  Lossless variable-length source coding with unequal cost function is
considered for general sources. In this problem, the codeword cost instead of
codeword length is important. The infimum of average codeword cost has already
been determined for general sources. We consider the overflow probability of
codeword cost and determine the infimum of achievable overflow threshold. Our
analysis is on the basis of information-spectrum methods and hence valid
through the general source.
