New soft- and hard decision decoding algorithms are presented for general Reed-Muller codes $\left\{\genfrac{}{}{0pt}{}{m}{r}\right\} $ of length
2m and distance
2m−r. We use Plotkin
(u,u+v) construction and decompose code $\left\{\genfrac{}{}{0pt}{}{m}{r}\right\} $ onto subblocks $u\in\left\{\genfrac{}{}{0pt}{}{m-1}{r}\right\} $ and
v∈{r−1m−1}. In decoding, we first try to find a subblock
v from the better protected code and then proceed with the block
u. The likelihoods of the received symbols are recalculated in a way similar to belief propagation. Thus, decoding is relegated to the two constituent codes. We repeat this recursion and execute decoding only at the end nodes $\left\{\genfrac{}{}{0pt}{}{j}{1}\right\} $ and $\left\{\genfrac{}{}{0pt}{}{j}{j-1}\right\} $. The overall complexity has low order of
nlogn. It is shown that this decoding substantially outperforms other algorithms of polynomial complexity known for RM codes. In particular, for medium and high code rates, the algorithm corrects most error patterns of weight
dlnd/2.Low latency communication requires soft-input decoding of binary block codes with small to medium block lengths. In this work, we consider generalized multiple concatenated (GMC) codes based on the Plotkin construction. These codes are similar to Reed-Muller (RM) codes. In contrast to RM codes, BCH codes are employed as component codes. This leads to improved code parameters. Moreover, a decoding algorithm is proposed that exploits the recursive structure of the concatenation. This algorithm enables efficient soft-input decoding of binary block codes with small to medium lengths. The proposed codes and their decoding achieve significant performance gains compared with RM codes and recursive GMC decoding.