On Functions Weakly Computable by Pushdown Petri Nets and Related Systems

We consider numerical functions weakly computable by grammar-controlled vector addition systems (GVASes, a variant of pushdown Petri nets). GVASes can weakly compute all fast growing functions $F_\alpha$ for $\alpha<\omega^\omega$, hence they are computationally more powerful than standard vector addition systems. On the other hand they cannot weakly compute the inverses $F_\alpha^{-1}$ or indeed any sublinear function. The proof relies on a pumping lemma for runs of GVASes that is of independent interest

Fast sphere decoder for MIMO systems

This work focuses on variants of the conventional sphere decoding technique for Multi Input Multi Output (MIMO) systems. Space Time Block Codes (STBC) have emerged as a popular way of transmitting data over multiple antennas achieving the right balance between diversity and spatial multiplexing. The Maximum Likelihood (ML) technique is a conventional way of decoding the transmitted information from the received data, but at the cost of increased complexity. The sphere decoder algorithm is a sub-optimal decoding technique that is computationally efficient achieving a ;symbol error rate that is dependent on the initial radius of the sphere. In this thesis, the decreasing rate of the radius of the sphere is increased by using a scaling factor of less than unity. This allows the algorithm to examine less number of vectors compared to the original algorithm making it much more computationally efficient. The sphere decoding algorithm is largely focused on the Alamouti codes that have two antennas at the transmitter. This work extends the sphere decoding algorithm to other STBC having more than 2 transmit and receive antennas. The performance and the computational complexity of the fast sphere decoder is compared with that of the original sphere decoder and its variants --Abstract, page iii