Slotted Gaussian Multiple Access Channel: Stable Region and Role of Side Information

In this paper, we study the relation between the stable throughput regions and the capacity regions for a Gaussian multiple access channel. Our main focus is to study how the extent of side information about source arrival statistics and/or instantaneous queue states at each transmitter influence the achievable stable throughput region. Two notions of MAC capacity are studied. The first notion is the conventional Shannon capacity which relies on large coding block lengths for finite SNR, while the second uses finite code blocks with high SNR. We find that the stable throughput region coincides with the Shannon capacity region for many scenarios of side-information, where side information is defined as a mix of statistical description and instantaneous queue states. However, a lack of sufficient side information about arrival statistics can lead to a significant reduction in the stable throughput region. Finally, our results lend strong support to centralized architectures implementing some form of congestion/rate control to achieve Shannon capacity, primarily to counter lack of detailed information about source statistics at the mobile nodes.