We analyze the performance of decoders for the 2D and 4D toric code which are local by construction. The 2D decoder is a cellular automaton decoder formulated by Harrington which explicitly has a finite speed of communication and computation. For a model of independent X and Z errors and faulty syndrome measurements with identical probability we report a threshold of 0.133% for this decoder. We implement a decoder for the 4D toric code which is based on a decoder by Hastings.