  We examine codes, over the additive Gaussian noise channel, designed for
reliable communication at some specific signal-to-noise ratio (SNR) and
constrained by the permitted minimum mean-square error (MMSE) at lower SNRs.
The maximum possible rate is below point-to-point capacity, and hence these are
non-optimal codes (alternatively referred to as "bad" codes). We show that the
maximum possible rate is the one attained by superposition codebooks. Moreover,
the MMSE and mutual information behavior as a function of SNR, for any code
attaining the maximum rate under the MMSE constraint, is known for all SNR. We
also provide a lower bound on the MMSE for finite length codes, as a function
of the error probability of the code.
