Decoding under integer metrics constraints

We investigate the problem of decoding digital data when soft decisions are constrained to take on values from a finite set. We propose a physically reasonable objective function for selecting the desired assignment of metrics to the received analog signals. We develop a search algorithm for designing a table-look-up that is used by the decoder to select the appropriate intermediate metrics and show that an optimum solution exists. We provide a number of illuminating examples to elucidate our ideas and work out in detail some practical cases.<>