  We introduce an efficient decoder of the color code in $d\geq 2$ dimensions,
the Restriction Decoder, which uses any $d$-dimensional toric code decoder
combined with a local lifting procedure to find a recovery operation. We prove
that the Restriction Decoder successfully corrects errors in the color code if
and only if the corresponding toric code decoding succeeds. We also numerically
estimate the Restriction Decoder threshold for the color code in two and three
dimensions against the bit-flip and phase-flip noise with perfect syndrome
extraction. We report that the 2D color code threshold $p_{\textrm{2D}} \approx
10.2\%$ on the square-octagon lattice is on a par with the toric code threshold
on the square lattice.
