Recursive error correction for general ReedMuller codes ?
ReedMuller (RM) codes of growing length n and distance d  are considered over a binary symmetric channel. A recursive decoding algorithm is designed that has complexity of order nlogn n log n and corrects most error patterns of weight (dlnd)/2 ( d ln d ) / 2 . The presented algorithm outperforms other algorithms with nonexponential decoding complexity, which are known for RM codes. We evaluate code performance using a new probabilistic technique that disintegrates decoding into a sequence of recursive steps. This allows us to define the most error-prone information symbols and find the highest transition error probability p p , which yields a vanishing output error probability on long codes.
reedmuller codes recursive decoding decoding threshold plotkin construction