19 the last row corresponding to a single non zero entry in the matrix r is evaluated for all possible values of s 1 from the constellation using the following distance metric computation d s1 u2225 y 1 u2212 r 1 1 s 1 u2225 2 20 the terms y 1 and r 1 1 are complex and in general can have any value within the specified bit width for a given variable the modulation symbol s 1 is chosen from a fixed set of constellation symbols for example from fig3 in case of 16 qam there are only 16 different values a symbol can take to select m minimum distance metrics from the first stage at the end of each distance computation cycle a comparison needs to be performed with the set of current minimum values it is also necessary to assign each symbol a unique index which is required to identify the symbol carried over to the second stage since the computation in eq 20 can be independently carried out multiple distance computation blocks can be employed taking advantage of parallelism finally m survivor symbols corresponding to m least distance metrics are carried over to the second stage for the second stage distance computations in eq 19 the m selected symbols from first stage corresponding to s 1 are substituted one at a time into the eq 21 the eq 21 is.