  Beyond the genetic code, there is another layer of information encoded as
chemical modifications on histone proteins positioned along the DNA.
Maintaining these modifications is crucial for survival and identity of cells.
How the information encoded in the histone marks gets inherited, given that
only half the parental nucleosomes are transferred to each daughter chromatin,
is a puzzle. We address this problem using ideas from Information theory and
understanding from recent biological experiments. Mapping the replication and
reconstruction of modifications to equivalent problems in communication, we ask
how well an enzyme-machinery can recover information, if they were ideal
computing machines. Studying a parameter regime where realistic enzymes can
function, our analysis predicts that, pragmatically, enzymes may implement a
threshold$-k$ filling algorithm which derives from maximum \`a posteriori
probability decoding. Simulations using our method produce modification
patterns similar to what is observed in recent experiments.
