The Effect of Fading Correlation on Average Source MMSE Distortion

This paper considers the end-to-end mean-square distortion in reconstructing a memoryless proper-complex Gaussian source transmitted over parallel block-fading Rayleigh AWGN channels. We characterize the distortion exponent of several source and channel coding strategies; that is, we characterize how fast the distortion decays to zero as the SNR increases. Unlike previous works, we consider networks with different received SNR´s and with correlated fading. We generalize the definition of distortion exponent to SNR-asymmetric channels. We show that fading correlation degrades the achievable mean-square distortion but does not affect the distortion exponent. The performance degradation is measured in terms of power-offset; that is, the power increment needed to achieve the same performance as the uncorrelated case. We show that the power-offset is proportional to the determinant of the fading correlation matrix. Our proposed methodology allows us to study any number of parallel channels and we are no longer restricted to two channels (as was commonly done in the previous literature). Finally, we show that determining the distortion exponent of multiple description coding (MDC) schemes in high SNR reduces to solving a linear programming problem.