On Secure and Sequential Source Coding
Time: Fri 2023-03-31 13.30
Location: F3, Lindstedtsvägen 26 & 28, Stockholm
Subject area: Electrical Engineering
Doctoral student: Hamid Ghourchian , Teknisk informationsvetenskap
Opponent: Professor Michèle Wigger, Télécom Paris
Supervisor: Professor Mikael Skoglund, Teknisk informationsvetenskap; Professor Tobias J. Oechtering, Teknisk informationsvetenskap
Secure source coding is an important research area in recent years as it deals with the problem of transmitting sensitive information over insecure channels while protecting it from unauthorized access. This is particularly relevant in the context of modern communication systems where the data transmitted is often sensitive in nature and the threat of eavesdropping or data breaches is high. By developing efficient and secure source coding techniques, it is possible to ensure the confidentiality and integrity of the transmitted information, thereby protecting the privacy and security of the users. In addition, secure source coding also plays a critical role in various applications such as sensor networks, wireless communications, and cloud computing. In this thesis, we explore the topic of secure source coding from an information theoretic perspective and focus on two main problems.
In the first problem, we have successfully characterized the entire achievable rate-distortion-equivocation region of a specific instance of a classic problem. We investigate the challenge of balancing the trade-off between the rate of data compression, the level of distortion in the compressed data, and the amount of information leaked to an eavesdropper when a private key is shared between the sender and the receiver. Specifically, we concentrate on a scenario where the decoder and eavesdropper have access to different side-informations that are correlated with the source.
In the second problem, the focus is on studying secure rate-distortion coding, where data is compressed and transmitted in a block-wise, causal manner, and the decoding is done non-causally. A new concept called cumulative rate distribution functions (CRDFs) is introduced to describe the rate resources that are spent sequentially to compress the sequence, while the concept of cumulative leakage distribution functions (CLFs) is used to characterize the security constraints on the amount of information leakage. Using techniques from majorization theory, necessary and sufficient conditions are derived for the achievable CRDFs for a given independent and identically distributed (IID) source and CLF, and it was found that the concave-hull of the CRDF characterizes the optimal achievable rate distribution. It is also extended to consider the scenario where there is a wiretap channel between the encoder, decoder, and eavesdropper, and inner and outer bounds as well as a closed-solution for a specific case of wiretap channels are found.