Simple maximum-likelihood decoding of generalized first-order Reed-Muller codes

An efficient decoder for the generalized first-order Reed-Muller code RM_q (1, m) is essential for the decoding of various block-coding schemes for orthogonal frequency-division multiplexing with reduced peak-to-mean power ratio. We present an efficient and simple maximum-likelihood decoding algorithm for RM^q (1, m). It is shown that this algorithm has lower complexity than other previously known maximum-likelihood decoders for RM_q (1, m).