In this work, we study two problems in information-theoretic security. Firstly, we study a wireless network where two nodes want to securely exchange messages via an honest-but-curious bidirectional relay. There is no direct link between the user nodes, and all communication must take place through the relay. The relay behaves like a passive eavesdropper, but otherwise follows the protocol it is assigned. Our objective is to design a scheme where the user nodes can reliably exchange messages such that the relay gets no information about the individual messages. We first describe a perfectly secure scheme using nested lattices, and show that our scheme achieves secrecy regardless of the distribution of the additive noise, and even if this distribution is unknown to the user nodes. Our scheme is explicit, in the sense that for any pair of nested lattices, we give the distribution used for randomization at the encoders to guarantee security. We then give a strongly secure lattice coding scheme, and we characterize the performance of both these schemes in the presence of Gaussian noise. We then extend our perfectly-secure and strongly-secure schemes to obtain a protocol that guarantees end-to-end secrecy in a multichip line network. We also briefly study the robustness of our bidirectional relaying schemes to channel imperfections. In the second problem, we consider the scenario where multiple terminals have access to private correlated Gaussian sources and a public noiseless communication channel. The objective is to generate a group secret key using their sources and public communication in a way that an eavesdropper having access to the public communication can obtain no information about the key. We give a nested lattice-based protocol for generating strongly secure secret keys from independent and identically distributed copies of the correlated random variables. Under certain assumptions on the joint distribution of the sources, we derive achievable secret key rates. The tools used in designing protocols for both these problems are nested lattice codes, which have been widely used in several problems of communication and security. In this thesis, we also study lattice constructions that permit polynomial-time encoding and decoding. In this regard, we first look at a class of lattices obtained from low-density parity-check (LDPC) codes, called Low-density Construction-A (LDA) lattices. We show that high-dimensional LDA lattices have several “goodness” properties that are desirable in many problems of communication and security. We also present a new class of low-complexity lattice coding schemes that achieve the capacity of the AWGN channel. Codes in this class are obtained by concatenating an inner Construction-A lattice code with an outer Reed-Solomon code or an expander code. We show that this class of codes can achieve the capacity of the AWGN channel with polynomial encoding and decoding complexities. Furthermore, the probability of error decays exponentially in the block length for a fixed transmission rate R that is strictly less than the capacity. To the best of our knowledge, this is the first capacity-achieving coding scheme for the AWGN channel which has an exponentially decaying probability of error and polynomial encoding/decoding complexities.

Elements of continuous variation such as tremolo, vibrato and portamento enable dimensions of their own in expressive melodic music in styles such as in Indian Classical Music. There is published work on parametrically modeling some of these elements individually, and to apply the modeled parameters to automatically generated musical notes in the context of machine musicianship, using simple rule-based mappings. There have also been many systems developed for generative musical accompaniment using probabilistic models of discrete musical elements such as MIDI notes and durations, many of them inspired by computational research in linguistics. There however doesn't seem to have been a combined approach of parametrically modeling expressive elements in a probabilistic framework. This documents presents a real-time computational framework that uses a multi-attribute trie / n-gram structure to model parameters like frequency, depth and/or lag of the expressive variations such as vibrato and portamento, along with conventionally modeled elements such as musical notes, their durations and metric positions in melodic audio input. This work proposes storing the parameters of expressive elements as metadata in the individual nodes of the traditional trie structure, along with the distribution of their probabilities of occurrence. During automatic generation of music, the expressive parameters as learned in the above training phase are applied to the associated re-synthesized musical notes. The model is aimed at being used to provide automatic melodic accompaniment in a performance scenario. The parametric modeling of the continuous expressive elements in this form is hypothesized to be able to capture deeper temporal relationships among musical elements and thereby is expected to bring about a more expressive and more musical outcome in such a performance than what has been possible using other works of machine musicianship using only static mappings or randomized choice. A system was developed on Max/MSP software platform with this framework, which takes in a pitched audio input such as human singing voice, and produces a pitch track which may be applied to synthesized sound of a continuous timbre. The system was trained and tested with several vocal recordings of North Indian Classical Music, and a subjective evaluation of the resulting audio was made using an anonymous online survey. The results of the survey show the output tracks generated from the system to be as musical and expressive, if not more, than the case where the pitch track generated from the original audio was directly rendered as output, and also show the output with expressive elements to be perceivably more expressive than the version of the output without expressive parameters. The results further suggest that more experimentation may be required to conclude the efficacy of the framework employed in relation to using randomly selected parameter values for the expressive elements. This thesis presents the scope, context, implementation details and results of the work, suggesting future improvements.