A reduced complexity maximum likelihood decoder receives a stream of symbols Y and channel estimate H. A transformation converts Y and H into Z and R by computing matrix R, such that the product of R and Q produces matrix H. A second transformation column-swaps matrix H to form H′, thereafter generating Q′ and R′ subject to the same constraints as was described for Q and R. Transformed variables Z and Z′ are formed by multiplying Y by QH and Q′H, respectively. Table entries with Z and R and Z′ and R′ have entries of all possible x2 accompanied by estimates of x1 derived from x2 and Z, and similar entries of all possible x1 accompanied by estimates of x2 derived from x1 and Z′. Hard and soft decisions are made by finding the minimum distance metric of the combined entries of the first and second table.