Capacity Theorems For Secure Transmission Of Correlated Sources Over Broadcast Channels

The communication of correlated sources over broadcast channel(BC) with correlated side information(SI) at the receivers is considered, where each receiver is kept in ignorance of the sources intended for the other receivers. The setting covers various practical applications in distributed video compression, peer-to-peer data distribution systems and sensor networks. The thesis investigates the reliability and security of this communication model from the perspective of Shannon information theory. In general, four fundamental issues need to be solved:(i) How to use the distributed source codes to decrease transmission load but increase secrecy rates?(ii) How to find capacity of BCs with arbitrary correlated sources?(iii) How to design the coding strategy for secure transmission?(iv) How to build a source-channel coding to derive the optimal bounds or make Shannon source-channel separation theorem hold?The thesis is devoted to establish secure capacity regions for secure transmission of discrete memoryless two correlated sources over discrete memoryless 2-receiver BC by using source-channel coding. Three key information theoretic problems are involved: source, channel and security, and two communication models are proposed:(i) BC with two confidential sources(BCCS);(ii) BCCS with SI at both receivers(BCCS-SI). BCCS can be seen as a generalization of Han-Costa reliable transmission model under the additional secrecy constraints on both receivers. BCCS-SI can be seen as a generalization of Tuncel’s a single source over BC-SI by considering arbitrary correlated sources. When adopting the optimal separate source-channel coding for these two models, Shannon separation theorem is extended from reliable bounds to secure bounds. The main contributions and results of the thesis are summarized as follows:(1) Secure capacity for BCCS is derived by using separate source-channel coding(SSCC).(i) The SSCC strategy based on Xu et al.’s secure channel coding scheme is established to guarantee the safety of information transferring. Using SSCC, the general inner bound of BCCS with Markov sources is proposed and can be seen as a generalization of Gray-Wyner optimal compression region, Marton-Gelfand-Pinsker inner bound of BC and Liu’s channel secrecy rate region of BC. If the BC can be seen as noisy free and the condition of Markov sources is cancelled, the general inner bound is extended to Tandon et al.’s the optimal source compression rate bound;(ii) The proposed general inner bound reaches local optimum——the perfect secrecy of non-relevant information between two sources and the optimal source compression rates, which are achieved when the common information of correlated sources is chosen to satisfy the certain condition;(iii) The general inner bound is tight for three special cases:(a) BCs with degraded source sets,(b) More-capable BCs,(c) Less-noisy BCs. For these cases, Shannon separation theorem holds, i.e., the optimal bounds are determined by simply comparing the source coding rate region with the known capacity region of the BCs, comparing the perfect secrecy of non-relevant information and the channel secrecy rate. In particular, for only reliable transmission, the capacity region of more-capable BCCS is equal to Kramer et al.’s. The latter is based on joint source-channel coding(JSCC), but the former leads to a simple design because of the separation coding.(2) Secure capacity for BCCS is derived by using strongly joint source-channel coding(S-JSCC). The S-JSCC strategy using the joint distribution of source and channel variables is proposed to guarantee the safety of information transferring.(i) A general inner bound is derived for BCCS, and extends Han-Costa inner bound for reliable transmission to the secure bound, and extends Xu et al.’s channel secrecy rate bound of independent sources to that of arbitrary correlated sources;(ii) A general outer bound of BCCS using the joint distributions of source and channel variables is obtained and can be seen as a generalizatioin of Kramer et al.’s outer bound for reliable transmission;(iii) The general outer bound is proved to be tight for two cases:(a) The sources satisfying a certain Markov property sent over semi-deterministic BCs or deterministic BCs;(b) Arbitrary correlated sources sent over less-noisy BCs or more capable BCs.(3) Secure capacity for BCCS-SI are determined by using S-JSCC.(i) The general inner and outer bounds for reliable transmissioin are proposed to BCCS-SI. The proposed bounds extend Tuncel and Kang-Kramer et al.’s results to arbitrary correlated sources and extend Timo et al.’s result for noiseless network to that for noisy BC;(ii) The general inner bound of BCCS-SI for secure transmissioin is proposed. It completely covers the general inner bound of BCCS and extends Villard’s secure transmission of single source over wiretap channel to that of two correlated sources over BC;(iii) The general outer bound of BCCS-SI is derived and is proved to be tight for two special cases:(a) Simutanously satisfying the following conditions: Markov sources, deterministic SI, degraded relationship betweeen the sources and the SI, semi-deterministic BC;(b) Under the conditions of the Markov relationship between the sources and SI, reliable transmission over more-capable BC and secure transmission over less-noisy BC. Secrecy capacity for the less-noisy BCCS-SI equals the source secrecy capacity plus the channel secrecy capacity.(4) Using independent distribution of sources and channel for the BCCS-SI, S-JSCC degrades into Weakly JSCC(W-JSCC). The optimal bounds for two cases are determined:(i) The inner bound is derived for BCCS-SI when the receiver obtains the source as a SI decoded by the other receiver, and the bound is tight when considering the known capacity BCs and extends Timo et al.’s source compression rate bound to noisy network;(ii) Broadcasting a single source is considered, and the proposed reliable capacity for this scenario is equal to Tuncel’s bound. Furthermore, considering degraded SI, secure capacity we derived extends Merhav’s result for degraded wiretap channel.(5) Secure capacity for the BCCS-SI is determined by using SSCC. Two cases are proven to be optimal by simply comparing the source coding rate region with the channel capacity region:(i) When two sources are conditional independent by the SI, the reliable capacity is derived. Under the same condition, the optimal equivocation rates are also derived;(ii) Secure capacity for the semi-deterministic BC with two independent sources is derived.