  In this paper we carefully study the MSE performance of the linear analog
codes. We have derived a lower bound of the MSE performance under
Likelihood(ML) and Linear Minimal Mean Square Error(LMMSE) decoding criteria
respectively. It is proved in this essay that a kind of linear analog codes
called \emph {unitary codes} can simultaneously achieve both of these two
bounds. At the same time, we compare the obtained linear analog codes' MSE
bounds with the performance of some existing nonlinear codes. The results
showed that linear analog codes are actually not very satisfying and convinced
us that more concerns should be cast onto the nonlinear class in order to find
powerful analog codes.
