Achievable Rate Region of Quantized Broadcast and MAC Channels

TL;DR

This paper investigates the achievable rate regions of quantized Gaussian multiuser channels, revealing that traditional capacity regions and decoding schemes are suboptimal under quantization, and proposes new quantization strategies to improve performance.

Contribution

It introduces the concept of quantized broadcast and multiple access channels, analyzes their achievable rate regions, and proposes non-uniform quantization to enhance rates.

Findings

Uniform quantization causes significant rate loss in QMAC.

Optimal decoding schemes for GBC are not suitable for QBC.

Non-uniform quantization significantly improves the rate region in QMAC.

Abstract

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.