On the distortion SNR 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 uses of a block-fading multiple-input multiple-output (MIMO) channel with M transmit and N receive antennas. We consider the case when we are allowed to code over L blocks. The channel gain is assumed to be constant over a block and channel gains for different blocks are assumed to be independent. 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 SNR exponent. We first show that using a broadcast strategy similar to that of Gunduz and Erkip, but with a different power and rate allocation policy, the optimal distortion SNR exponent can be achieved for 0 [less than or equal to] b < ([absolute value of N - M] + 1)/min (M, N) and for b > MN[L.sup.2]. This is the first time the optimal exponent is characterized for 1/min(M, N) < b < ([absolute value of N - M] + 1)/min (M, N). Then, we propose a digital layered transmission scheme that uses both time layering and superposition. The new scheme is at least as good as currently known schemes for the entire range of bandwidth expansion factors b, whereas at least for some M, N, and b, it is strictly better than the currently known schemes. Index Terms--Broadcast, distortion signal-to-noise ratio (SNR) exponent, diversity-multiplexing tradeoff, joint source-channel coding, layered source-channel coding, multiple-input multiple-output (MIMO), successive refinement, superposition.