On Molecular Timing Channels with α-Stable Noise

This work studies communication over molecular timing (MT) channels with α-Stable noise. The transmitter simultaneously releases multiple small information particles, where the information is encoded in the time of release. The receiver decodes the transmitted information based on the random time of arrival of the information particles, which is represented as an additive noise channel. For a diffusion-based MT channel, without flow, this noise follows the Lévy distribution. For this case, the maximum-likelihood (ML) detector is derived and shown to have high computational complexity. It is further shown that for any additive channel with α-stable noise, α < 1, such as the DBMT channel, a linear receiver is not able to take advantage of the release of multiple information particles. Thus, instead of the common low complexity linear approach, a new detector, which is based on the first arrival (FA) among all the transmitted particles, is derived. It is shown that for small number of particles the performance of the FA detector is very close to that of the ML detector. On the other hand, via error exponent analysis, it is shown that the performance of the two detectors differ when the number of sent particles is large. Thus, in the regime of small to medium number of sent particles, the FA detector is an attractive alternative to the relatively complicated ML detector.