Zero Delay Joint Source Channel Coding for Multivariate Gaussian Sources over Orthogonal Gaussian Channels

Abstract: Communication of a multivariate Gaussian source transmitted over orthogonaladditive white Gaussian noise channels using delay-free joint source channel codes (JSCC)is studied in this paper. Two scenarios are considered: (1) all components of the multivariateGaussian are transmitted by one encoder as a vector or several ideally collaborating nodesin a network; (2) the multivariate Gaussian is transmitted through distributed nodes in asensor network. In both scenarios, the goal is to recover all components of the multivariateGaussian at the receiver. The paper investigates a subset of JSCC consisting of directsource-to-channelmappingsthatoperateonasymbol-by-symbolbasistoensurezerocodingdelay. A theoretical analysis that helps explain and quantify distortion behavior for suchJSCC is given. Relevant performance bounds for the network are also derived withno constraints on complexity and delay. Optimal linear schemes for both scenarios arepresented. Results for Scenario 1 show that linear mappings perform well, except whencorrelation is high. In Scenario 2, linear mappings provide no gain from correlation whenthe channel signal-to-noise ratio (SNR) gets large. The gap to the performance upper boundis large for both scenarios, regardless of SNR, when the correlation is high. The maincontribution of this paper is the investigation of nonlinear mappings for both scenarios. Itis shown that nonlinear mappings can provide substantial gain compared to optimal linearschemes when correlation is high. Contrary to linear mappings for Scenario 2, carefully

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