The present invention is to provide a wireless communication system and a receiving device each capable of restraining a circuit scale and obtaining an excellent error rate performance. In a wireless communication system in which a transmitting device and a receiving device communicate in an orthogonal frequency division multiplexing system, the transmitting device includes a partition unit partitioning a transmission data sequence into a plurality of data streams and a mapping unit mapping the plurality of data streams to each of transmitting antennas by using, for a precoding matrix, columns, corresponding to a stream count of the plurality of data streams, of a right singular matrix acquired by singular value decomposition of a channel matrix, and the receiving device includes a decoding unit that Viterbi-decodes the received signals by weighting a path metric by using a weighting coefficient corresponding to a signal-to-noise ratio obtained from the present channel matrix.