This dissertation treats a recently introduced modern random access protocol known as unsourced random access (U-RA). This protocol belongs to the family of grant-free random access protocols which, in contrast to the established grant-based protocols of current mobile communication standards, do not rely on an initial access phase, in which the active devices identify themselves and await the grant of dedicated transmission resources (e.g. time-frequency blocks) from the base station (BS).

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... messages are short and the number of active devices is large, which is a central specification of upcoming massive machine-type-communication (mMTC) scenarios, such a grant-based procedure is overly wasteful and may increase the delay to an unacceptable level. In a grant-free scenario the active devices transmit their payload right away without awaiting the grant of dedicated resources. A commonly discussed approach is to assign devices unique fixed identification sequences (called pilots in the following). Active devices then transmit their pilot followed directly by their message. The idea of unsourced random access is to go one step further and, ideally, abolish the identification step, such that active devices directly transmit a message from a common predefined message set. Information-theoretically such a behavior is captured by letting each user employ the same codebook, as opposed to the classical information-theoretic treatment of the multiple access problem where each user is assigned an individual codebook. The assumption of a common codebook allows to treat the random access problem in a way that captures the effect of short messages while still taking into account the physical properties of the channel. In this work I build on a previously introduced coding scheme for the U-RA problem on the AWGN channel termed coded compressed sensing (CCS). I introduce a novel decoding algorithm for the CCS scheme based on approximate message passing (AMP) and give an asymptotic analysis. The analysis shows that it is possi [...]