  Dirty paper codes are a powerful tool for combating known interference.
However, there is a significant difference between knowing the transmitted
interference sequence and knowing the received interference sequence,
especially when the channel modifying the interference is uncertain. We present
an upper bound on the capacity of a compound vector dirty paper channel where
although an additive Gaussian sequence is known to the transmitter, the channel
matrix between the interferer and receiver is uncertain but known to lie within
a bounded set. Our bound is tighter than previous bounds in the low-SIR regime
for the scalar version of the compound dirty paper channel and employs a
construction that focuses on the relationship between the dimension of the
message-bearing signal and the dimension of the additive state sequence.
Additionally, a bound on the high-SNR behavior of the system is established.
