On Coding Techniques for Unsourced Multiple-Access
Gianluigi Liva, Yury Polyanskiy · 2021 55th Asilomar Conference on Signals, Systems, and Computers · 2021
In this paper, we attempt to gain insights on designing codes for unsourced multiple access by investigating an important special case of a two-user unsourced binary adder channel (2-UBAC). In 2-UBAC the receiver observes a noiseless real sum of two binary vectors. We show several results. First, for a linear code the per-user probability of error (PUPE) equals the fraction of nonminimal codewords, implying that such codes can at most achieve rate-1/2 while capacity of 2-UBAC is 3/4. Second, for sparse-graph codes to jump start an iterative peeling decoder we need to reveal ("pivot") one of the ambiguous symbols. If the pivot is selected randomly then any irregular LDPC code ensemble has a non-vanishing error probability. If the pivot is selected optimally then we show that three regular LDPC code ensembles attain vanishing PUPE: (3, 4), (4, 5) and (5, 6). Our proof does not apply to any other regular LDPC code ensembles, but we believe that they should all have a non-vanishing error probability. Finally, we discuss ideas about (nonlinear) coding to break through the rate-1/2 bottleneck.