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In 2017, Polyanskiy [1] showed that the trade-off between power and bandwidthefficiency for massive Gaussian random access is governed by two fundamentallydifferent regimes: low power and high power. For both regimes, tightperformance bounds were found by Zadik et al. [2], in 2019. This work utilizesrecent results on the exact block error probability of Gaussian random codes inadditive white Gaussian noise to propose practical methods based on iterativesoft decoding to closely approach the bounds in [2]. In the low power regime,this work finds that orthogonal random codes can be applied directly. In thehigh power regime, a more sophisticated effort is needed. This work shows thatpower-profile optimization by means of linear programming as pioneered by Caireet al. [3], in 2001, is a promising strategy to apply. The proposed combinationof orthogonal random coding and iterative soft decoding even outperforms theexistence bounds of Zadik et al. [2] in the low power regime and is very closeto the non-existence bounds for message lengths around 100 and above. Finally,the approach of power optimization by linear programming proposed for the highpower regime is found to benefit from power imbalances due to fading whichmakes is even more attractive for typical mobile radio channels.

Soft Interference Cancellation for Random Coding in Massive Gaussian Multiple-Access