This paper considers the end-to-end mean squared error distortion in reconstructing a memoryless proper-complex Gaussian source transmitted over a set of parallel block-fading Gaussian noise channels, where the fading gains are modeled as correlated Rayleigh distributed random variables with different average powers, thus resulting in asymmetric average received signal noise ratios (SNRs). The distortion exponent (i.e., how fast the average distortion decays to zero as the average received SNR increases) of several coding strategies based on separate source and channel coding is characterized. The definition of distortion exponent commonly used in the literature for SNR-symmetric channels is generalized to the case of SNR-asymmetric channels. It is shown that fading correlation degrades the achievable mean squared error distortion, but does not affect the distortion exponent in the analyzed achievable schemes. The logarithm of the determinant of the fading correlation matrix is found to be a proxy for measuring the performance degradation due to correlation as compared with the case of independent fading. The proposed framework allows one to study any number of correlated parallel channels, contrary to the most of the literature that restricts attention to two channels only, with the same received SNR and with independent fading. In particular, a scheme based on the multiple description coding with more than two descriptions is analyzed; it is shown that determining the distortion exponent in this setting reduces to solving a linear program, which can be done numerically very efficiently. The proposed methodology relies on combining the ideas from linear innovation sequences and properties of determinant of sub-matrices. Interestingly, it is found that SNR-asymmetry is beneficial for multiple description coding when the total average received SNR in decibel is held constant. Even in the SNR-symmetric case, asymmetry in the compression rates is shown to lead to a larger distortion exponent than symmetric rates.

We consider the problem of transmitting a Gaussian source over a Rayleigh fading channel where some side-information may be available to the receiver. Our objective is to minimize the average distortion at the receiver. We consider two source models with side-information: 1) the Heegard-Berger model where "side-information may be absent", and 2) successive refinement with degraded side-information. We show that the average distortion problem can be numerically solved by convex optimization techniques. Furthermore, in high SNR, we obtain an analytical solution that shows that the side-information does not affect the distortion exponent, but causes an offset with respect to the case without side information. Numerical results show that our analytical high SNR approximation gives accurate results even at medium SNR.

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.

The problem of optimal rate allocation to streams constituting multiple description coding (MDC) has largely been addressed under the assumption that the multiple paths available for transmission are uncorrelated. In this paper, we model the transmission paths as correlated erasure channels and then examine the problem of allocating a given coding rate to the multiple descriptions in order to minimize the average distortion of the reconstructed message. We also investigate the relationship between the optimal average distortion and correlation of channels and prove that the bound on the average distortion will decrease as the correlation increases. Furthermore, we derive a closed-form solution for the contour which determines the region where multiple description coding (MDC) or single description coding (SDC) yields the minimal bound on the average distortion. Relying on this contour, we present a heuristic of the optimal rate allocation problem to determine the number of descriptions and relative rates.

In this paper, we study the optimal rate allocation of multiple description coding over multiple erasure channels in order to attain the minimum average distortion of the recovered message at the receiver. The results of this investigation are subsequently used to determine conditions under which the optimal rate allocation is characterized by transmission of one description over a single channel, i.e. single description coding. We formulate the optimal rate allocation problem by using rate- distortion theory under the constraint that the total coding rate is fixed and solve the problem by using numerical methods. Furthermore, we derive a closed-form analytical solution to the optimal rate allocation problem under four conditions and verify that the analytical solution is consistent with the numerical results. Also, we present a heuristic that captures the solution to the optimal rate allocation problem and can be used to determine the number of descriptions and relative rates required to achieve optimality.