We consider the problem of (practical) capacity-approaching coding for a compound 
Gaussian MIMO channel that can assume one of a finite number of states (i.e., matrices).
Special cases include rateless coding and coding over parallel Gaussian channels. 
A coding scheme based on the recently proposed joint unitary triangularization (of matrices) is proposed.
We extend the decomposition to a general number of matrices (rather than two as was previously established).  
The proposed coding scheme involves linear pre/post processing and successive decoding, 
and requires only a single ``good'' (fixed-rate) scalar AWGN code.