Techniques for transmitting and receiving signals using a linear propagation channel, and the detection and decoding of the signals, are described. The symbols are decoded by computing the likelihood of each bit in a block of data in light of all blocks of received complex data and the constraints imposed by the channel code. Extrinsic information and a priori information are exchanged in an iterative fashion until desired performance is achieved. Extrinsic probability values are computed by searching through hypotheses in the constellation of available symbols to maximize the extrinsic probability values, with decoding employing a stored list of candidate points for discovered within a search radius, the list comprising the solution points found within the smallest radii.