Joint Source-Channel Secrecy Using Analog Coding: Towards Secure Source Broadcast

This paper investigates joint source-channel secrecy for Gaussian broadcast communication in Shannon cipher system. We use a recently proposed secrecy measure, list secrecy, to measure secrecy, in which an eavesdropper is allowed to produce a list of reconstruction sequences and the secrecy is measured by the minimum distortion over the entire list. For achievability part, we propose a novel joint source-channel secrecy scheme, which cascades the traditional linear joint source-channel coding (analog coding) with a random orthogonal transform. For this scheme, we characterize the set of achievable tuples (secret key rate, list rate, eavesdropper distortion, distortions of all legitimate users). Besides, one of existing schemes, sign-change based scheme, is analyzed, and by comparison the proposed scheme outperforms this sign-change based scheme. For the converse part, we provide a necessary condition on the achievability of any tuple, and comparing this converse with the achievability result of the proposed scheme shows that the proposed scheme is optimal under some certain conditions. Besides, we also extend the proposed scheme and the corresponding achievability result to vector Gaussian communication scenario. No matter for scalar or vector Gaussian communication case, the codebook in the proposed scheme consists of a sequence of random matrices. This is very different from the traditional construction of codebook in information theory that usually consists of a sequence of random samples.