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During cell devision, maintaining the epigenetic information encoded in histone modification patterns is crucial for survival and identity of cells. The faithful inheritance of the histone marks from the parental to the daughter strands is a puzzle, given that each strand gets only half of the parental nucleosomes. Mapping DNA replication and reconstruction of modifications to equivalent problems in communication of information, we ask how well enzymes can recover the parental modifications, if they were ideal computing machines. Studying a parameter regime where realistic enzymes can function, our analysis predicts that enzymes may implement a critical threshold filling algorithm which fills unmodified regions of length at most k. This algorithm, motivated from communication theory, is derived from the maximum à posteriori probability (MAP) decoding which identifies the most probable modification sequence based on available observations. Simulations using our method produce modification patterns similar to what has been observed in recent experiments. We also show that our results can be naturally extended to explain inheritance of spatially distinct antagonistic modifications. Author summary: Chromatin is essentially the DNA that is folded and packaged with the help of proteins. While the nucleotide sequence in the DNA codes genetic information, the packaging of the DNA into chromatin encodes extra layer of information. This epigenetic code regulates reading of the genetic code and provides identity to cells—whether the cell is a skin cell or a brain cell, for example. In this work we examine a long standing puzzle, that is, how the epigenetic code in the form of histone modification patterns may get inherited, when a cell divides. Using theoretical arguments, we present an algorithm that enzymes could be executing so that the epigenetic code can be inherited with minimal error, soon after DNA replication. [ABSTRACT FROM AUTHOR]