Short-packet Transmission via Variable-Length Codes in the Presence of Noisy Stop Feedback

We present an upper bound on the error probability achievable using variable-length stop feedback codes, for a fixed size of the information payload and a given constraint on the maximum latency and the average service time. Differently from the bound proposed in Polyanskiy et al. (2011), which pertains to the scenario in which the stop signal is sent over a noiseless feedback channel, our bound applies to the practically relevant setup in which the feedback link is noisy. By numerically evaluating our bound, we illustrate that, for fixed latency and reliability constraints, noise in the feedback link can cause a significant increase in the minimum average service time, to the extent that fixed-length codes without feedback may be preferable in some scenarios.Comment: Submitted to a Transactions on Wireless Communication

Mechanisms for Robust Local Differential Privacy

We consider privacy mechanisms for releasing data X =(S,U), where S is sensitive and U is non-sensitive. We introduce the robust local differential privacy (RLDP) framework, which provides strong privacy guarantees, while preserving utility. This is achieved by providing robust privacy: our mechanisms do not only provide privacy with respect to a publicly available estimate of the unknown true distribution, but also with respect to similar distributions. Such robustness mitigates the potential privacy leaks that might arise from the difference between the true distribution and the estimated one. At the same time, we mitigate the utility penalties that come with ordinary differential privacy, which involves making worst-case assumptions and dealing with extreme cases. We achieve robustness in privacy by constructing an uncertainty set based on a Rényi divergence. By analyzing the structure of this set and approximating it with a polytope, we can use robust optimization to find mechanisms with high utility. However, this relies on vertex enumeration and becomes computationally inaccessible for large input spaces. Therefore, we also introduce two low-complexity algorithms that build on existing LDP mechanisms. We evaluate the utility and robustness of the mechanisms using numerical experiments and demonstrate that our mechanisms provide robust privacy, while achieving a utility that is close to optimal

Weakly Secure Symmetric Multilevel Diversity Coding

Multilevel diversity coding is a classical coding model where multiple mutually independent information messages are encoded, such that different reliability requirements can be afforded to different messages. It is well known that {\em superposition coding}, namely separately encoding the independent messages, is optimal for symmetric multilevel diversity coding (SMDC) (Yeung-Zhang 1999). In the current paper, we consider weakly secure SMDC where security constraints are injected on each individual message, and provide a complete characterization of the conditions under which superposition coding is sum-rate optimal. Two joint coding strategies, which lead to rate savings compared to superposition coding, are proposed, where some coding components for one message can be used as the encryption key for another. By applying different variants of Han's inequality, we show that the lack of opportunity to apply these two coding strategies directly implies the optimality of superposition coding. It is further shown that under a set of particular security constraints, one of the proposed joint coding strategies can be used to construct a code that achieves the optimal rate region.Comment: The paper has been accepted by IEEE Transactions on Information Theor

Coding for storage and testing

The problem of reconstructing strings from substring information has found many applications due to its importance in genomic data sequencing and DNA- and polymer-based data storage. Motivated by platforms that use chains of binary synthetic polymers as the recording media and read the content via tandem mass spectrometers, we propose new a family of codes that allows for both unique string reconstruction and correction of multiple mass errors. We first consider the paradigm where the masses of substrings of the input string form the evidence set. We consider two approaches: The first approach pertains to asymmetric errors and the error-correction is achieved by introducing redundancy that scales linearly with the number of errors and logarithmically with the length of the string. The proposed construction allows for the string to be uniquely reconstructed based only on its erroneous substring composition multiset. The asymptotic code rate of the scheme is one, and decoding is accomplished via a simplified version of the Backtracking algorithm used for the Turnpike problem. For symmetric errors, we use a polynomial characterization of the mass information and adapt polynomial evaluation code constructions for this setting. In the process, we develop new efficient decoding algorithms for a constant number of composition errors. The second part of this dissertation addresses a practical paradigm that requires reconstructing mixtures of strings based on the union of compositions of their prefixes and suffixes, generated by mass spectrometry devices. We describe new coding methods that allow for unique joint reconstruction of subsets of strings selected from a code and provide upper and lower bounds on the asymptotic rate of the underlying codebooks. Our code constructions combine properties of binary $B_h$ and Dyck strings and can be extended to accommodate missing substrings in the pool. In the final chapter of this dissertation, we focus on group testing. We begin with a review of the gold-standard testing protocol for Covid-19, real-time, reverse transcription PCR, and its properties and associated measurement data such as amplification curves that can guide the development of appropriate and accurate adaptive group testing protocols. We then proceed to examine various off-the-shelf group testing methods for Covid-19, and identify their strengths and weaknesses for the application at hand. Finally, we present a collection of new analytical results for adaptive semiquantitative group testing with combinatorial priors, including performance bounds, algorithmic solutions, and noisy testing protocols. The worst-case paradigm extends and improves upon prior work on semiquantitative group testing with and without specialized PCR noise models

