On the Distortion Exponent of Some Layered Transmission Schemes

We consider the problem of joint source-channel coding for transmitting K samples of a complex Gaussian source over T = bK users of a quasi-static multiple input multiple output (MIMO) channel with M transmit and N receive antennas. The performance measure of interest is the rate of decay of the expected mean squared error with the signal-to-noise ratio (SNR), called the distortion exponent. We first show that using a broadcast strategy as in [D. Gunduz and E. Erkip, 2006], but with a different power and rate allocation policy, the optimal distortion exponent can be achieved for bandwidth efficiencies, 0 les b < (|N - M| + 1)/min(M, N). This is the first time the optimal exponent for 1/min(M, N) < b < (|N - M| + l)/min(M, N) is characterized. We then propose a digital layered transmission scheme that uses both time layering and superposition. This includes many known schemes in [D. Gunduz and E. Erkip, 2006; G. Caire and K. Narayanan, 2005] as special cases. The proposed scheme is at least as good as the currently best known schemes for the entire range of bandwidth efficiencies, whereas at least for some M , N, and b, it is strictly better than the currently best known schemes.