Abstract
In this letter, we analyse the trade-off between collision probability and code-ambiguity, when devices transmit a sequence of preambles as a codeword, instead of a single preamble, to reduce collision probability during random access to a mobile network. We point out that the network may not have sufficient resources to allocate to every possible codeword, and if it does, then this results in low utilisation of allocated uplink resources. We derive the optimal preamble set size that maximises the probability of success in a single attempt, for a given number of devices and uplink resources.