Orthogonal Time Frequency Space (OTFS) Modulation for Wireless Communications

The orthogonal time frequency space (OTFS) modulation is a recently proposed multi-carrier transmission scheme, which innovatively multiplexes the information symbols in the delay-Doppler (DD) domain instead of the conventional time-frequency (TF) domain. The DD domain symbol multiplexing gives rise to a direct interaction between the DD domain information symbols and DD domain channel responses, which are usually quasi-static, compact, separable, and potentially sparse. Therefore, OTFS modulation enjoys appealing advantages over the conventional orthogonal frequency-division multiplexing (OFDM) modulation for wireless communications. In this thesis, we investigate the related subjects of OTFS modulation for wireless communications, specifically focusing on its signal detection, performance analysis, and applications. In specific, we first offer a literature review on the OTFS modulation in Chapter~1. Furthermore, a summary of wireless channels is given in Chapter 2. In particular, we discuss the characteristics of wireless channels in different domains and compare their properties. In Chapter 3, we present a detailed derivation of the OTFS concept based on the theory of Zak transform (ZT) and discrete Zak transform (DZT). We unveil the connections between OTFS modulation and DZT, where the DD domain interpretations of key components for modulation, such as pulse shaping, and matched-filtering, are highlighted. The main research contributions of this thesis appear in Chapter 4 to Chapter 7. In Chapter 4, we introduce the hybrid maximum a posteriori (MAP) and parallel interference cancellation (PIC) detection. This detection approach exploits the power discrepancy among different resolvable paths and can obtain near-optimal error performance with a reduced complexity. In Chapter 5, we propose the cross domain iterative detection for OTFS modulation by leveraging the unitary transformations among different domains. After presenting the key concepts of the cross domain iterative detection, we study its performance via state evolution. We show that the cross domain iterative detection can approach the optimal error performance theoretically. Our numerical results agree with our theoretical analysis and demonstrate a significant performance improvement compared to conventional OTFS detection methods. In Chapter 6, we investigate the error performance for coded OTFS systems based on the pairwise-error probability (PEP) analysis. We show that there exists a fundamental trade-off between the coding gain and the diversity gain for coded OTFS systems. According to this trade-off, we further provide some rule-of-thumb guidelines for code design in OTFS systems. In Chapter 7, we study the potential of OTFS modulation in integrated sensing and communication (ISAC) transmissions. We propose the concept of spatial-spreading to facilitate the ISAC design, which is able to discretize the angular domain, resulting in simple and insightful input-output relationships for both radar sensing and communication. Based on spatial-spreading, we verify the effectiveness of OTFS modulation in ISAC transmissions and demonstrate the performance improvements in comparison to the OFDM counterpart. A summary of this thesis is presented in Chapter 8, where we also discuss some potential research directions on OTFS modulation. The concept of OTFS modulation and the elegant theory of DD domain communication may have opened a new gate for the development of wireless communications, which is worthy to be further explored