Secure broadcast channels with receiver side information: coding techniques and capacity bounds

This thesis studies the problem of secure broadcasting for the two-receiver discrete memoryless broadcast channel with receiver side information and with an eavesdropper under the constraints of individual secrecy. We tackle this problem by looking into the strategic usage of asymmetrical receiver side information, error-correcting coding scheme and information theoretic secrecy techniques. We study the role of asymmetrical receiver side information in secure broadcasting by first looking into the linear deterministic broadcast channel with one-sided receiver side information. Combining existing secrecy techniques, we propose a secrecy coding scheme which is shown to be capacity achieving. This allows us to fully characterize the individual secrecy capacity region of the linear deterministic broadcast channel with receiver side information. We also extend this secrecy coding scheme to cater for the discrete memoryless broadcast channel with one-sided receiver side information. Our study concludes that the availability of asymmetrical receiver side information is beneficial when available at the weaker legitimate receiver. In addition, we revisit the problem of discrete memoryless broadcast channel with symmetrical receiver side information and manage to identify a simpler scheme for the discrete memoryless broadcast channel with complementary receiver side information. This result allows us to further propose a universal secrecy coding scheme for the discrete memoryless broadcast channel with receiver side information. Next, we shift our perspective and show that the Marton error-correcting coding scheme can achieve secure broadcasting without relying on existing secrecy techniques. At the cost of two additional rate constraints, the Marton random components provide sufficient randomness to achieve message protection. We also show that in the Blackwell channel, this strategy provides an individual secrecy rate region that covers regions unachievable using existing secrecy coding scheme. Moving on, we focus on unique applications of existing secrecy techniques. Despite the unavailability of receiver side information, we propose a one-time pad enabled secrecy coding scheme for the discrete memoryless broadcast channel with no receiver side information. This is possible with a necessary message retransmission step. Our strategy outperforms existing secrecy coding scheme in the compound binary symmetric broadcast channel with an eavesdropper. Lastly, we investigate the feasibility of replacing Wyner secrecy coding with Carleial-Hellman secrecy coding. We attempt this on the secrecy coding scheme we proposed for the discrete memoryless broadcast channel with complementary receiver side information. This results in a structurally simplified secrecy coding scheme that preserves the achievable individual secrecy rate region of its predecessor.