  In this paper, the authors provide a weak decoding version of the traditional
source coding theorem of Claude Shannon. The central bound that is obtained is
\[ \chi>\log_{\epsilon}(2^{-n(H(X)+\epsilon)}) \] where \[
\chi=\frac{\log(k)}{n(H(X)+\epsilon)} \] and $k$ is the number of unsupervised
learning classes formed out of the non-typical source sequences. The bound
leads to the conclusion that if the number of classes is high enough, the
reliability function might possibly be improved. The specific regime in which
this improvement might be allowable is the one in which the atypical-sequence
clusters are small in size and sparsely placed; similar regimes might also show
an improvement.
