Information Theory (cs.IT)

Abstract: This note provides a simplified exposition of the proof of hierarchical Kraft lemma proven by Barmpalias and Lewis-Pye and its consequences for the oracle use in the Ku\v{c}era--G\'acs theorem (saying that every sequence is Turing reducible to a random one).

Abstract: This paper considers massive Internet of Things systems, especially for LoW Power Wide Area Networks, that aim at connecting billions of low-cost devices with multi-year battery life requirements. Current systems for massive Internet of Things exhibit severe problems when trying to pursue the target of serving a very large number of users. In this paper, a novel asynchronous spread spectrum modulation, called Golden Modulation, is introduced. This modulation provides a vast family of equivalent waveforms with very low cross-interference even in asynchronous conditions, hence enabling natural multiuser operation without the need for inter-user synchronization or for interference cancellation receivers. Thanks to minimal interference between waveforms, coupled with the absence of coordination requirements, this modulation can accommodate very high system capacity. The basic modulation principles, relying on spectrum spreading via direct Zadoff-Chu sequences modulation, are presented and the corresponding theoretical bit error rate performance in an additive white Gaussian noise channel is derived and compared by simulation with realistic Golden Modulation receiver performance. The demodulation of the Golden Modulation is also described, and its performance in the presence of uncoordinated multiple users is characterized.