| In our work we analyze many different situations where the transmission of information is corrupted by noise. In communications systems noise can be naturally occurring, artificially generated, or self-generated. It is the job of communications engineers to combat the effects of noise on their designs. In this thesis we examine two main areas of noise mitigation: channel coding and filtering.; In the channel coding realm, we examine optimum code rates for a product code in the presence of AWGN and intelligent partial band jamming interference, and we provide asymptotic analysis of Reed-Solomon based product codes. The comparison of the optimal code rates for finite length product codes with the rates determined by asymptotic analysis illustrate the importance of considering undetected error in the code design. We develop a method of determining the probability of undetected error for the underlying Reed-Solomon codes that offers attractive advantages over known methods.; In the realm of noise mitigation by filtering, we consider MEMS filters which show great promise in achieving very high Q's at passband frequencies. We examine the performance of sub-sampled systems and systems with cosite interference which employ filters of varying Q. We quantify the tradeoff between noise performance and required Q for these systems. Additionally we address the issues of power added efficiency (PAE) in systems that employ high Q filters and nonlinear amplifiers. We show that the application of a MEMS filter to a fixed bias power amplifier increases the PAE in the presence of strong interferers, but that there is not a clear link between lowering the bias power and increases in PAE.; For the analysis of nonlinear systems, we motivate and propose a new method called the modified instantaneous quadrature method (MIQM). With this method we can analyze, rather than simulate, the effects of a nonlinear element in weakly and strongly nonlinear systems with large or small dynamic range inputs. Once the system is known to be memoryless, or have a limited degree of memory, the MIQM will produce accurate results that match the output of more numerically complex simulation systems. |
