  We propose a rigorous analysis approach for the subset sum problem in the
context of lossless data compression, where the phase transition of the subset
sum problem is directly related to the passage between ambiguous and
non-ambiguous decompression, for a compression scheme that is based on
specifying the sequence composition. The proposed analysis lends itself to
straightforward extensions in several directions of interest, including
non-binary alphabets, incorporation of side information at the decoder
(Slepian-Wolf coding), and coding schemes based on multiple subset sums. It is
also demonstrated that the proposed technique can be used to analyze the
critical behavior in a more involved situation where the sequence composition
is not specified by the encoder.
