  We propose a new strategy to decode color codes, which is based on the
projection of the error onto three surface codes. This provides a method to
transform every decoding algorithm of surface codes into a decoding algorithm
of color codes. Applying this idea to a family of hexagonal color codes, with
the perfect matching decoding algorithm for the three corresponding surface
codes, we find a phase error threshold of approximately 8.7%. Finally, our
approach enables us to establish a general lower bound on the error threshold
of a family of color codes depending on the threshold of the three
corresponding surface codes. These results are based on a chain complex
interpretation of surface codes and color codes.
