Abstract: A receiving apparatus includes: a transmission-channel estimating unit that estimates a transmission-channel response matrix; a hard-decision sequence estimating unit that estimates a hard decision sequence and outputs the hard decision sequence and likelihood information ? corresponding to the hard decision sequence; and a soft-decision value creating unit that creates likelihood information ? corresponding to a sequence that a specific bit in the hard decision sequence is inversed by using the received signal vector, a transmission-channel response matrix reconstructed by reducing the dimension of the transmission-channel response matrix, and the hard decision sequence, and that creates a soft decision value of the hard decision sequence based on the likelihood information ? and the likelihood information ?.

Abstract: A metric calculating unit calculates a metric based on a provisional determination of a transmission signal and a reception signal. A lattice-point-range setting/estimate-symbol generating unit forms a hypersphere centering around a reception signal point based on the calculated metric or an updated metric, and determines whether a candidate of an estimate symbol is present within the hypersphere. A metric calculating/comparing unit calculates a metric based on the candidate of the estimate symbol and the reception signal, stores a minimum metric and corresponding candidate of the estimate symbol, and updates stored information when a newly calculated metric is minimum.