On the Distortion SNR Exponent of Hybrid Digital–Analog Space–Time Coding

We consider the transmission of a real independent and identically distributed (i.i.d.) "analog" source over a quasi-static M-input N-output multiple-input multiple-output (MIMO) block-fading channel. The relevant performance criterion is end-to-end average quadratic distortion D versus channel signal-to-noise ratio (SNR), for given spectral efficiency eta, defined as the ratio of the source bandwidth over the channel bandwidth. In the limit of high SNR, we define the distortion SNR exponent a*(eta) as the largest a such that D esdot snr^-a, over all possible source-channel coding schemes of spectral efficiency eta. We find a simple upper bound on a*(eta), an achievable lower bound a_sep(eta) achievable by separated (tandem) source-channel coding, and a tighter lower bound a_hybrid(eta) achievable by new hybrid digital analog space-time coding schemes. As a corollary, we have that a*(eta) is completely determined for the scalar case M = N = 1 and for the "bandwidth compression" case eta ges 2 min{M, N}. Expiicit and simple construction of hybrid space-time codes achieving a_hybrid(eta) are also given.