Capacity and coding for continuous phase modulation and networks

We derive upper bounds on the capacity of an additive Gaussian noise channel using binary Continuous Phase Modulation (CPM). To derive the capacity bounds, we decompose CPM into a sum of linear, filtered pulses. Using this decomposition, capacity bounds for additive Gaussian noise channels using CPM are derived by showing that the system can be transformed into a Multiple Input Single Output (MISO) channel with intersymbol interference (ISI). The capacity of this Gaussian MISO ISI channel is used for the upper bound. Numerical results of these bounds are presented for an additive Gaussian noise channel using CPM. The bounds show a significant capacity gap between a channel using CPM and a channel with unconstrained modulation.; We then investigate the behavior of an "almost" constant amplitude CPM by deriving a minimum mean square approximation to the linear decomposition of arbitrary binary input CPM. We show that finding the MMSE approximation only requires the solution of a single polynomial matrix equation and we provide a simple method for finding the solution. Not only does the approximation allow us to study the signal envelope behavior, but the approximation gives a simple decomposition for CPM.; We next study the performance of serially concatenated codes using the inherent memory of the CPM as an inner code. The simplified structures from the MMSE approximation are also combined with an inner code in an iterative decoding scheme. The performance of the resulting turbo-coded CPM schemes are simulated and evaluated using the capacity bounds.; We also explore network codes for wired and wireless networks. We summarize the main results for algebraic network coding and extend the algebraic framework for robust, wired, multicast networks to wireless multicast networks and show that the network coding a method for finding point-to-point network codes. Finally, we present some observations on the usefulness and limitations of network codes and a method for finding point-to-point network codes. Finally, we present some observations on the usefulness and limitations of network codes.