Analyze the distortion region in Gaussian broadcast channel by bandwidth compression and expansion using different coding schemes

Broadcasting Gaussian sources over a Gaussian broadcast channel is a major problem in information theory. Consider the problem of sending a correlated Gaussian source S = (S₁,S₂... ... .S_m) over a power limited Gaussian broadcast channel. User i (1,2,..m) observes the transmitted signal which is affected by Gaussian noise with power σ_i² and desires to estimate S_i. This paper aims to analyze the distortion (squared error) regions that are simultaneously achievable at the receivers by using hybrid digital analog (HDA) joint source channel coding (JSCC) coding scheme. First, consider the problem of broadcasting a bivariate Gaussian source over a two-user power limited Gaussian broadcast channel to two users. Two bandwidth mismatch cases are considered: i) broadcasting with bandwidth compression, and ii) broadcasting with bandwidth expansion. This paper also considers the problem of broadcasting three Gaussian sources over a three user power limited Gaussian broadcast channel. First two sources are correlated and the third one is independent to other two sources. Finally, compare the achievable inner bound distortion region to outer bound distortion region.