  This article presents a novel transmission scheme for the unsourced,
uncoordinated Gaussian multiple access problem. The proposed scheme leverages
notions from single-user coding, random spreading, minimum-mean squared error
(MMSE) estimation, and successive interference cancellation. Specifically,
every message is split into two parts: the first fragment serves as the
argument to an injective function that determines which spreading sequence
should be employed, whereas the second component of the message is encoded
using a polar code. The latter coded bits are then spread using the sequence
determined during the first step. The ensuing signal is transmitted through a
Gaussian multiple-access channel (GMAC). On the receiver side, active sequences
are detected using a correlation-based energy detector, thereby simultaneously
recovering individual signature sequences and their generating information bits
in the form of preimages of the sequence selection function. Using the set of
detected active spreading sequences, an MMSE estimator is employed to produce
log-likelihood ratios (LLRs) for the second part of the messages corresponding
to these detected users. The LLRs associated with each detected user are then
passed to a list decoder of the polar code, which performs single-user decoding
to decode the second portion of the message. This decoding operation proceeds
iteratively by subtracting the interference due to the successfully decoded
messages from the received signal, and repeating the above steps on the
residual signal. At this stage, the proposed algorithm outperforms alternate
existing low-complexity schemes when the number of active uses is below 225.
