{'fraction_non_alphanumeric': 0.033084311632870865, 'fraction_numerical': 0.0, 'mean_word_length': 5.090909090909091, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Delay-limited capacity of fading multiple access and broadcast channels in the low power regime

We study delay-limited (also called zero-outage) capacity region of the fading multi-access channel (MAC) with Gaussian noise and perfect channel state information (CSI) at the receiver and at the transmitters (CSI-TR), in the low-power regime. We show that for fading channels where the MAC capacity region is strictly positive, it has a multidimensional rectangle structure and thus is simply characterized by single user capacity points. More specifically, we show that at low power, the boundary surface of the capacity region shrinks to a single point corresponding to the sum-rate maximizer and that the coordinates of this point coincide with single user capacity bounds. Using the duality of the Gaussian MAC and broadcast channels (BC), we show that time-sharing (or time division multiple access (TDMA)) is asymptotically optimal.