  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 of Gunduz and Erkip, but with a different power
and rate allocation policy, the optimal distortion SNR exponent can be achieved
for bandwidth efficiencies 0 < b < (|N-M|+1)/min(M,N). This is the first time
the optimal exponent is characterized for 1/min(M,N) < b < (|N-M |+ 1)/ min(M,
N). Also, for b > MNL^2, we show that the broadcast scheme achieves the optimal
exponent of MNL. Special cases of this result have been derived for the L=1
case and for M=N=1 by Gunduz and Erkip. We then propose a digital layered
transmission scheme that uses both time layering and superposition. This
includes many previously known schemes 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.
