection point of view or which radionuclides usually occur in it and can therefore be expected from the analysis of such a sample. A great collection of data about the content of radioactivity in four categories of materials (raw materials, residues, products and effluents) from twelve NORM involving industrial sectors has been carried out. The collection considers radiological data (in terms of activity concentrations of 238U, 226Ra, 210Pb, 210Po, 232Th, 228Ra and 40K) for more than 6200 samples, taken from international and national literature. Collected radiological data have been analyzed and the most significant results will be shown here. Complete data, instead, are reported in Appendix. An inventory of the industries currently operating in Italy was updated in order to understand the impact of the Italian radiation protection legislation on NORMrelated industrial activities and to identify the industrial sectors with an important radiological impact on population and workers. Moreover, given the large number of industrial sectors, a general methodological approach was developed, which can be adapted and declined for the different NORM industry sectors indicated in the legislation. The methodology, elaborated taking into account a graded approach, consinsts of two phases and provides indications about the characterization of the most critical exposure scenarios and of the radiological content of NORMs involved in the different phases of the industrial processes. Lastly, all data collected and analyzed in this study will be soon available online. In fact in the framework of the research project it is nearing completion a database on the “Physical Agents Portal (PAF)” website (https://www.portaleagentifisici.it/) that will allow not only data consultation, but also dose assessment for different scenarios

Strong Coordination with Polar Codes

In this paper, we design explicit codes for strong coordination in two-node networks. Specifically, we consider a two-node network in which the action imposed by nature is binary and uniform, and the action to coordinate is obtained via a symmetric discrete memoryless channel. By observing that polar codes are useful for channel resolvability over binary symmetric channels, we prove that nested polar codes achieve a subset of the strong coordination capacity region, and therefore provide a constructive and low complexity solution for strong coordination.Comment: 7 pages doublespaced, presented at the 50th Annual Allerton Conference on Communication, Control and Computing 201

Secret key generation from Gaussian sources using lattice hashing

We propose a simple yet complete lattice-based scheme for secret key generation from Gaussian sources in the presence of an eavesdropper, and show that it achieves strong secret key rates up to 1/2 nat from the optimal in the case of "degraded" source models. The novel ingredient of our scheme is a lattice-hashing technique, based on the notions of flatness factor and channel intrinsic randomness. The proposed scheme does not require dithering.Comment: 5 pages, Conference (ISIT 2013