Constellation shaping for communication channels with quantized outputs

This paper considers a technique to maximize the mutual information between the channel input and channel output of an AWGN channel when the input is chosen from a fixed signal constellation and the output is quantized by a uniform scalar quantizer. The goal is to jointly optimize the input distribution and the quantizer spacing. These parameters have previously been optimized individually, by Le Goff et. al, who optimize the input distribution, and by Singh et. al, who optimize the quantizer spacing. The contribution of our paper is the joint optimization. We consider 16-PAM modulation and investigate the performance of the system with a quantizer resolution of between 4 and 8 bits. Shaping gains in excess of 0.6 dB are observed, even when the output is quantized, when the data is transmitted at rates between 2.5 and 3.2 bits per channel use.