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This article presents a novel transmission scheme for the unsourced,uncoordinated Gaussian multiple access problem. The proposed scheme leveragesnotions 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 theargument to an injective function that determines which spreading sequenceshould be employed, whereas the second component of the message is encodedusing a polar code. The latter coded bits are then spread using the sequencedetermined during the first step. The ensuing signal is transmitted through aGaussian multiple-access channel (GMAC). On the receiver side, active sequencesare detected using a correlation-based energy detector, thereby simultaneouslyrecovering individual signature sequences and their generating information bitsin the form of preimages of the sequence selection function. Using the set ofdetected active spreading sequences, an MMSE estimator is employed to producelog-likelihood ratios (LLRs) for the second part of the messages correspondingto these detected users. The LLRs associated with each detected user are thenpassed to a list decoder of the polar code, which performs single-user decodingto decode the second portion of the message. This decoding operation proceedsiteratively by subtracting the interference due to the successfully decodedmessages from the received signal, and repeating the above steps on theresidual signal. At this stage, the proposed algorithm outperforms alternateexisting low-complexity schemes when the number of active uses is below 225.

Polar Coding and Random Spreading for Unsourced Multiple Access