Performance of Reed-Muller codes and a maximum-likelihood decoding algorithm for OFDM

The performance of Reed-Muller encoding and a maximum-likelihood decoding algorithm for orthogonal frequency-division multiplexing is presented. The example codes have a tightly bounded peak-to-mean envelope power ratio, while simultaneously enabling powerful error correction. We present a maximum-likelihood decoder that makes use of a distance-preserving map and multiple fast Hadamard transforms. Its operation is described in detail and its performance is assessed under realistic channel conditions.