João Paulo Vilela

Abstract
In this work, we present an optimal mapper for OFDM with index modulation (OFDM-IM). By optimal we mean the mapper achieves the lowest possible asymptotic computational complexity (CC) when the spectral efficiency (SE) gain over OFDM maximizes. We propose the spectro-computational (SC) analysis to capture the trade-off between CC and SE and to demonstrate that an -subcarrier OFDM-IM mapper must run in exact time complexity. We show that an OFDM-IM mapper running faster than such complexity cannot reach the maximal SE whereas one running slower nullifies the mapping throughput for arbitrarily large . We demonstrate our theoretical findings by implementing an open-source library that supports all DSP steps to map/demap an-subcarrier complex frequency-domain OFDM-IM symbol. Our implementation supports different index selector algorithms and is the first to enable the SE maximization while preserving the same time and space asymptotic complexities of the classic OFDM mapper.

Abstract
AbstractLocation privacy has became an emerging topic due to the pervasiveness of Location-Based Services (LBSs). When sharing location, a certain degree of privacy can be achieved through the use of Location Privacy-Preserving Mechanisms (LPPMs), in where an obfuscated version of the exact user location is reported instead. However, even obfuscated location reports disclose information which poses a risk to privacy. Based on the formal notion of differential privacy, Geo-indistinguishability has been proposed to design LPPMs that limit the amount of information that is disclosed to a potential adversary observing the reports. While promising, this notion considers reports to be independent from each other, thus discarding the potential threat that arises from exploring the correlation between reports. This assumption might hold for the sporadic release of data, however, there is still no formal nor quantitative boundary between sporadic and continuous reports and thus we argue that the consideration of independence is valid depending on the frequency of reports made by the user. This work intends to fill this research gap through a quantitative evaluation of the impact on the privacy level of Geo-indistinguishability under different frequency of reports. Towards this end, state-of-the-art localization attacks and a tracking attack are implemented against a Geo-indistinguishable LPPM under several values of privacy budget and the privacy level is measured along different frequencies of updates using real mobility data.

Abstract
In this letter, we demonstrate a mapper that enables all waveforms of OFDM with Index Modulation (OFDM-IM) while preserving polynomial time and space computational complexities. Enabling all OFDM-IM waveforms maximizes the spectral efficiency (SE) gain over the classic OFDM but, as far as we know, the computational overhead of the resulting mapper remains conjectured as prohibitive across the OFDM-IM literature. We show that the largest number of binomial coefficient calculations performed by the original OFDM-IM mapper is polynomial on the number of subcarriers, even under the setup that maximizes the SE gain over OFDM. Also, such coefficients match the entries of the so-called Pascal's triangle (PT). Thus, by assisting the OFDM-IM mapper with a PT table, we show that the maximum SE gain over OFDM can be achieved under polynomial (rather than exponential) time and space complexities.