On the Design of a Quantizer for Coded Systems

For any coded system the optimal decoder has to use a metric which is proportional to the log likelihood-ratio of the channel. To simplify the decoding process, the metric is required to have an additivity property, and to take on values from a finite set which are not always matched to the channel. The Generalized R , (GR) in this case is a function of the decoder set of memcs, the channel transition probabilities, and the partition of the received signal space to finite decision regions which is done by the quantizer. Here, an optimal quantizer, in the sense of maximizing GR, under metric constraint is derived. An iterative procedure for finding the optimal quantization boundaries is introduced.