  In this paper, we study the achievable rate region of Gaussian multiuser
channels with the messages transmitted being from finite input alphabets and
the outputs being {\em quantized at the receiver}. In particular, we focus on
the achievable rate region of $i)$ Gaussian broadcast channel (GBC) and $ii)$
Gaussian multiple access channel (GMAC). First, we study the achievable rate
region of two-user GBC when the messages to be transmitted to both the users
take values from finite signal sets and the received signal is quantized at
both the users. We refer to this channel as {\em quantized broadcast channel
(QBC)}. We observe that the capacity region defined for a GBC does not carry
over as such to QBC. We show that the optimal decoding scheme for GBC (i.e.,
high SNR user doing successive decoding and low SNR user decoding its message
alone) is not optimal for QBC. We then propose an achievable rate region for
QBC based on two different schemes. We present achievable rate region results
for the case of uniform quantization at the receivers. Next, we investigate the
achievable rate region of two-user GMAC with finite input alphabet and
quantized receiver output. We refer to this channel as {\em quantized multiple
access channel (QMAC)}. We derive expressions for the achievable rate region of
a two-user QMAC. We show that, with finite input alphabet, the achievable rate
region with the commonly used uniform receiver quantizer has a significant loss
compared to the achievable rate region without receiver quantization. We
propose a {\em non-uniform quantizer} which has a significantly larger rate
region compared to what is achieved with a uniform quantizer in QMAC.
